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  • Articles  (584)
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  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160101
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  • 2
    Electronic Resource
    Electronic Resource
    Behaviour of mushy regions under the action of a volumetric heat source (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 35-47 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider solutions to Stefan problems in spatial dimensions N ≥ 1. We find the necessary conditions on the heat source for the appearance of a ‘mushy region’ (i.e. a region where the temperature coincides identically with the temperature of the change of phase) inside a purely liquid (or solid) phase. For sources depending on energy such conditions are connected only with the local behaviour of the source near the energy level corresponding to the beginning of the change or phase. Both weak and smooth solutions are considered; in the latter case the behaviour of the solution at the free boundary is investigated in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160104
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  • 3
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    On the asymptotic growth of the solutions of the vlasov-poisson system (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 75-85 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show the global existence of classical solutions of the Vlasov-Poisson system and improve the known growth estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160202
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  • 4
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    High-frequency asymptotics in inverse scattering by ellipsoids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 1-12 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A triaxial ellipsoid of unknown position, size and orientation is located somewhere in space. High-frequency asymptotics for the scattering amplitude and the sojourn time for the travelling of a high-frequency acoustic plane wave are utilized to determine the position of a supporting plane for the ellipsoid. We describe a method that identifies the coordinates of the centre, the three semiaxes, and the three angles of the ellipsoid from the knowledge of nine sojourn times corresponding to nine directions of excitation. The method is independent of boundary conditions, it is applicable to any restricted non-zero-measure angle of observation, and leads to numerics that avoid elliptic integrals. A priori information about the location of the ellipsoid reduces the number of measurements to six, while the corresponding algorithm demands the solution of a linear system and the inversion of a dyadic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160102
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  • 5
    Electronic Resource
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160201
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  • 6
    Electronic Resource
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    Schauder estimates for boundary layer potentials (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 877-894 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Boundary layer potentials with Hölder-continuous densities are widely used for representing solutions of boundary value problems for certain partial differential equations. These potentials are of the type with |ρ| odd and a density λ of class Ck+α. This paper presents a self-contained exposition of the fact that the potential v may be continued as Ck+α-functions onto G and ∝n\G respectively (together with estimates for the Hölder-norms) under the least possible regularity assumption for the boundary ∂G: it has to be of class Ck+1+α.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161204
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  • 7
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    A non-isentropic Euler-Poisson model for a collisionless plasma (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 409-442 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We analyse transonic solutions of the one-dimensional Euler-Poisson model for a collisionless gas of charged particles in the non-isentropic steady-state case. The model consists of the conservation of mass, momentum and energy equations. The electric field is modelled self-consistently (Coulomb field). Boundary conditions on the particle density and particle temperature are imposed.The analysis is based on representing solutions piecewise as orbits in the particle-density-electric-field phase plane and connecting the orbit segments by the jump and entropy conditions.We characterize the set of all solutions of the Euler-Poisson problem. In particular, we show that, depending upon the length of the interval on which the boundary value problem is posed, fully subsonic, one-shock and (in certain cases) two-shock transonic and smooth transonic solutions exist. Also, numerical computations illustrating the structure of the solutions are reported.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160603
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  • 8
    Electronic Resource
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    Resonance phenomena in a semi-infinite string with a periodic end (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 501-531 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the propagation of linear waves, generated by a compactly supported time-harmonic force distribution, in a semi-infinite string under the assumption that the material properties depend p-period-ically on the space variable outside a sufficiently large interval [0, a]. The spectrum of the self-adjoint extension A of the spatial part of the differential operator consists of a finite or countable number of bands and a (possibly empty) discrete set of eigenvalues located in the gaps of the continuous spectrum. We show that resonances of order t or t½, respectively, occur if either ω2 is an eigenvalue of A or (i) ω2 is a boundary point of the continuous spectrum of A and (ii) the corresponding time-independent homogeneous problem has a non-trivial solution which is p-periodic or p-semiperiodic for x 〉 a (‘standing wave’).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160704
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  • 9
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    Relative entropy maximization and directed diffusion equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 545-554 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Motivated by the concept of maximum entropy methods in signal and image processing, we introduce and discuss a class of ‘directed diffusion equations’ with suitable boundary conditions. The paradigmatic ‘directed diffusion equation’ is The relative entropy \documentclass{article}\pagestyle{empty}\begin{document}$ Sb[f](t): = - \int_\Omega {f(t,x)} \;\ln \;(f(t,x)/b(x))dx $\end{document} is rapidly increasing along solution trajectories of (i). This suggests that solving (i) will yield efficient procedures for entropy maximization. We also discuss the asymptotic behavior of solutions of (i) - this is readily done because (i) has a large family of Ljapunov functionals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160803
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  • 10
    Electronic Resource
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    A normal crack in an elastic half-space with stress-free surface (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 563-579 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of an elastic half-space with stress-free surface and a crack of arbitrary shape with prescribed displacements or tractions is reduced to an equivalent system of integral equations on the crack. For a pressurized crack in a plane perpendicular to the free surface, a scalar integral equation is derived. In properly chosen function spaces, unique solvability of the integral equation and regularity of solutions for regular data are proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160805
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  • 11
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    Global existence for one-dimensional motion of non-isentropic viscous fluids (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 609-624 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the p-system with viscosity given by vt - ux = 0, ut + p(v)x = (k(v)ux)x + f(∫0x vdx, t), with the initial and the boundary conditions (v(x, 0), u(x,0)) = (v0, u0(x)), u(0,t) = u(X,t) = 0. To describe the motion of the fluid more realistically, many equations of state, namely the function p(v) have been proposed. In this paper, we adopt Planck's equation, which is defined only for v 〉 b(〉 0) and not a monotonic function of v, and prove the global existence of the smooth solution. The essential point of the proof is to obtain the bound of v of the form b 〈 h(T) ≤ v(x, t) ≤ H(T) 〈 ∞ for some constants h(T) and H(T).
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160902
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  • 12
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    Classical solutions of two-dimensional stokes problems on non-smooth domains. Part 1: The radon integral operators (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 643-664 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The applicability of the Neumann indirect method of potentials to the Dirichlet and Neumann problems for the two-dimensional Stokes operator on a non-smooth boundary Γ is subject to two kinds of sufficient and/or necessary conditions on Γ. The first one, occurring in electrostatic, is equivalent to the boundedness on C(Γ) of the velocity double-layer potential W as well as to the existence of jump relations of potentials. The second condition, which forces Γ to be a simple rectifiable curve and which, compared to the Laplacian, is a stronger restriction on the corners of Γ, states that the Fredholm radius of W is greater than 2. Under these conditions, the Radon boundary integral equations defined by the above-mentioned jump relations are solvable by the Fredholm theory; the double- (for Dirichlet) and the single- (for Neumann) layer potentials corresponding to their solutions are classical solutions of the Stokes problems.
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    URL: http://dx.doi.org/10.1002/mma.1670160904
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  • 13
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    Boundary conditions in acoustic scattering with respect to the reciprocity relation (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 725-738 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new concept associated with the reciprocity relation in acoustic scattering is introduced. Motivated by this well-known relation, which holds in all the classical cases, more general boundary value problems for the scalar Helmholtz equation are studied. These generalized boundary conditions are characterized by the validity of the reciprocity relation and seem to be an appropriate unification of a large class of boundary value problems in acoustic scattering. The well-known results for the classical problems can be extended to this general case and also new connections with the question about existence and uniqueness of solutions to the boundary value problems can be derived. A constructive procedure shows that this approach is applicable for a large class of boundary conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161005
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  • 14
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    An Lq-theory for weak solutions of the stokes system in exterior domains (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 707-723 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We introduce a new concept for weak solutions in Lq-spaces, 1 〈 q 〈 ∞, of the Stokes system in an exterior domain Ω ⊂ ∝n, n ≥ 2. Defining the variational formulation in the homogeneous Sobolev space \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop H\limits^.{_{0}}^{1,q} (\Omega )^n = \{ u \in L_{1{\rm oc}}^q (\overline \Omega )^n;\nabla u \in L^q (\Omega )^{n^2 },u\left| {_{\partial \Omega } = 0} \right.\},$\end{document} we prove existence and uniqueness of weak solutions for an arbitrary external force and a prescribed divergence g = div u. On the other hand, solutions in the sense of distributions which are defined by taking test functions only in C0∞(Ω)n are not unique if q 〉 n/(n-1). In this case, a hidden boundary condition related to the force exerted on the body may be imposed to single out a unique solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161004
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  • 15
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    Non-linear singular diffusion with non-linear boundary conditions (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 779-798 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161103
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  • 16
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    Outgassing and contamination: Strict solution of a Boltzman-like model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 799-817 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a Boltzmann-like model of a problem of outgassing and contamination in a region R. For simplicity, we assume that R = R1 ∪ R2 ∪ R3, where R1 is the slab {x: -a 〈 x 〈 0}, R2 = {x:0 〈 x 〈 b}, R3 = {x: b 〈 x 〈 b1}. R1 is the region where the contaminant particles are produced, R2 is the ‘cavity’ where such particles migrate and interact with some inert gas, usually at low pressure, and R3 is the region which is contaminated by the particles coming from R2. In each of the three regions, the behaviour of the contaminant particles is represented by means of a Boltzmann-like equation.We prove that such a mathematical problem has a unique positive strict solution, belonging to a suitable Banach space Y. A system of ordinary differential equations is also derived, which gives the global balances of the contaminant particles in each of the three regions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670161104
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  • 17
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    A remark on a compactness result in electromagnetic theory (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 123-129 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Calderon's extension theorem is a crucial tool in the proof of the compactneσs of the resolvent for the Maxwell operator, and whence this result is proved for domains with the strict cone property. However, the proof only requires an extension operator that extends W2,2-functions compactly as W1,2-functions. It is shown that this can be achieved under weaker regularity conditions on the domain: the cone may be replaced by some cusp of an appropriate order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160205
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  • 18
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    Resonance frequencies of a cavity containing a compressible viscous fluid (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 185-202 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this paper is to study the resonance spectrum of a cavity containing a compressible viscous fluid. This system admits a discrete infinite sequence of eigenvalues whose real parts are negative, which is interpreted as the damping effect introduced by viscosity. Only a finite number of them have non-zero imaginary parts and this number depends on viscosity; a simple criterion is given for their position in the complex plane. The case of a cavity containing an elastic mechanical system immersed in the fluid is also examined; from a qualitative point of view, the nature of the resonance spectrum remains unchanged.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160303
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  • 19
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670160401
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  • 20
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    The transient behaviour of multidimensional PN-diodes in low injection (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 265-279 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An initial boundary value problem modelling the transient behaviour of a pn-junction semiconductor diode is simplified by formal asymptotics, where the scaled minimal Debye length and the scaled intrinsic number are considered as small parameters. The implicit assumption on the biasing situation is that of low injection. The simplified model is shown to be equivalent to an integral relation between the evolution of the current and of the contact voltage. A simple switching application is governed by a non-linear Volterra integral equation for the current. This equation is shown to possess a unique solution globally in time converging to the unique steady state.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160403
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  • 21
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    Modelling of dynamic networks of thin elastic plates (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 379-407 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to derive junction conditions for networks of thin elastic plates and to analyse the dynamic equations of such networks. Junction conditions for networks of Kirchhoff plates and networks of Reissner-Mindlin plates are derived based on geometric considerations of the deformation at a junction. It is proved that the dynamic system which describes the Reissner-Mindlin network is well-posed is an appropriate energy space. It is further established that the Kirchhoff network is obtained in the limit of the Reissner-Mindlin network as the shear moduli go to infinity.
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    URL: http://dx.doi.org/10.1002/mma.1670160602
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  • 22
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    The boundary equation method in the third initial boundary value problem of the theory of elasticity. Part 2: Methods for approximate solutions (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 217-227 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This work considers the methods for solving approximately the four types of boundary equations arising when the third initial boundary value problem of the theory of elasticity is solved with the help of retarded elastic potentials. The convergence of these methods is proved.
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    URL: http://dx.doi.org/10.1002/mma.1670160305
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  • 23
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    An implicit finite-difference algorithm for the numerical simulation of supersonic flow over blunted bodies (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 229-263 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to compute axisymmetric laminar supersonic flow we use an unsteady implicit finite-difference scheme. This scheme solves numerically either the inviscid Euler equations or the ‘thin-layer’ Navier-Stokes equations. In both cases the scheme leads to large sparse non-linear systems, which can be solved by a genuine iteration process. The convergence of this process is shown and numerical results are given.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160402
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  • 24
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670160501
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  • 25
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670160801
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  • 26
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    Modelling and solving fixed-bed adsorption (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 533-544 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we develop a mathematical model for packed-bed adsorption of a single component, directed toward the purification of β-lactamic antibiotics. The model describes the removal of sorbates from an aqueous stream entering a bed packed with spherical sorbent particles. Then, assuming that the adsorption isotherm is linear, an exact solution for this model is found.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160802
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  • 27
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    Global existence of classical solutions to the dynamical von Kármán equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 581-586 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper derives an improved energy inequality for the non-linear dynamical von Kármán equations. The existence of global classical solutions is a consequence of this a priori inequality.
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    URL: http://dx.doi.org/10.1002/mma.1670160806
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  • 28
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    Weak solutions of the Vlasov-Poisson initial boundary value problem (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 587-607 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with existence results for a Vlasov-Poisson system, equipped with an absorbing-type law for the Vlasov equation and a Dirichlet-type boundary condition for the Poisson part. Using the ideas of Lions and Perthame [21], we prove the existence of a weak solution having good Lp estimates for moment and electric field, by a good control on the higher moments of the initial data. As an application, we establish a homogenization result in the Hilbertian framework for this type of problem in non-homogeneous media, following the work by Alexandre and Hamdache [2] for general kinetic equations, and Cioranescu and Mural [11] for the Laplace problem.
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    URL: http://dx.doi.org/10.1002/mma.1670160807
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    Classical solutions of two-dimensional stokes problems on non-smooth domains. Part 2: Collocation method for the radon equation (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 665-679 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The non-uniquely solvable Radon boundary integral equation for the two-dimensional Stokes-Dirichlet problem on a non-smooth domain is transformed into a well posed one by a suitable compact perturbation of the velocity double-layer potential operator. The solution to the modified equation is decomposed into a regular part and a finite linear combination of intrinsic singular functions whose coefficients are computed from explicit formulae. Using these formulae, the classical collocation method, defined by continuous piecewise linear vector-valued basis functions, which converges slowly because of the lack of regularity of the solution, is improved into a collocation dual singular function method with optimal rates of convergence for the solution and for the coefficients of singularities.
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    On directed diffusion with measurable background (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 681-690 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show that the ‘directed diffusion equation’ \documentclass{article}\pagestyle{empty}\begin{document}$$ b(x)\frac{{\partial u}}{{\partial t}}(t,\,\;x) = div(b^2 (x)\nabla _x u(t,\;x)), $$\end{document} with periodic boundary conditions has a unique weak solution u whenever b is measurable and bounded above and below by positive constants. Also, limt→∞u(t,x) in Lp, 1≤p≤∞.
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    The trend to a stationary state for the Lebowitz Stick model (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 739-757 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The asymptotic behaviour of the Lebowitz stick model in kinetic theory is studied in weak* measure, L1- and L∞-sense.
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    URL: http://dx.doi.org/10.1002/mma.1670161006
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    Masthead (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670161201
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    Local bifurcation from characteristic values with finite multiplicity and its application to axisymmetric buckled states of a thin spherical shellThis research was supported by the Alexander von Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne. (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 13-33 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to study bifurcation points of the equation T(v) = L(λ,v) + M(λ,v), (λ,v) ∊ Λ × D in Banach spaces, where for any fixed λ ∊ Λ, T, L(λ,·) are linear mappings and M(λ,·) is a nonlinear mapping of higher order, M(λ,0) = 0 for all λ ∊ Λ. We assume that λ is a characteristic value of the pair (T, L) such that the mapping T - L(λ,·) is Fredholm with nullity p and index s, p 〉 s ≥ 0. We shall find some sufficient conditions to show that (λ,0) is a bifurcation point of the above equation. The results obtained will be used to consider bifurcation points of the axisymmetric buckling of a thin spherical shell subjected to a uniform compressive force consisting of a pair of coupled non-linear ordinary differential equations of second order.
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    URL: http://dx.doi.org/10.1002/mma.1670160103
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    Radially symmetric global classical solutions of non-linear wave equations (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 131-149 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The Cauchy problem for semilinear wave equations utt - Δu + h(|x|)up = 0 with radially symmetric smooth ‘large’ data has a unique global classical solution in arbitrary space dimensions if h is non-negative and p any odd integer provided the smooth factor h vanishes with sufficiently high order at the origin and is bounded together with its derivatives.
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    URL: http://dx.doi.org/10.1002/mma.1670160206
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    Vector spherical spline interpolation - basic theory and computational aspects (1993)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 16 (1993), S. 151-183 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Vector spherical interpolation is discussed from both the theoretical and computational points of view. The theory of vector spherical harmonics is an essential tool. An estimate is given for the absolute error of the interpolation process; an efficient algorithm is developed for the computation of a vector spherical interpoiant. The displacement boundary value problem of determining the elastic field from a finite number of discretely given displacement vectors is solved by the use of vector splines.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/mma.1670160302
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    Computation of outflow flux for convection-dominated transport equations (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 639-647 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An a posteriori point-wise outflow flux recovery scheme which capitalizes on the hyperbolic nature of convection-dominated transport models is proposed. The scheme is seen to be robust in that it can be applied to any upwind finite-difference or finite-element approximation, and gives a superconvergent approximation to the outflow flux.
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    URL: http://dx.doi.org/10.1002/cnm.1640090803
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    Application of iterative global/local finite-element analysis. Part 2: Geometrically non-linear analysis (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 757-766 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear global/local technique was developed and tested. This technique uses separate global and local finite-element models. Iteration is used to enforce equilibrium between the global and local models. The results of this initial study suggest that the technique can be used to reduce both computer memory and CPU requirements.
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    URL: http://dx.doi.org/10.1002/cnm.1640090906
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 785-785 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/cnm.1640090909
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    Consistent concept for line search algorithms in combination with arc-length constraints (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 773-784 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general line search concept is presented, which can be applied for the solution of non-linear equations in the presence of constraint conditions as in arc-length methods in a consistent manner.
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    Two problems with GGP generalized geometric programming algorithm (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 767-772 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The generalized geometric programming algorithm GGP has been found to be one of the better algorithms for optimizing algebraic functions subject to algebraic constraints. The paper discusses two problems with the GGP algorithm presented by Avriel et al. (1980). The first problem is that, because of the way that constraint tolerances are checked, the checks may pass even when a constraint is violated beyond the acceptable tolerance. This problem can affect an acceleration technique suggested for the algorithm. This paper presents two possible solutions to this problem. The second problem is the algorithm's weakness in handling equality constraints. This problem seems to especially affect the ‘Phase I’ part of the algorithm, which finds a feasible solution from a random starting point. While extensions have been made to get around this limitation, no discussion on why the original algorithm has problems with equality constraints has been made. This paper discusses why the problems exist.
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/cnm.1640091001
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    Matrix filter for correcting experimental data (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 797-803 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if any additional information about the measured values is known. The algorithm is very effective in one-dimensional as well as in two-dimensional problems where additional constraints are presented in the form of differential equations. For example, this technique can be used to correct the measurements of certain dynamic quantities if some information about motion of examined bodies is known. It can also be used to correct the strain field measurements if the conditions of continuity of strain field are included.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091003
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    Finite-element computer simulation of atmospheric convection with anisotropic eddys (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 805-814 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer simulation is made of cellular convection in an anisotropic atmosphere in an attempt to more closely approximate the observed values with those obtained from mathematical models. A finite-element Galerkin technique, with Taylor approximation and Crank-Nicolson, is employed and comparisons are made with the author's earlier finite-element models of isotropic convection and with finite-difference models. It is found that postulates from physics on the effect of anisotropy on cellular atmospheric convection, with its increase in the aspect ratio, are well modelled with this finite-element technique.
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    URL: http://dx.doi.org/10.1002/cnm.1640091004
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    Application of augmented Lagrangian techniques for non-linear constitutive laws in contact interfaces (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 815-824 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm.
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    Finite-element analysis of elastic contact between a shell of revolution and a rigid plate (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 883-888 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Elastic contact between a thick shell of revolution and a rigid plate in the case when the plate is brought into contact with the shell by giving a finite displacement to the plate is analysed by the finite-element method. Field-consistent higher-order strain-displacement relations with vanishing shear stresses on the surfaces are used. A finite element based on these relations is developed and used for the analysis. The contact conditions are imposed by use of the Lagrangian multipliers method, and the resulting minimization problem is solved iteratively. This procedure will lead to reduced memory requirements and computation time.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/cnm.1640091104
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    Computation of isotropic tensor functions (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 889-896 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An explicit formulation and a procedure for the computation of isotropic tensor-valued tensor functions is discussed. The formulation is based on a spectral decomposition in terms of second-order eigenvalue bases, which avoids the costly computation of eigenvectors. As an important result a compact structure of the fourth-order derivatives of general second-order isotropic tensor functions is presented.
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    Conference diary (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 933-935 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/cnm.1640091110
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    Masthead (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993) 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640091201
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    Macro finite element using subdomain integration (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 937-949 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For some heterogeneous materials, it is not practical to model the microstructure directly using traditional finite elements. Furthermore, it is not always accurate to use homogenized properties. Macro elements have been developed which permit microstructure within a single element. These macro elements performed well in initial tests.
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    Mapping of finite elements around corner singularities of the quasi-harmonic equation (1993)
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    Communications in Numerical Methods in Engineering 9 (1993), S. 957-974 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the solution of the quasi-harmonic equation by the finite element method in a domain with corners on its boundary. A mapping technique, which can be used for locating the nodes of standard isoparametric elements in a subgrid (patch) of finite elements in the vicinity of a corner singularity point, is presented. The equations of the mapping are based on the analytical singular solution of the problem. Some analytical and numerical results to show the efficiency of the technique are presented.
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    Arbitrary Lagrangian-Eulerian thermomechanical finite-element model of material cutting (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 975-987 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An arbitrary Lagrangian-Eulerian model is described for the prediction of metal flow in a steady-state forming process. The formulation is shown to be capable of dealing with free surface and boundary friction; the coupling with thermal effects is also considered. The numerical techniques are based on the finite elements for spatial discretization of the momentum equation and on an explicit integration scheme for discretization relative to time. The mass and energy equations are integrated by a finite-volume method. Details on the application to an orthogonal cutting process are given in the final Section of the paper.
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    Optimization analysis of the three-level time schemes (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 951-956 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure was implemented to determine the optimum values for the two parameters of the Zienkiewicz three-level time schemes which could be utilized for the numerical solution of a system of ordinary differential equations. A multivariable search method was implemented to estimate optimum values for these parameters. The resultant optimum three-level time scheme produced very accurate results, satisfied physical reality, and did not produce any oscillations for the various problems that were investigated. The optimum values for the two parameters β and γ in the three-level scheme were β = 0·50005 and γ = 1·0007. A comparison was made between this optimum scheme and other existing three-level time schemes. The optimum scheme demonstrated superior results for all the problems that were analysed. However, the results of the optimization analysis produced a set of optimum parameters that were identical to the values that would reduce the general three-level time scheme into a central-difference two-level time scheme, i.e. β = 1/2 and γ = 1.
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    New assumed natural strain formulation of the shallow shell element (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 989-1004 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new efficient formulation of the 36 degree-of-freedom conforming shallow shell element of an arbitrary triangular shape is presented. This formulation is based on natural co-ordinates and independently assumed natural strain fields, and applied to shallow shell analysis. The 3-node element incorporates the normal displacement and its first and second derivatives plus the tangential displacements and their first derivatives at each vertex. A closed form of the element stiffness matrix is achieved. The form of the stiffness matrix derived in this formulation explicitly reveals the essence of the shallow shell theory.The presented approach results in avoiding definite integrals and matrix inversions, and permits operation with lower-order numerical matrices, which are the same for all elements. The example applications presented demonstrate that accurate predictions of stresses as well as displacements are obtained with only a few elements.
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    Locking-free straight beam element based on curvature (1993)
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    Communications in Numerical Methods in Engineering 9 (1993), S. 1005-1011 
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    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The formulation of a straight beam element to eliminate the shear locking phenomenon is presented. The element is based on curvature so that the bending energy is fully represented, and the shear strain energy is incorporated into the formulation by the equilibrium equation. Four examples are chosen to verify the concept of the element employed and its capability of the analysis. The solutions obtained reveal that the element describes the behaviour of the straight beam quite exactly and efficiently, showing no locking and that it is also applicable to the analysis of both thin and thick straight beams.
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    Conference diary (1993)
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    Communications in Numerical Methods in Engineering 9 (1993), S. 1013-1015 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/cnm.1640091208
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    Masthead (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620360101
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    Triangular C0 bending elements based on the Hu-Washizu principle and orthogonality conditionsDedicated to Professor Walter Wunderlich on the occasion of his sixtieth birthday anniversary. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 181-200 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with simple and effective C0 linear triangular bending elements based on the Hu-Washizu variational principle. The following key features are inherent in the proposed formulation: extensional, flexural and transverse shear strains and the corresponding stresses are referred to the directions of the triangle sides. The independent variation of displacements, strains and stresses yields discrete approximations consistent with the continuum theory. Furthermore, a proper identification of the deformational modes and the orthogonality requirements between the assumed transverse shear forces and the undesirable strain fields lead to element formulations with important attributes: minimization of superfluous energy, properly justified assumptions, simplicity of formulation and straightforward extension to non-linear problems. Alternative approximations of strains and stresses, also presented, enhance the element performance in the case of both thick and thin plates and shells. Test examples demonstrate the characteristic properties of the proposed element formulations.
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    Boundary element analysis of two-dimensional elastoplastic contact problems (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 221-235 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a boundary element method for two-dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic-perfectly plastic or work-hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral or six-noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.
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    Non-singular boundary integral equation implementation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 237-254 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The basis of the boundary integral equation (BIE) development is the singular field solution for the Kelvin point load problem. The presence of the mathematical singularity in an otherwise non-singular problem has created over the years a variety of numerical coping strategies. The current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms. The resulting formulation is fully non-singular and is shown to be amenable to simple, low-order Gaussian integration. The critical class of problems involving thin sections and/or highly graded BIE meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear BIE equations. Extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi-analytical BIE implementation reported herein.
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    An application of preconditioned conjugate gradients to relative placement in chip design (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 255-271 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-large-scale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.
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    Application of block Lanczos method for analysis of cyclic symmetric structures (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 273-285 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this study the free vibration of circumferentially periodic structures has been analysed using the block Lanczos method in a semi complex domain for extracting real natural frequencies and complex mode shapes. The influence of the number of vectors in the block and also the effect of renumbering of nodes, depending on whether they are internal, adjacent or boundary nodes, on the CPU time are studied. The efficiency of the present method is compared with the subspace iteration schemes.
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    Interpolation of curved shell geometries by low order finite elements - errors and modificationsThis contribution is dedicated to Professor Dr.-Ing. Walter Wunderlich, Lehrstuhl für Statik, Institut für Bauingenieur-wesen I, Technical University of Munich, on the occasion of his 60th birthday. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 287-302 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Low order finite elements are of vital interest for practical applications in linear and non-linear structural analysis. The possible discretization errors, when Reissner-Mindlin shell elements with bilinear shape functions are used, and modifications to prevent these errors are presented. On some numerical examples the influence of these errors and of various modifications on the results is shown. Finally, the case of membrane locking with low order Reissner-Mindlin elements for particular assumptions concerning the base vectors and methods to prevent this locking are discussed.
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    An efficient implementation of stress resultant plasticity in analysis of Reissner-Mindlin plates (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 303-320 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution procedure for elasto-plastic analysis of Reissner-Mindlin plates has been proposed in this work. The main ingredients which render efficiency are: what appears to be an optimally tuned four-node plate element with assumed shear strains and incompatible bending modes; an elasto-plastic constitutive model given directly in terms of stress resultants; and efficient computation of plastic flow which simplifies to a solution of a single scalar equation and remaining state update computation. The performance of the element has been proved very satisfying in both elastic singularity-dominated and elasto-plastic problems.
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    Solution of the Helmholtz eigenvalue problem via the boundary element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 321-330 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The numerical solution of the Helmholtz eigenvalue problem is considered. The application of the boundary element method reduces it to that of a non-linear eigenvalue problem. Through a polynomial approximation with respect to the wavenumber, the non-linear eigenvalue problem is reduced to a standard generalized eigenvalue problem. The method is applied to the test problems of a three-dimensional sphere with an axisymmetric boundary condition and a two-dimensional square.
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    Announcement (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 355-355 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620360212
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    Analysis of the anisotropic viscoplastic-damage response of composite laminates - continuum basis and computational algorithmsThis work is supported by NASA-Lewis Grant No. NAG3-901 (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1629-1660 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.
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    An adaptive multigrid technique for three-dimensional elasticity (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1703-1716 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A program for finite element analysis of 3D linear elasticity problems is described. The program uses quadratic hexahedral elements. The solution process starts on an initial coarse mesh; here error estimators are determined by the standard Babuška-Rheinboldt method and local refinement is performed by partitioning of indicated elements, each hexahedron into eight new elements. Then the discrete problem is solved on the second mesh and the refinement process proceeds in the following way-on the ith mesh only the elements caused by refinement on the (i-1)th mesh can be refined. The control of refinement is the task of the user because the dimension of the discrete problem grows very rapidly in 3D. The discrete problem is being solved by the frontal solution method on the initial mesh and by a newly developed and very efficient local multigrid method on the refined meshes. The program can be successfully used for solving problems with structural singularities, such as re-entrant corners and moving boundary conditions. A numerical example shows that such problems are solved with the same efficiency as regular problems.
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    New strategy for assumed stresses for 4-node hybrid stress membrane element (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1747-1763 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An oblique (skew) co-ordinate system defined at the origin of the isoparametric co-ordinates is introduced as the reference co-ordinate system for assumed stresses in the formulation of a 4-node hybrid membrane element. The initially uncoupled stresses in these reference co-ordinates can be constrained to satisfy the equilibrium conditions pointwise by using the procedure of Pian and Wu7, when suitable incompatible displacements are introduced. Such strategy allows the element stiffness to be formulated by using either the Hellinger-Reissner or the complementary energy functional. Numerical results show that the performances of three elements, constructed by using different sets of incompatible displacements in this paper, are practically identical and are all of slightly higher accuracy than that of the Pian-Sumihara element6.
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    Boundary element method solutions for elastic wave scattering in 3D (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 437-455 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Time-harmonic elastic wave scattering problems such as those encountered in ultrasonic non destructive evaluation are solved by the boundary element method (BEM). Selected results for spherical and spheroidal shaped voids and inclusions are compared with analytical and other numerical solutions. Results for ellipsoids, which require a full three-dimensional formulation, are provided as a benchmark for comparison when other numerical methods would be developed for this problem class in the future. The modelling of cracklike defects with this formulation is discussed. Recent theoretical findings regarding the fictitious eigenfrequency difficulty (FED) are confirmed by a numerical study.
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    The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 457-497 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non-linear GMRES algorithm, for solving the Navier-Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non-linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill-McKee and snake, and consider preconditionings without fill-in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non-linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.We also consider the effect of orderings when an incomplete factorization which allows some fill-in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill-in.Finally, following the principal ideas of non-linear GMRES algorithm, we suggest other inexact Newton methods.
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    An algorithm for adaptive refinement of triangular element meshes (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 499-509 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple algorithm is developed for adaptive and automatic h refinement of two-dimensional triangular finite element meshes. The algorithm is based on an element refinement ratio that can be calculated from an a posteriori error indicator. The element subdivision algorithm is robust and recursive. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several example problems are presented to illustrate the utility of the approach.
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    An approach to optimal design of structures with non-linear response (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 511-521 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A commonly adopted procedure to solve a structural optimum design problem is to improve the design iteratively by solving a sequence of simpler problems, where each of these is obtained as an approximation of the original problem. Considering structures with linear response, this procedure works very well and can be implemented quite straightforwardly. However, considering structures with non-linear response, the situation is more sophisticated since structural stability properties have to be taken into account.The paper presents an approach to optimal design of statically loaded structures with non-linear response. It is proposed to replace the original problem with a sequence of similar problems from which corresponding approximate problems can easily be obtained. These similar problems additionally contain an estimation of the critical load constraint while other constraints are imposed at some properly chosen load level, which is lower or at most equal to the critical load level. By this approach, the structural stability requirements are taken into account in an effective manner. The efficiency is illustrated with several examples involving kinematic as well as material non-linear effects.
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 537-538 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Masthead (1993)
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    International Journal for Numerical Methods in Engineering 36 (1993) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620360401
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    Computation of heat conduction in materials with random variable thermophysical properties (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 523-536 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A method for the direct computation of mean values and variances of the temperature in conduction-heated objects with random variable thermophysical properties is presented. This method is based on a Taylor expansion of the finite element formulation of the heat conduction equation and offers a powerful alternative to the computationally expensive Monte Carlo method. Both steady-state and transient problems are considered. Some example problems are solved and the results discussed. The simulations indicate that the variability of the thermophysical properties may cause a considerable variability of the temperature within the heated object. This may have important consequences on the design of heating operations in food process engineering.
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    The problem of the selection of an a posteriori error indicator based on smoothening techniques (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 539-567 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper addresses the problem of assessing the quality of an a posteriori error estimate of a finite element solution. An error estimate based on local L2-projections is analysed in the case of translation-invariant meshes. It is shown that for general meshes this technique does not lead to an asymptotically exact estimator. The problem is analysed in detail in the one-dimensional setting. It is shown that an asymptotically exact estimator is not the optimal one when the solution is not sufficiently smooth. An optimal estimator for adaptively constructed meshes is given. Finally, a general mathematical framework for the quality assessment of estimators is introduced.
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    An augmented Lagrangian method for discrete large-slip contact problems (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 569-593 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An augmented Lagrangian formulation is proposed for large-slip frictionless contact problems between deformable discretized bodies in two dimensions. Starting from a finite element discretization of the two bodies, a node-on-facet element is defined. A non-linear gap vector and its first variation are derived in terms of the nodal displacements. The relevant action and reaction principle is stated. The gap distance is then related to the conjugate pressure by a (multivalued non-differentiable) unilateral contact law. The resulting inequality constrained minimization problem is transformed into an unconstrained saddle point problem using an augmented Lagrangian function. Large slip over several facets is possible and the effects of target convexity or concavity are investigated. A generalized Newton method is used to solve the resulting piecewise differentiable equations necessary for equilibrium and contact. The proper tangent (Jacobian) matrices are calculated. The primal (displacements) and dual (contact forces) unknowns are simultaneously updated at each iteration.
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    A finite element procedure for axisymmetric elastomeric solids under general loading (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2031-2048 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element procedure, which utilizes Fourier series, is developed to compute the large deformations and deflections in axisymmetric elastomeric solids subjected to non-axisymmetric loading. Nearly incompressible and incompressible, isotropic strain energy density functions describe the elastic properties. The nearly incompressible functions become compatible with an analytical integration scheme by using a novel variable to approximate the dilatation. A large spherical elastomeric bearing is analysed with this procedure.
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    A new approach to magnetic field analysis by the dual reciprocity boundary element method (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2073-2085 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an application of the dual reciprocity boundary element method to non-linear magnetic field analysis. Advanced techniques employed in the procedure include discontinuous elements, quasi-singular and hyper-singular integration schemes and the Galerkin formulation. Numerical results are included to show the performance of the proposed approach.
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    Discrete micromechanics of elastoplastic crystals (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3815-3840 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The theoretical prediction of elastoplastic behaviour of single crystals is a basic problem which is central to the prediction of the overall behaviour of the crystal aggregate. It is generally well known that quasi-static and isothermal plastic deformation in single crystals arises almost solely from slip on specific crystallographic planes, and that this process occurs when the resolved shear stress on a critical slip system reaches a certain maximum value. What is not obvious is how one can identify the specific slip systems activated by a given load increment, since the process usually involves selection from a pool of linearly dependent slip systems. In this paper we use small-deformation multisurface plasticity theory to phrase properly the problem of crystal slips at infinitesimal increments. We then describe an ‘ultimate’ algorithm for systematically identifying the active slip systems at finite increments. We arrive at the following major conclusions when the ultimate algorithm is applied to f.c.c. crystals: For perfectly plastic crystals the combination of active slip systems may or may not be unique; however, the imposition of the discrete Kuhn-Tucker conditions is sufficient to determine the (unique) final crystal stresses. For Taylor hardening crystals in which active and latent slip systems harden by the same amount, the discrete Kuhn-Tucker conditions are also sufficient to make the mathematical problem of crystal stress integration well posed, i.e. the final stresses can be determined uniquely albeit the combination of active slip systems may not be unique. To illustrate the latter point, an accurate return-mapping algorithm for perfectly plastic and Taylor hardening crystals is described and tested against the ultimate algorithm to demoustrate numerically that it is possible to generate different combinations of active slip systems and yet produce identical final stresses.
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    Moving-grid finite element modelling of thermal ablation and consolidation in porous mediaWork performed in part under the auspices of the U.S. Department of Energy (DOE), Idaho Operations Office, under Contract No. DE-ACO7-76ID01570, the INEL Long Term Research Initiative in Computational Mechanics, the National Science Foundation and the CEOGRR Industrial Associates. (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 717-744 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A moving-grid finite element model for the analysis of thermal ablation, fluid flow and deformation in elastic porous media is presented. The model is formulated in terms of temperatures, fluid pressures and solid displacements, and takes into account a moving phase boundary. Supporting algorithms for treating the moving phase boundary and solving the coupled equations are described. The model has application to several important moving-boundary geotechnical problems. Numerical test cases are provided for model verification and example applications corresponding to thermal ablation, consolidation and underground coal gasification are given.
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    Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 745-764 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360503
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    Boundary stress calculation using regularized boundary integral equation for displacement gradients (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 783-797 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Accurate computation of boundary stress components is important in stress-base shape optimization. The boundary element method usually gives us more accurate solutions of them compared with those obtained by the finite element method. In the present paper we propose a new approach to calculate the boundary stress components by using the regularized boundary integral equation relating the boundary displacement gradients to the tractions. Although the original integral equation must be evaluated in the sense of the Cauchy principal value, it can be regularized by subtracting and adding the displacement gradients at the source point from and to the original integral equation. When the displacement gradients satisfy the Hölder continuity at the source point, the regularized integral equation becomes non-singular and can be evaluated numerically by using the standard Gaussian quadrature formula. The numerical implementation of the proposed integral equation is presented and the effectiveness of the approach is also discussed through some numerical demonstrations.
    Additional Material: 18 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360505
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    Boundary element solution of heat conduction problems in multizone bodies of non-linear material (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 799-809 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel algorithm for handling material non-linearities in bodies consisting of subregions having different, temperature dependent heat conductivities is developed. The technique is based on Kirchhoff's transformation. The material non-linearity is reduced to a solution dependent function of unified form added to unknown nodal Kirchhoff's transforms. Assembling of element contributions brings the non-linearity to the right hand sides of the global set of equations. The first step of the solution of this set is the Gaussian pre-elimination (condensation) of linear degrees of freedom. At this stage efficient block solvers can be used. Then, a set of non-linear equations is extracted from the condensed one and solved employing the Newton-Raphson technique. The iteratively solved set consists of the least possible number of equations and its Jacobian matrix is calculated efficiently by taking advantage of the specific form of the equations.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360506
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2681-2682 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361511
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    A new first-order interior feasible direction method for structural optimization (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 4009-4025 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new interior feasible direction method for optimization problems with linear objective functions but non-linear constraints is proposed. The method is particularly suitable for weight minimization problems in structural design where the design variables are the cross-sectional areas of members and arbitrary stress and displacement constraints are applied. Four truss structures are analysed and in each case the minimum weight consistent with or lower than that currently available in the literature is achieved. Although still expensive in its current version, the method is comparable in cost and robustness with other methods such as the ‘trust region’ multiplier method. Apart from one tolerance value, a reconnaissance parameter needs to be specified. The fact that the same value of the parameter was used for all the examples, and that the method is relatively insensitive to the choice thereof, confirms the robustness of the method.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620362306
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    A fully non-linear axisymmetrical quasi-kirchhoff-type shell element for rubber-like materials (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 4027-4043 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An axisymmetrical shell element for large deformations is developed by using Ogden's non-linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a ‘quasi-Kirchhoff-type theory’ emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non-linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two-node element is given. Several examples show the applicability and performance of the proposed formulation.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620362307
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 4111-4113 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620362310
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    Modelling edge effects with the C0 plate bending elements: Part 2. The performance of the reformulated four-node element (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 4069-4109 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The reformulated four-node element has exhibited an excellent behaviour in static finite element analyses being free of shear and machine locking problems and of zero energy modes and modelling accurately relatively thick plates. In the present paper, the element under consideration is shown to exhibit an analogous excellent performance in modelling highly demanding boundary layer plate bending problems.
    Additional Material: 39 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620362309
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    A variational boundary integral equation method for an elastodynamic antiplane crack (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 969-984 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper investigates the transient wave scattering by a crack by means of the Boundary Integral Equation Method (BIEM). The author has developed a new formulation to solve the BIE for the Crack Opening Displacement (COD). The resolution is done directly in the time domain. The solution is represented by means of a retarded double layer potential, and the resulting BIE, with the COD as unknown, has a hypersingular kernel. The corresponding difficulty is overcome by using a variational method. We present the application of this method to an antiplane crack, describe the approximate problem and finally give some numerical results.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360606
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    Singularity in structural optimization (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 931-944 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Singularity conditions that arise during structural optimization can seriously degrade the performance of the optimizer. The singularities are intrinsic to the formulation of the structural optimization problem and are not associated with the method of analysis. Certain conditions that give rise to singularities in linear elastic structures have been identified in earlier papers, along with a proposition to alleviate the consequences of their presence.1-3 These singularities were global in nature, encompassing the entire structure. Further examination revealed more complex sets of conditions in which singularities occur. Some of these singularities are local in nature, being associated with only a segment of the structure. Moreover, the likelihood that one of these local singularities may arise during an optimization procedure can be much greater than that of the global singularity identified earlier. This paper provides examples of these additional forms of singularities. It gives a framework in which these singularities can be recognized. In particular, the singularities can be identified by examination of the stress-displacement relations along with the compatibility conditions and/or the displacement-stress relations derived in the integrated force method of structural analysis. Methods for the elimination of the effects of these singularities are suggested and numerical illustrations are given.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360604
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    A generalized forward gradient procedure for rate sensitive constitutive equations (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 985-995 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Many forward gradient schemes have been proposed for the time-integration of the stiff constitutive equations of rate sensitive solids. It is shown here that one of these methods can be interpreted as a hybrid ordinary differential equation integrator which combines explicit and semi-implicit Runge-Kutta methods. This observation permits development of higher order schemes, illustrated here by one of second order. An embedded first order estimate provides a reliable step-size control. The method is applied to an overstress model and to an internal variable model, and is used in a finite element analysis of hydrostatic bulging of sheet metal.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360607
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    Axially-loaded damped Timoshenko beam on viscoelastic foundation (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1013-1027 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The study of an axially-loaded damped Timoshenko beam on a viscoelastic foundation is presented. The effects of the axial force, viscoelastic foundation and all the various damping components to a Timoshenko beam are considered in the formulation. The dynamic stiffness matrix is established and intensively discussed for applications. Free vibrations and the overall dampings are solved accordingly. Examples and discussions are also included.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360609
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    A new 3-D finite element model to evaluate added mass for analysis of fluid-structure interaction problems (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 997-1012 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted. A new 8-noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620360608
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    Authors' reply (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1065-1065 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360612
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1067-1069 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360613
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    A parallel row-oriented sparse solution method for finite element structural analysis (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2895-2919 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a parallel implementation of LDLT factorization on a distributed-memory parallel computer. Specifically, the parallel LDLT factorization procedure is based on a row-oriented sparse storage scheme. In addition, a strategy is proposed for the parallel solution of a triangular system of equations. The strategy is to compute the inverses of the dense principal diagonal block submatrices of the factor L, stored in a row-oriented structure. Experimental results for a number of finite element models are presented to illustrate the effectiveness of the parallel solution schemes.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620361704
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    A boundary element formulation based on the three-dimensional elastostatic fundamental solution for the infinite layer: Part I - theoretical and numerical development (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3097-3130 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work presents a specialization of the integral identities used in the boundary element method. This modification is especially tailored to deal with three-dimensional elastostatic problems involving geometries which contain two parallel planar surfaces (e.g. three-dimensional plate problems). The formulation makes use of the three-dimensional fundamental solution for a point load acting in the interior of an infinite layer of uniform thickness (obtained by Benitez and Rosakis8,9).It is shown that this procedure is especially suited for the analysis of three-dimensional problems involving cavities in plate structures. In such problems it is demonstrated that, in addition to the cavity surfaces, only the lateral surfaces of the structure need to be discretized, with no discretization required on the traction-free parallel surfaces.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620361805
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    Adaptive multivlevel methods in three space dimensions (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3187-3203 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the approximate solution of self-adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.
    Additional Material: 16 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620361808
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    Conference diary (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 3221-3221 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361810
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