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  • Articles  (27)
  • finite element method  (27)
  • Wiley-Blackwell  (27)
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  • Articles  (27)
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  • Wiley-Blackwell  (27)
  • American Chemical Society
  • American Physical Society
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  • 1
    Electronic Resource
    Electronic Resource
    Comparison of several mesh refinement strategies near edges (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; mesh refinement ; adaptivity ; singularities near edges ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with several refinement techniques of finite element meshes for treating elliptic boundary value problems in domains with re-entrant edges and corners. A priori mesh grading is explained, and it is combined with the well-known adaptive finite element method. For two representative examples the numerically determined error norms are recorded, and the different strategies are compared.
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  • 2
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    Three and four step least squares finite element schemes in the time domain (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
    Details
    ISSN: 1069-8299
    Keywords: time integration ; finite element method ; least squares formulation ; multistep methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is A0-stable but inconsistent.
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  • 3
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    Adaptive procedure for approximating functions by continuous piecewise polynomials (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
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  • 4
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    Superconvergent patch recovery technique for the finite element method in acoustics (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    Details
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
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  • 5
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    Accurate stress extraction for nearly incompressible materials by the displacement formulation of the p-version FEM (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    Details
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
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  • 6
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    Study of warping torsion of thin-walled beams with closed cross-section using macro-elements (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
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    ISSN: 1069-8299
    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for computing the deformation of thin-walled beams with closed cross-section under warping torsional loading is presented. In comparison to the classical theory (Umanski), the hypothesis of no deformation of the contour of the cross-section of the beam is maintained and the assumption of no distortion of the cross-section plane is modified. The new approach gives better results than the classical theory when both are compared to a standard finite element technique (using shell elements). The central idea of the new approach lies in the usage of a new finite element called a macro-element, which is especially well suited for thin-walled beam computations.
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  • 7
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    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - I. SHAPE OPTIMIZATION METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 33-50 
    Details
    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forming process ; optimal design ; forging ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest a shape optimization method for a non-linear and non-steady-state metal forming problem. It consists in optimizing the initial shape of the part as well as the shape of the preform tool during a two-step forging operation, for which the shape of the second operation is known. Shapes are described using spline functions and optimal parameter values of the splines are searched in order to produce, at the end of the forging sequence, a part with a prescribed geometric accuracy, optimal metallurgical properties and for a minimal production cost. The finite element method, including numerous remeshing operations, is used for the simulation of the process. We suggest using a least-squares-type algorithm for the unconstrained optimization method (based on external penalty) for which we describe the calculation of the derivatives of the objective function. We show that it can reduce to calculations which are equivalent to the derivative calculations of steady-state processes and to evolution equations. Therefore, the computational cost of such an optimization is quite reasonable, even for complex forging processes. Lastly, in order to reduce the errors due to the numerous remeshings during the simulation, we introduce error estimation and adaptive remeshing methods with respect to the calculation of derivatives.
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  • 8
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    THREE-DIMENSIONAL TRANSIENT MOLD COOLING ANALYSIS BASED ON GALERKIN FINITE ELEMENT FORMULATION WITH A MATRIX-FREE CONJUGATE GRADIENT TECHNIQUE (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3049-3064 
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    ISSN: 0029-5981
    Keywords: mold cooling ; injection molding ; finite element method ; three-dimensional ; Jacobi conjugate gradient ; matrix-free algorithm ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A methodology is presented to simulate the three-dimensional heat transfer within a mold during the injection molding process. The mold cooling analysis assists cooling channel design and paves the way for part shrinkage and warpage analysis. The transient temperature distributions in the mold and the polymer part are simultaneously computed by Galerkin Finite Element Method (GFEM) using a matrix-free Jacobi Conjugate Gradient (JCG) scheme. The numerical method presented here is efficient and has shown to require a fraction of the memory and computing time required by conventional methods. The matrix-free algorithm is initially validated using an injection mold designed to produce a plaque with a molded-in hole. Subsequently, the method is further applied to a representative automotive plastic component.
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  • 9
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    CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THE h-ADAPTIVE FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4039-4061 
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    ISSN: 0029-5981
    Keywords: finite element method ; optimal mesh ; strategy ; refinement ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five Adaptive Modification Strategies (AMSs) are studied as means to obtain nearly optimal meshes using an adaptive finite element modelling system based on the h-version of the FEM. These strategies include the method traditionally seem in the literature as well as four additional methods. The five strategies are tested over five numerical examples, one of them producing convergence oscillations in one example. The principal characteristic of our system is that it permits the user to control certain parameters of the adaptive process, which contributes to an improvement in the results.
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  • 10
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    Eigenvalue extraction for large finite element models using a new conjugate gradient algorithm (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 77-83 
    Details
    ISSN: 1069-8299
    Keywords: eigenvalue extraction ; conjugate gradient method ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new conjugate gradient algorithm is presented for extracting eigenvalues from large systems of equations encountered in finite element analysis. The new algorithm involves applying the conjugate gradient method (CGM) to a static problem to generate an equivalent tridiagonal matrix used for eigenvalue computation. The eigenvalues of the tridiagonal matrix are then extracted using a QR factorization. The similarity of the new CGM with the Lanczos method is discussed regarding the need for matrix inversion and reorthogonalization. Several examples using the new method are presented to illustrate its performance.
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  • 11
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    A SPACE-TIME FINITE ELEMENT METHOD FOR THE EXTERIOR STRUCTURAL ACOUSTICS PROBLEM: TIME-DEPENDENT RADIATION BOUNDARY CONDITIONS IN TWO SPACE DIMENSIONS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1635-1657 
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    ISSN: 0029-5981
    Keywords: finite element method ; radiation boundary conditions ; absorbing boundary conditions ; discontinuous Galerkin method ; structural acoustics ; wave equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space and time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time-dependent radiation boundary conditions, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the matrix problem emanating from the space-time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space-time method.
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  • 12
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    THE p-VERSION OF THE FINITE ELEMENT METHOD IN INCREMENTAL ELASTO-PLASTIC ANALYSIS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 1859-1878 
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    ISSN: 0029-5981
    Keywords: p-version ; finite element method ; elasto-plasticity ; cold-working ; non-linear problems ; continuum mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Whereas the higher-order versions of the finite element method (p- and hp-versions) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. In this paper, we discuss which aspects of incremental elasto-plastic finite element analysis are particularly amenable to improvements by the p-version. These theoretical considerations are supported by several numerical experiments. First, we study an example for which an analytical solution is available. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared with the traditional h-version but also with respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-working lug - is presented which demonstrates how the modelling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.
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  • 13
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    A GENERALIZED NEWTON METHOD FOR HIGHER-ORDER FINITE ELEMENT APPROXIMATIONS IN NON-LINEAR ELASTICITY (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2635-2646 
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    ISSN: 0029-5981
    Keywords: non-linear elasticity ; finite element method ; Newton method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.
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  • 14
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    CONSIDERATION OF AGING OF SHOTCRETE IN THE CONTEXT OF A 3-D VISCOPLASTIC MATERIAL MODEL (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3123-3143 
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    ISSN: 0029-5981
    Keywords: shotcrete ; finite element method ; viscoplasticity ; smeared cracking ; aging ; Rankine criterion ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of the classical theory of viscoplasticity and its algorithmic formulation in the context of an operator split scheme is extended to account for the effect of aging. Within this framework, a 3-D multisurface constitutive model for shotcrete is proposed. A rotating-crack model based on the Rankine criterion is adopted in conjunction with a Drucker-Prager yield criterion for describing the mechanical behaviour of young concrete in the compressive regime. The model is suitable for the representation of the time-dependent behaviour of shotcrete including creep and the time dependence of strength and stiffness. A computationally effective return mapping scheme is achieved by formulating the material model in terms of the principal directions and transforming the obtained relations to global axes. Linearization of the return mapping algorithm yields the algorithmic tangent moduli.
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  • 15
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    STRESS- AND ROTATION-BASED HIERARCHIC MODELS FOR LAMINATED COMPOSITES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2647-2671 
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    ISSN: 0029-5981
    Keywords: hierarchic models ; laminated composites ; stress-based formulation ; complementary energy ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchic sequence of equilibrium models in terms of stresses assumed to be not a priori symmetric is derived for cylindrical bending of laminated composites, using first-order stress functions. The stress field of each hierarchic model satisfies a priori (i) the translational equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and (ii) the continuity requirement for the transverse shear and normal stresses at the lamina interfaces. The levels of hierarchy correspond to the degree to which the two first-order compatibility equations and the rotational equilibrium equation of two-dimensional elasticity are satisfied. The numerical solution is based on Fraeijs de Veubeke's dual mixed variational principle, employing the p-version of the finite element method. The number of degrees of freedom is independent of the number of the layers in the laminate. Results are obtained directly for the stresses and rotations; the displacement field is obtained in the post-processing phase by integration. Numerical results with comparisons show the capability of the mathematical and numerical models proposed.
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  • 16
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    DIRECT FORMULATION FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL GROUNDWATER POLLUTION MODELLING WITH A COMPARISON WITH CONVENTIONAL FINITE ELEMENT METHOD (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 2575-2591 
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    ISSN: 0029-5981
    Keywords: finite element method ; numerical analysis ; numerical method ; groundwater modelling ; subsurface modelling ; groundwater pollution modelling ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Real world ground water pollution modelling deals with solute transport through anisotropic, heterogeneous media. The applicability of analytical solutions for such a real world system is extremely limited. As an effective tool, numerical models, such as finite difference and finite element methods, are usually employed to model field scenarios. Nevertheless, ground water pollution modelling is a hallenging task and frequently ends up with misleading results. Most of the time insufficient data are blamed for such erratic results. A recent investigation shows that the shortcomings of numerical formulations may be the major cause for many disputes and confusions in numerical analyses. In reality, a point injection of water in a static, homogeneous and isotropic groundwater system shows a radial dissipation of water forming a sphere; and a full-depth line injection shows a radial dissipation forming a cylinder. The finite difference method completely ignores this fundamental flow principles and allows water only to flow along orthogonal directions. To overcome this limitation, the finite element method was developed as a flexible approach in order to connect a node with the neighbouring nodes in various directions where water is assumed to flow in any directions along node connections. In a recent investigation, it has been found that the conventional finite element method does not keep the commitments; and its formulation techniques lead to a global matrix where a solution domain is not connected with all the neighbouring nodes and does not comply with the control-volume mass balance concept. A consistent finite element formulation approach which does not need imaginary mathematical formulation and overcomes the limitations of both the conventional finite difference and finite element methods has been developed. This method allows fluid flow and solute transport in a porous medium in radial directions. The global matrices for flow and transport obtained from this technique are field representative, diagonally dominant and easily convergent. The new method is robust, needs less mathematical computation and has many advantages over the conventional finite difference and finite element methods.
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  • 17
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    GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3391-3403 
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    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
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  • 18
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    NUMERICAL ANALYSES OF TUNNEL LININGS BY MEANS OF A VISCOPLASTIC MATERIAL MODEL FOR SHOTCRETE (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3145-3162 
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    ISSN: 0029-5981
    Keywords: shotcrete ; tunnelling ; cap model ; New Austrian Tunnelling Method (NATM) ; finite element method ; viscoplasticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the parameter identification, verification and selected applications of a 3D viscoplastic material model for shotcrete proposed by Meschke. The performance of the shotcrete model is evaluated by means of reanalyses of short-term and creep tests on shotcrete specimen. The most essential items of a viscoplastic cap model used for the representation of soil including the determination of the model parameters are also presented. Both models are employed in a 3D finite element simulation of the excavation of a single-track tunnel driven according to the New Austrian Tunnelling Method. Comparisons between in situ measurements and numerical results are presented.
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  • 19
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    AN IMPLICIT PROJECTION ALGORITHM FOR SIMULTANEOUS FLOW OF PLASTICITY AND DAMAGE IN STANDARD GENERALIZED MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3065-3082 
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    ISSN: 0029-5981
    Keywords: biomechanics ; damage ; finite element method ; plasticity ; standard generalized material ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Motivated by mechanical analysis of cancellous bone, a 3D constitutive law describing the simultaneous flow of rate-independent plasticity and damage is developed in the framework of thermodynamics of irreversible processes with internal variables. Following the hypothesis of standard generalized materials, a free energy and a dissipation potential are postulated and the associated flow rules derived with the tools of convex analysis. On the computational side, the classical implicit projection (or catching up) algorithm used in plasticity is extended to account for the additional flow of damage. Due to the existence of a dissipation potential, linearization of the incremental algorithm provides a symmetric tangent operator. Numerical resolutions of several boundary value problems and a biomechanical application are presented to illustrate the potential of the constitutive model and demonstrate the quadratic convergence of the algorithm.
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    OPTIMAL DESIGN FOR NON-STEADY-STATE METAL FORMING PROCESSES - II. APPLICATION OF SHAPE OPTIMIZATION IN FORGING (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 51-65 
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    ISSN: 0029-5981
    Keywords: finite element method ; shape optimization ; sensitivity analysis ; forging ; preform design ; optimal design ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is the second part of a two-part article about shape optimization of metal forming processes. This part is focused on numerical applications of the optimization method which has been described in the first paper. The main feature of this work is the analytical calculations of the derivatives of the objective function for a non-linear, non-steady-state problem with large deformations. The calculations are based on the differentiation of the discrete objective function and on the differentiation of the discrete equations of the forging problem. Our aim here is to show the feasibility and the efficiency of such a method with numerical examples. We recall the formulation and the resolution of the direct problem of hot axisymmetrical forging. Then, a first type of shape optimization problem is considered: the optimization of the shape of the initial part for a one-step forging operation. Two academic problems allow for checking the accuracy of the analytical derivatives, and for studying the convergence rate of the optimization procedure. Both constrained and unconstrained problems are considered. Afterwards, a second type of inverse problem of design is considered: the shape optimization of the preforming tool, for a two-step forging process. A satisfactory shape is obtained after few iterations of the optimization procedure.
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    A NEW TWO-DIMENSIONAL FINITE ELEMENT MODEL FOR THE SHALLOW WATER EQUATIONS USING A LAGRANGIAN FRAMEWORK CONSTRUCTED ALONG FLUID PARTICLE TRAJECTORIES (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 4159-4182 
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    ISSN: 0029-5981
    Keywords: shallow water equations ; finite element method ; Lagrangian framework ; fluid particle trajectories ; Tay estuary ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a new finite element model for the tidal hydrodynamics in estuaries. The mathematical model is based on the solution of the two-dimensional shallow water equations in a Lagrangian framework which is defined along the trajectories of fluid particles. This method gives a flexible and robust numerical scheme for moving boundary flows encountered in tidal water systems. In order to validate the developed model we have, at first instance, compared our numerical results with analytical solutions obtained for domains with simple geometries. Further tests are then conducted to demonstrate the model's ability to cope with conditions such as hydraulic shock, abrupt changes in the flow domain geometry and gradual changes of water surface breadth. The change in the water surface breadth corresponds to the drying and wetting of the plains along the banks of a typical tidal river/estuary reach. The drying and wetting of flood plains result in the existence of very shallow depth of water at some sections of the flow domain during a tidal cycle. The flow equations under these conditions are strongly convection dominated. Previously published tidal models rely on either, some form of upwinding or the use of extremely fine meshes to give stable results for the convection dominated very shallow depth computations in estuaries. We show that our model can yield stable and accurate results for very shallow depths in the tidal flow domains without using any kind of artifical damping or excessive mesh refinement. Computational costs of simulating hydrodynamical conditions in a natural water course, even using a depth averaged two-dimensional approach, can be very high. The ability of our scheme to cope with convection dominated conditions has enabled us to economize the computational efforts by using coarse meshes in our finite element calculations. After the validation stage, the developed model is applied to simulate the tidal conditions in a real estuary. The comparison of the model results with the field observations shows a close agreement between these sets of data
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    MANAGEMENT OF GROUND TEMPERATURE BY BANG-BANG CONTROL BASED ON FINITE ELEMENT APPLICATION (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 885-901 
    Details
    ISSN: 0029-5981
    Keywords: ground temperature ; golf links ; pesticide pollution ; finite element method ; optimal control ; bang-bang control ; practical use ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation and physical experiment related to control of the ground temperature by bang-bang control theory are discussed in this paper. Comparing the computed results with the results obtained by the experiments and measurements, it is shown that the bang-bang control theory is adaptable for practical use. The basic equation of the ground temperature is discretized by the finite element method in space and the Crank-Nicolson method in time. To obtain the optimal control temperature, the performance function is minimized by the Sakawa-Shindo method.
    Additional Material: 27 Ill.
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  • 23
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    APPLICATION OF k-STEP LANCZOS METHOD TO EXTRACT THE INTERIOR EIGENVALUES OF SKELETAL SYSTEMS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 705-716 
    Details
    ISSN: 0029-5981
    Keywords: free vibration analysis ; eigenvalue problem ; non-linear eigenproblem ; Lanczos method ; finite element method ; interior eigenproblem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Unlike analyses performed to determine structural response to environmental loadings (i.e., wind or earthquake), where only a few of the lowest natural modes are assumed to participate in the overall response, mechanically induced loadings can excite higher-order modes and require solution of the interior eigenvalue problem. In such applications, care must be taken to ensure that the finite element model of the vibrating structure effectively models the higher-order modal response and that the eigensolver used to extract the natural frequencies does not encounter convergence problems due to the close spacing of the interior eigenvalues. This paper formulates and applies an implicitly restarted Lanczos-based eigensolver for computing the natural frequencies of skeletal systems from the interior of the eigenvalue spectrum. This interior eigenvalue problem is formulated using a finite element method which utilizes both the polynomial- and frequency-dependent shape functions in representing beam deformation; thus, the resulting eigenvalue problem is nonlinear, or eigenvalue dependent. Planar frame examples are given which illustrate the effectiveness of the proposed modelling technique and eigensolver.
    Additional Material: 5 Ill.
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    FINITE ELEMENT SOLUTIONS WITH FEEDBACK NETWORK MECHANISM THROUGH DIRECT MINIMIZATION OF ENERGY FUNCTIONALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 867-883 
    Details
    ISSN: 0029-5981
    Keywords: neural network ; feedback neuron ; incompressible viscous flow ; massively parallel computer ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a new algorithm for solving a minimization problem of the functional of a variational principle was proposed by focusing on the state transition process of the interconnected neural network. A new concept of neuron called ‘feedback neuron’ was introduced into the conventional interconnected neural network. This method was readily applied to the finite element analyses of incompressible viscous flows. Furthermore, favourable feature of the neural network for parallel platform was explored on a massively parallel computer AP1000.
    Additional Material: 14 Ill.
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    AN EULEREAN FINITE ELEMENT MODEL FOR PENETRATION IN LAYERED SOIL (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 865-886 
    Details
    ISSN: 0363-9061
    Keywords: finite element method ; large deformation ; cone penetration test ; layered soil ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: An Eulerean large-strain finite element formulation is presented to simulate static soil penetration. The method is an extension of the Updated Lagrangean description to an Eulerean formulation taking into account convection of deformation-history-dependent properties as well as material properties. The strength of the soil is characterized by a non-associated Drucker-Prager criterion which depends on peak and critical friction angles. The model is applied to cone penetration in two-layer systems: (a) clay on sand and (b) sand on clay.
    Additional Material: 15 Ill.
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    AN INTERFACE MODEL TO DESCRIBE VISCOPLASTIC BEHAVIOR (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 231-252 
    Details
    ISSN: 0363-9061
    Keywords: interfaces and joints ; landslides ; viscoplastic behavior ; hierarchical single surface models ; laboratory testing ; calibration ; finite element method ; validations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A constitutive model to describe viscoplastic or time-dependent behaviour of interface materials is presented. Viscoplastic characteristics of the interface material are modeled based on Perzyna's theory of viscoplasticity and the Hierarchical Single Surface (HiSS) series of constitutive models. Experiments performed using a new interface test device to characterize the behaviour of cohesive soil-rock interfaces are described. Procedures to derive model parameters are presented together with validation of the model. Finite element implementation of the interface element is described along with verification of the model with respect to field behaviour of a creeping natural slope.
    Additional Material: 15 Ill.
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    PARAMETER AND VARIANCE ESTIMATION IN GEOTECHNICAL BACKANALYSIS USING PRIOR INFORMATION (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 20 (1996), S. 119-141 
    Details
    ISSN: 0363-9061
    Keywords: inverse analysis ; parameter identification ; underground excavation ; optimization technique ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young's modulus, K0 value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young's modulus and K0 are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage.
    Additional Material: 13 Ill.
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