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  • 1
    Electronic Resource
    Electronic Resource
    A unidimensional convergence test for matrix iterative processes applied to Strapdown Navigation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 115-130 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110112
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  • 2
    Electronic Resource
    Electronic Resource
    A note on an element ordering schemeThis work was supported by S R C Grant B/RG/5549/4 made jointly to Brunel University and Imperial College of Sceience and Technology for research on Finite Element Techniques. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 194-198 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper contains an algorithm for the ordering of elements in the finite element method, which can be utilized in the Non-assembly Method of the author and in the Frontal Solution Method of B. M. Irons.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110120
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  • 3
    Electronic Resource
    Electronic Resource
    Calculation of vibration frequencies by a hybrid element method based on a generalized complementary energy principle (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 231-246 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on a generalized complementary energy principle the derivation of the element matrices is presented for calculation of natural frequencies. The degrees-of-freedom are not defined on nodal points but in an abstract way. No restrictions about the number of interpolation functions in the interior and at the boundaries of the element have been introduced. The exact solution of the discretized element equations leads to the dynamic stiffness matrix while the approximate solution results in a linear eigenvalue problem. Plate bending problems are used to study the convergence of frequencies depending on the degrees of interpolation functions within the element and on its boundaries and on the number of elements.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110203
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  • 4
    Electronic Resource
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    A Block-Stodola eigensolution technique for large algebraic systems with non-symmetrical matrices (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 247-267 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Block-Stodola eigensolution method is presented for large algebraic eigensystems of the form AU = λBU where A is real but non-symmetric. The steps in this method parallel those of a previous technique for the case when both A and B were real and symmetric. The essence of the technique is simultaneous iteration using a group of trial vectors instead of only one vector as is the case in the classical Stodola-Vianello iteration method. The problem is then transformed into a subspace where a direct solution of the reduced algebraic eigenvalue problem is sought. The main advantage is the significant reduction of computational effort in extracting a subset of eigenvalues and corresponding eigenvectors. Theorems from linear algebra serve to underlie the basis of the present technique. Complex eigendata that emerge during iteration can be handled without doubling the size of the problem. Higher order eigenvalue problems are reducible to first order form for which this technique is applicable. The treatment of the quadratic eigenvalue problem illustrates the details of this extension.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110204
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  • 5
    Electronic Resource
    Electronic Resource
    A hybrid crack element for rectilinear anisotropic material (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 377-382 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110211
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  • 6
    Electronic Resource
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    Application of the front solution to two and three-dimensional elastoplastic crack problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 393-395 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110215
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  • 7
    Electronic Resource
    Electronic Resource
    Comment on the paper ‘a finite element solution program for large structures’ (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 404-405 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110219
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  • 8
    Electronic Resource
    Electronic Resource
    A homework exercise in finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We suggest an exercise which illustrates many of the fundamental ideas of finite elements, and is nevertheless easily programmed and quickly solved. It is governed by a partial differential equation on a circular region, but by maintaining symmetry the stiffness matrix becomes small and tridiagonal. The accuracy of linear elements can be studied in detail, and a straightforward extension leads to the eigenvalue problem, elements of higher degree, numerical integration, isoparametric elements, and a simple example in plasticity.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110302
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  • 9
    Electronic Resource
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    Numerical Fourier analysis in the range of higher frequencies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 469-480 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel method is proposed for the numerical computation of Fourier coefficients in the range of higher frequencies for which hitherto no practical method was available. The accuracy of the results obtained by application of this method is discussed, and bounds of a correction term are determined accordingly. An example from the field of Diesel engine research is given, and the computed spectrum is compared with the spectrum recorded by an electronic harmonic analyzer.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110307
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  • 10
    Electronic Resource
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    Least square and Galerkin finite element solution of flow past a flat plate (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 185-190 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110118
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  • 11
    Electronic Resource
    Electronic Resource
    Announcements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 204-207 
    Details
    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.1620110123
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  • 12
    Electronic Resource
    Electronic Resource
    Finite element solutions of the non-self-adjoint convective-dispersion equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 269-287 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element formulations based on the Galerkin and variational principles have been developed for the self-adjoint and non-self-adjoint problems represented respectively by the flow and convective-dispersion equations in the cylindrical polar system of co-ordinates. The formulation based on the variational principle is shown to be restricted to dispersion-dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110205
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  • 13
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    The indirect design of fluid channels using a global variational method with trial functions not satisfying the prescribed boundary conditions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 579-591 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The indirect design problem for compressible fluid flow in a channel determines the physical shape of the channel from the prescribed flow on the channel boundary. In this paper, a global variational method for the solution of this problem is described.The non-linear equations are solved by iteration; at each step of this iteration the solution to the equations (which are now linear) is found by a global variational method. The variational method differs from conventional methods in that the trial function does not satisfy the prescribed boundary conditions, but the method reproduces the conditions on the boundary.Results are presented for various physical quantities associated with the channel.Some comments are made on the extensions of these methods to supersonic flow and to the realistic cascade design problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110314
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  • 14
    Electronic Resource
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    Matrices for scientists and engineers, W. W. Bell (University of Aberdeen), Van Nostrand Reinhold, 1974. £3·95 paperback £7·75 cloth (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 605-605 
    Details
    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.1620110318
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  • 15
    Electronic Resource
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    On computer-aided analytic element analysis and the similarities of tetrahedron elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 611-622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complete analytical analysis of three-dimensional, quadratic displacement tetrahedron elements is presented. The results show that the element stiffness can readily be obtained from the much simpler stiffness matrix of the linear displacement element. Thus, the task of obtaining the matrix of the quadratic displacement element is, in effect, reduced to finding that of the linear displacement element.The analysis has been made possible only by using a symbolic manipulation language (PL/I-FORMAC) on a computer. A rather general program for computer-aided basic element analysis is presented. It seems that the extremely effective tool of symbolic manipulation has hardly been used until now in mechanics.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110402
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  • 16
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    Fuller Obituary on Professor B. Fraeijs de Veubeke (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 407-407 
    Details
    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.1620110221
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  • 17
    Electronic Resource
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    A numerical method for the solution of certain classes of nonlinear Volterra integro-differential and integral equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 431-438 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct numerical method is presented for the solution of classes of non-linear, singular Volterra integral and integro-differential equations of the types where y is the unknown and the Fs and Gs are given but to a large extent arbitrary functions of their arguments. The adaptation of the method to other equations, in particular with different kernels, is immediate.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110304
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  • 18
    Electronic Resource
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    On the elastic plastic initial-boundary value problem and its numerical integration (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 817-832 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An interative approach is proposed for the numerical analysis of elastic-plastic continua. This approach gives after convergence an implicit scheme of integration of the evolution problem, and is concerned with elastic-perfectly plastic materials and with hardening standard materials. Under a generalized assumption of positive hardening, the proof of convergence of the iterative solutions is given. Some numerical examples by the finite element method are also discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110505
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  • 19
    Electronic Resource
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    Elasto-plastic finite element analysis (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 875-881 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An elasto-plastic finite element small displacement procedure to predict the behaviour of structures under cyclic loads is presented. The solution combines incremental procedure with correction for equilibrium and iterative scheme. Applications are made for a rectangular strip and a notched bar under cyclic axial loads. Flow theory of plasticity with either isotropic hardening or kinematic linear hardening is used.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110509
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  • 20
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    A classification and survey of numerical methods for boundary value problems in ordinary differential equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 771-796 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of the paper is a survey and classification of available numerical methods for boundary value problems with an emphasis on two point boundary value problems. In the paper a general two point boundary value problem is stated first and later available numerical methods are classified into five main groups according to their approach in numerical solution. In the next sections of the paper, each of these main groups are described and appropriate subgroups are defined and discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110503
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  • 21
    Electronic Resource
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    An isoparametric Hermitian element for the solution of field problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 945-962 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-dimensional isoparametric Hermitian element is investigated for use in potential field problems with irregular geometry. Nodal degrees-of-freedom are the potential, the gradients in the directions normal and tangential to the element sides, and the twist. In applying the isoparametric principle a simple approximation is used which in general guarantees C1 continuity only at the element corners. The present version is restricted to 90-degree interior angles.The element is applied in the Galerkin solution of the steady-state continuity equation and several examples are presented. It is found that in cases where the potential field is simple but the element is strongly distorted, gradients obtained from the Hermite are not as accurate as those from the Lagrange-type cubic element having the same number of degrees-of-freedom. When the potential field is complex and the distortion is small, the Hermitian gradients are comparable to those of the Lagrange cubic; with increasing distortion they are comparable at the boundaries but less so in the interior. The errors in the potentials themselves are very similar, both elements giving a high degree of accuracy.Since all of its degrees-of-freedom are shared by four elements in the interior of a grid, the Hermite element is approximately 20 per cent more efficient than the Lagrange cubic for all but the smallest grids. Also, since the Hermite uses fewer nodes, data handling is greatly reduced. The element appears to be attractive at least in the area of groundwater flow.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110604
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  • 22
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    Optimization methods applied to hydrodynamic bearing design (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1005-1027 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Optimization techniques are applied to the design of both hydrodynamic journal and tilting pad thrust bearings. Fletcher's adaptation of Davidon's gradient search method is further modified to deal with non-linear constraints in journal bearing design. A form of the Sequential Simplex is used for tilting pad thrust bearings. Penalty functions and variable transformations are used in both cases. Composite objective functions are included and the effect of weighting on each component of the composite function is investigated.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110608
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  • 23
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    Optimum design of laminated fibre composite plates (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 623-640 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for the minimum weight optimum design of laminated fibre composite plates, subject to multiple inplane loading conditions, which includes stiffness, strength and elastic stability constraints. The buckling analysis is based on an equivalent orthotropic plate approach leading to two uncoupled eigenproblems per load condition. Overall computational efficiency is achieved by using constraint deletion techniques in conjunction with Taylor series approximations for the constraints retained. The optimization algorithm used, namely the method of inscribed hyperspheres, is a sequence of linear programs technique which exhibits rapid convergence in this application. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for the fundamental and recurring problem treated.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110403
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  • 24
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    Error analysis of penalty function techniques for constraint definition in linear algebraic systems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 709-728 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The penalty function approach has been recently formalized as a general technique for adjoining constraint conditions to algebraic equation systems resulting from variational discretization of boundary value problems by finite difference or finite element techniques. This paper studies the numerical behaviour of the penalty function method for the special case of individual equation constraints imposed on a symmetric system of linear algebraic equations. Constraint representation and computational roundoff error components are distinguished and asymptotically characterized in terms of the penalty function weight coefficients. On the basis of this study, practical rules for the automatic assignment of values to those coefficients within the linear equation solver are proposed. Numerical problems encountered in the case of more general constraints are briefly discussed, and procedures for circumventing such difficulties are suggested.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110408
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  • 25
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    Application of optimization and finite element methods to a cracking problem in timber (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 756-758 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110412
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  • 26
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    Announcements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 766-767 
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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.1620110415
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  • 27
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    Erratum (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 770-770 
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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.1620110502
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  • 28
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    Superposition method of finite element and analytical solutions for transient creep analysis (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1107-1115 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non-linear and/or time-dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.
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    An introduction to the mathematical theory of finite elements, J. T. Oden and J. N. Reddy, Wiley, New York, 1976. No. of pages 429. Price $32·00, £17·50 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1198-1198 
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    ISSN: 0029-5981
    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/nme.1620110715
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    Creep analysis of reinforced and prestressed concrete structures under non-uniform temperature distributions, using elastic solutions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 883-895 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The analysis of stresses and deformations in concrete structures subjected to temperature gradients is described. As a result of the spatial variation of temperature, the creep compliance is a function of position. Previous work has shown that the constitutive equations for concrete creep can be expressed in a form which is invariable although ageing is included in the analysis. Thus viscoelastic methods can be used and correspondence principles can be developed; emphasis is placed in the present work on those which are based on the Laplace transform. A particular form is described, in which replacement of the elastic modulus by a function of the transformed creep compliance gives transformed values of stress; these values are easily obtained numerically by the finite element method using elastic analyses. The transformed values of stress are then expressed as approximate functions of the transformed creep compliance; inversion of the ensuing functions gives the stress as an approximate function of time. Two applications are given; the first considers a simple axially loaded column with reinforcement and the second deals with a thick cylinder subjected to a temperature gradient.
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    Discussion of ‘Finite element residual schemes for unconfined flow’ by Chandrakant S. DesaiInt. J. num. Meth. Engng, 10, 1415-1418 (1976). (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 908-910 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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    A finite element free boundary formulation for the problem of multiphase heat conduction (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 933-943 
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    Keywords: Engineering ; Engineering General
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    Notes: The problem of heat conduction in a multiphase medium is a free boundary problem in which the free boundary is the phase transition line. The solution to this problem is highly irregular in that the temperature gradient is discontinuous at the free boundary. Two-dimensional, discontinuous, space-time finite elements are introduced to obtain a finite element, free boundary formulation for this problem. The jump in heat flux and position of the phase transition line become dependent variables in the finite element model. The resulting models give accurate results while allowing the calculation of free boundary problems with a fixed finite element mesh.
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    Numerical analysis of flow with or without wake past a symmetric two-dimensional profile without incidence (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 975-993 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Formulated in the hodograph plane, the bi-dimensional flow of a perfect fluid past a symmetric body leads to an elliptic variational inequality. By this way we show the existence of a one-parameter family of solutions. Furthermore the study gives us a simple and effective method for calculating the solutions. The results obtained with some typical profiles are given and compared with previous works.
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    Static stability of plates using fully conforming element (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 995-1003 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper the geometric stiffness matrices of a 12 degree-of-freedom rectangular element based on a fully compatible displacement field are developed for the first time and used to solve the elastic stability problem of rectangular plates under combined in-plane forces.The rapid convergence of buckling solutions based on the derived geometric stiffness matrices is demonstrated for plates with various boundary and loading conditions. Comparison of results shows that the present conforming element gives in all cases better results than the well known 12 degree-of-freedom non-conforming rectangular element.
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    An alternate finite difference operator for plates of variable stiffness (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1044-1048 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite difference approximation for the equilibrium equation of a thin, laterally loaded, elastic plate of variable stiffness is developed; it uses plate stiffnesses at node points and at points midway between the nodes of the rectangular grids. Displacement and moment results using this operator and an alternate one are compared.
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    Call for papers (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1056-1056 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Compact computation of natural frequencies and buckling loads for plane frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1067-1081 
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    Keywords: Engineering ; Engineering General
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    Notes: Existing theory is assembled to give a method which needs only the core of a mini-computer to calculate the eigenvalues of large rigidly jointed plane frames with certainty, the eigenvalues being natural frequencies and critical load factors in free vibration and buckling problems, respectively. The method is illustrated by annotated listings of vibration and buckling programs, each involving under two hundred Fortran statements and with low number storage requirements (see Table I). The use of the programs as ‘black boxes’ is fully explained, with illustrative examples.The member theory used is the ‘exact’ classical Bernoulli-Euler uniform member theory. Possible applications include: evaluation of answers from approximate methods; calculation of critical loads for substitution in the modified Merchant-Rankine formula to estimate collapse loads of frames; and calculation of shifts in natural frequencies caused by structural damage, in connection with structural integrity monitoring of inaccessible structures.
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    A finite element convergence study for accelerating flow problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1155-1174 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The convergence properties of several non-linear solution procedures were examined with respect to the accelerated flow of a fluid in a converging channel (the Hamel problem), using two different finite element computer programs with different elemental construction. The Reynolds number varied from that for creeping flow to 1088 without exceeding the radius of convergence. Special attention was given to the successive substitution and Newton-Raphson solution algorithms, with a significant advantage in rate of convergence noted for the latter.
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    An unconditionally stable explicit algorithm for structural dynamics (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1579-1592 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents an unconditionally stable explicit algorithm for the direct integration of the structural dynamic equations of motion. The algorithm is restricted to a diagonal mass matrix and positive definite symmetric stiffness and damping matrices. The algorithm is based on splitting the stiffness and damping matrices into strictly lower and upper trangular form. Unconditional stability is proven, but only for the undamped case and a completely symmetric splitting of the stiffness matrix. An alternate splitting method is also presented and numerical examples indicate superior performance over the symmetric splitting, but only a conditional stability. A spring-mass-dashpot model is used to illustrate the algorithm.
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    Differentiation and integration using Bernstein's polynomials (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1627-1630 
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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/nme.1620111012
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    Newtonian die swell evaluation for axisymmetric tube exits using a finite element method (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1621-1626 
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    Keywords: Engineering ; Engineering General
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    Notes: Using a finite element method, a value of 13.2 per cent is obtained for the die swell of a highly-viscous Newtonian fluid flowing at very low Reynolds number from a circular tube of constant radius. The same method is then used to obtain die swell values for a variety of axisymmetric tube exits. It is found that, in general, conical constrictions at or near the tube exit result in a decrease in die swell, while conical expansions increase the die swell.
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    The steady state response of geometrically non-linear shallow arches (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1261-1269 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The non-linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non-linear differential equations.These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree-of-freedom Duffing's equation with a quadratic term. The non-symmetric amplitude-frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.
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    Temperature load on thick curved shell elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1329-1333 
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    Keywords: Engineering ; Engineering General
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    Notes: Temperature load on a shell is usually represented as initial strains in the tangent plane directions of the shell, since strains in shell surface normal directions are neglected. It is shown, however, that this simplification may give rise to significant errors for thick curved shell elements. A procedure to overcome this problem is presented. In particular the eight-node subparametric thick shell element is considered.
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    A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1879-1892 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the non-linear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C0-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
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    Closed form elastic-plastic stiffness matrix for axisymmetric finite elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 59-65 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This note presents the closed form equations for the stiffness terms in the elastic-plastic stiffness matrix for axisymmetric finite elements. The element considered is a triangular ring element characterized by linear displacement relationships and an averaged state of stress. The physical law is modelled by the incremental theory of plasticity utilizing the Prandtl-Reuss flow rule and von-Mises Yield Criterion. Results are presented comparing stiffness terms as computed by numerical integration to those computed from the closed form equations. Significant errors in stiffness terms arising from numerical integration are observed for axisymmetric elements located near the line of axial symmetry as a result of the logarithmic nature of some of the stiffness terms.
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    Certain properties of numerical schemes used to solve the blade-to-blade flow problem (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 85-92 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The compressible potential flow on a blade-to-blade surface of a turbomachine is analysed using the Thomas algorithm. The numerical properties of resulting non-linear simultaneous equations are studied with respect to grid aspect ratios and convergence. The heuristic approach has established which are the important factors that affect the flow solution in typical blade-to-blade configurations.
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    Modification to the Suhara-Fukuda method of network generation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 93-99 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This note describes improvements to the Suhara-Fukuda method for generating a triangular finite element network. These are based on the use of a node generation procedure which distributes nodes is a regular pattern across the network area and is sufficiently flexible to permit any variation in element density. Because of the regular node distribution, poorly shaped elements will not arise and so the procedure for connecting the nodes to form elements can be simplified. Examples of networks generaed in this way are given.
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    Discussion of a paper by E. O. FrindInt. J. num. Meth. Engng, 945-962 (1977). (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 183-185 
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    Notes: In a recent paper, Dr. Frind has formulated a two-dimensional isoparametric finite element based upon the Hermite bicubic interpolation scheme. The present discussion focuses upon certain simplifications in the derivation which appear to have diminished the accuracy of the resulting element, and suggests a simpler approach to the element formulation. This author agrees strongly with Dr. Frind's recommendation of the Hermite parametric element as an efficient and useful tool for general field problems; the present comments are offered to point out that, in fact, the accuracy comparisons presented by Dr. Frind are biased against the Hermite finite element.
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    Masthead (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A least squares finite element approach to unsteady gas dynamics (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
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    Finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 47-57 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A viscous approximation for steady creeping flow is extended to include the effect of elastic strains. Two examples are presented which illustrate both the method and the need for including elastic strains in the analysis of steady-state visco-plastic flows.
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    A finite element formulation for large elastic-plastic deformation analysis of polycrystals and some numerical considerations on polycrystalline plasticity (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 101-114 
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    Notes: A finite element formulation for large elasto-plastic deformation of polycrystalline materials is proposed in incremental form. The effect of rotation of crystal axes besides usual element rotaion is taken into account. Some numerical considerations on polycrystalline plasticity (i.e. stress-strain curves for several proportional loadings, effect of change of loading path on stress-strain curve, subsequent yield loci for uniaxial and equi-biaxial loadings and so forth) are given for the case of small deformation by using a plate model which consists of 121 square FCC crystals.
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    Addendum to the paper ‘finite element analysis of steady-state elasto-visco-plastic flow by the initial stress-rate method’ (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 382-383 
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    Keywords: Engineering ; Engineering General
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    URL: http://dx.doi.org/10.1002/nme.1620120216
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    A 2nd order numerical method for laminar flow at moderate to high Reynolds numbers: Entrance flow in a duct (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 405-414 
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    Keywords: Engineering ; Engineering General
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    On least squares approximations to indefinite problems of the mixed type (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 453-469 
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    Notes: A least squares method is presented for computing approximate solutions of indefinite partial differential equations of the mixed type such as those that arise in connection with transonic flutter analysis. The mehod retains the advantages of finite difference schemes namely simplicity and sparsity of the resulting matrix system. However, it offers some great advantages over finite difference schemes. First, the method is insensitive to the value of the forcing frequency i.e., the resulting matrix system is always symmetric and positive definite,. As a result, iterative methods may be successfully employed to solve the matrix system, thus taking full advantage of the sparsity. Furthermore, the method is insensitive to the type of the partial differential equation, i.e., the computational algorithm is the same in elliptic and hyperbolic regions. In this work the method is formulated and numerical results for model problems are presented. Some theoretical aspects of least squares approximations are also discussed.
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    Finite element methods for an optimal steady-state control problem (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1375-1382 
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    Notes: An optimal steady-state control problem governed by an elliptic state equation is solved by several finite element methods. Finite element discretizations are applied to different variational formulations of the problem yielding accurate numerical results as compared with the given analytical solution. It is sated that, for minimum computational effort and high accuracy, ‘mixed’ finite elements requiring only C° continuity, and approximating the control and state functions simultaneously are better suited to similar ‘fourth order’ problems.
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    Sensitivity Of matrix eigenvaluesThis work was done while both authors were summer visitors to Argonne National Laboratory in connection with the LINPACK project. (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1367-1373 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A recent paper by Donald Gignac describes some difficulties with a certain matrix eigenvalue problem. This paper shows that the difficulties result from the naturue of the matrix itself. Quantities called condition numbers, which measure the sensitivity of the eigenvalues, are computed, and numerical results given.
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    Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1383-1397 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The boundary-integral equation medthod is particularly well suited for solution of stress concentration and elastic fracture mechanics problems. The method was not previously applicable to anisotropic three dimensional problems because no efficient technique existed for calculation of the required point load solution for an infinite body. A technique has been developed to evaluate numerically the anisotropic point load soultions, and used to generate data bases for various materials. An intrpolation technique is used to evaluate the point load solutions efficiently within a higher order boundary-intgral equation code. The effectiveness of the technique is verified by solution of problems involving both uniaxial stress states and stress concentrations.
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    Numerical fourier transformation: Singularity expansions and product integration (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1473-1477 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    ‘Potential energy with iterative correction’… or deterioration, that is the question (Reply by Authors to M. Crisfield's Discussion1 of ‘A Critical Assessment of the simplified Hybrid Displacement Method’2) (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1461-1472 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    A frontal-based solver for frequency analysis (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1659-1666 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Lumped mass matrices with non-zero inertia for general shell and axisymmetric shell elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1635-1650 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A diagonal lumped mas formulation with non-zero inertia terms is presented for Ahmad's general shell element. The effect of co-ordinate transformation of the mas matrix is demonstrated. Due to arbitray co-ordinate transformation on nodal variables, the diagonal lumped mas matrix becomes a banded matrix of half bandwidth three. It is shown that with some approximations this matrix can be made diagnoal without effecting the results appreciably. Numerical examples are presented to illustrate the accuracy of the formulation. Similar lumped mass matrix formulation is also given for axisymmetric shell elements.
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    A systematic procedure for generating useful conformal mappings (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1651-1657 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Procedure is presented for generating a class of conformal mappings useful in the formulation of finite-difference problems involving curved boundaries. The method provides a systematic approach that is capable, in principle, of reducing the geometry to a nearly-rectangular domain for a wide variety of partical problems. The introduction of sheared co-ordinates in this computational domain then provides for solution of the problem in a nearly-orthogonal (in fact, nearly-conformal) co-ordinate system, with its boundaries corresponding to co-ordinate lines. The method is based upon the Schwarz-Christoffel transformation and is quite simple to apply. Several examples illustrating the types of geometries which can be treated in this manner are presented.
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    Thin plate semiloof element for structural analysis-including stability and natural vibrations (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1667-1676 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a thin plate element formulated along parallel lines to the general three-dimensional Semiloof shell element. This plate version possesses only one half of the total number of degrees-of-freedom of the shell element and has the advantqage that the formulation of the strains and other terms is very much simplified. The element is first assessed in static situations and then its performance in the solution of eigenvalue problems is considered.
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    Central difference approximations to the heat transport equation (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1697-1704 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper analyses the oscillatory nature of central difference approximations to the heat transport equation when convection is the important mechanism of heat transport. The effects of three different boundary conditions, various heat source profiles, the Peclet Number and the parity of the number of meshes on the amplitudes of these oscillations are described. A boundary condition is presented which suppresses the oscillations to insignificant amplitudes in the one-dimensional situation.
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    Upwinding of high order Galerkin methods in conduction-convection problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1764-1771 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Upwinded parabolic and cubic elements are derived on a uniform grid of size h for the finite element Galerkin method applied to the solution of the model conduction-convection problem εu″  -  Ku′ = 0, ε, K 〉 0, subject to the boundary conditions u(0) = 1, u (1) = 0. Extension of the results to more complicated problems is indicated. Finally numerical results are given comparing some of the methods derived for a range of L(=Kh/2ε), the grid Peclet number.
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    Hybrid stress finite element model for non-linear shell problems (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1819-1839 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper describes a hybrid stress finite element formulation for geometrically non-linear analysis of thin shell structures. The element properties are derived from an incremental form of Hellinger-Reissner's variational principle in which all quantities are referred to the current configuration of the shell. From this multi-field variational principle, a hybrid stress finite element model is derived using standard matrix notation. Very simple flat triangular and quadrilateral elements are employed in the present study. The resulting non-linear equations are solved by applying the load in finite increments and restoring equilibrium by Newton-Raphson iteratioin. Numerical examples presented in the paper include complete snap-through buckling of cylindrical and spherical shells. It turns out that the present procedure is computationally efficient and accurate for non-linear shell problems of high complexity.
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    On thick superparametric shell element (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1883-1889 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    Improved three point integration schemes for triangular finite elements (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1890-1896 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Symmetric three point quadrature schemes are at present available for triangles for exact integration of polynomials of degree 2. There are other possible symmetries, which provide higher accuracies. Exact integration of polynomials of a higher degree is possible. General formulations are made and a set of three integration points for improved accuracy is given.
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    Announcements (1978)
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    International Journal for Numerical Methods in Engineering 12 (1978), S. 1898-1900 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Non-linear ordinary differential equations, D. W. Jordan and P. Smith, Oxford University Press (part of Oxford Applied Mathematics and Computing Science Series), 1977. No. of pages: 360. Price:£6.50 (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1897-1898 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Structural optimization: A review and some recommendations (1978)
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    International Journal for Numerical Methods in Engineering 13 (1978), S. 203-228 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.
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    Masthead (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Discrete transfinite mappings for the description and meshing of three-dimensional surfaces using interactive computer graphics (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 41-66 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A system for describing three-dimensional surfaces in a form suitable for finite element analysis is described. The system makes extensive use of real-time interactive computer graphics techniques for both input and display. Discrete transfinite mappings are used as the mathematical basis for the surface representation. The mathematical basis and the reasons for choosing this form of representation are discussed. Explicit forms of the mappings based on Lagrange polynomial interpolation functions are presented. Finally, the interactive graphics procedures for defining finite element meshes are described.
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    Investigation of highly accurate integration formulae for transient heat conduction analysis using the conjugate gradient method (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 99-109 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two highly accurate implicit Padé approximations to the transient heat conduction equation are investigated using the conjugate gradient method to solve, for the temperatures. The accuracy and stability of the approximations are discussed and numerical examples are presented showing the relative performance. Comparisons with the Crank-Nicolson method are also presented.
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    Obituary (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. i 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Reduced integration and the shear-flexible beam element (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 195-210 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A clearer insight into the ‘shear locking’ phenomenon, which appears in the development of C0 continuous element using shear-flexible or penalty type formulations, is obtained by a careful study of the Timoshenko beam element. When a penalty type argument is used to degenerate thick elements to thin elements, the various approximations of the shear related energy terms act as different types of constraints and, depending on the formulation, two types of constraints which are classified as true or spurious may emerge. The spurious constraints, where they exist, are responsible for the ‘shear locking’ phenomenon, and its manifestation and elimination is demonstrated in a very simple example. The source of difficulty is shown to be the mathematical operations involved in the various shape function definitions and subsequent integration of functionals. It is seen that formulations that ensure only true constraints in the extreme penalty limit cases display far superior performance in the thick element situation as well, and thus guidelines for the development of efficient elements are drawn. A similar type of behaviour is observed in a shallow curved beam element and here ‘inplane locking’ can be eliminated by selective integration to obtain an improved curved beam element. However, ‘inplane locking’ does not cause a spurious constraint as the error quickly vanishes with the reduction of element size for a reasonable radius of curvature conforming with shallow shell theory.
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    Announcements (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 321-322 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    On the rates of convergence of the finite element method (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 323-341 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The rate of convergence of the finite element method is a function of the strategy by which the number of degrees-of-freedom are increased. Alternative stragegies are examined in the light of recent theoretical results and computational experience.
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    An ‘upwind’ finite element method via numerical intergration (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 381-396 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Upwind finite element schemes remove spurious oscillations that occur in the solution of diffusion convection equations. Up to now these schemes lose part of their accuracy when the Peclet is large. As an improvement, it is proposed to move the integration nodes along the ‘streamlines’ before evaluating the elementary convection matrices. The displacements of the nodes along the streamlines, which are one-dimensional manifolds, are calculated analogously to well-known one-dimensional formulae. The last section of this paper illustrates this new method with the help of four examples which show its validity.
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    A warning against misuse of quarter-point elements (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 314-320 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Quarter-point elements are used very frequently for fracture mechanics computations, because the quarter-point technique yields the required singular interpolation without any modification to existing software. This advantage is particularly significant for three-dimensional stress intensity factor computations because of the difficulty of implementing other techniques. However, in practical 3-D applications, the crack front is usually curved, and this note proves that a crack front distortion leads to a negative Jacobian in the region surrounding the crack front. The numerical difficulties to be expected depend on the aspect ratio of the elements.
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    A smoothing technique for reduced integration penalty methods in contact problems (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 343-350 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a smoothing technique to the oscillated contact pressure obtained by penalty methods for a class of unilateral contact problems in linear elasticity. The main result is to show that the smoothed contact pressure satisfies the so-called Babuska-Brezzi condition which dominates the convergence of the penalty method. One numerical example is described.
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    Use of screw translational symmetry for the vibration analysis of structures (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 435-444 
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    Keywords: Engineering ; Engineering General
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    Notes: A method for the exploitation of screw translation symmetry for the vibration analysis of structures is presented. The method is capable of providing significant computational economies over the use of the lower axial translational symmetry of such structures.
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    Discussion on a paper by Y-T. Leung (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 629-630 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Announcement (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 632-634 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Three-dimensional shape optimization (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 661-673 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Optimal structural desingn generally deals with frame or shell structures where the optimization is limited to resizing of structural members to obtain optimum cross-sections or thicknesses. Shape optimization solves another class of problems involving continuous structural components where the optimum shape (the shape of the boundaries and the surfaces of the components) is determined. This report describes shape optimization of three-dimensional structural components. The finite element method of analysis is used employing the 20-noded isoparametric element. The objective function, mass, is minimized by the direct use of nonlinear mathematical programming, specifically the feasible direction method. Numerical shape representation and the selection of design variables are the most important aspects of the problem. The problem is addressed from a practical standpoint and techniques are presented to minimize the number of desingn variables. Isoparametric representation of the surfaces and the numerical superposition of shapes are discussed. These techniques are compared and demonstrated on simple cantilever beams and their minimum mass designs are obtained. In one example, the optimum shape of a non-uniform cross-sectinal beam is obtained under stress constraint. The final design has a crosssectional shape varying over the length of the beam which could not be predicted using the bending theory of beams. One major difficulty encountered in some problems was that the shape changes during the optimization process may require a change in the finite element mesh because the initial configuration of the finite element mesh may result in very distorted elements for the new shape. The analyis with a mesh containing distorted elements may not be possible at all or the results of the analysis may be inaccurate.
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    Some vector expansion functions for quadrilateral and triangular domains (1982)
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    International Journal for Numerical Methods in Engineering 18 (1982), S. 727-735 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Vector functions having a constant or zero divergence over a quadrilateral domain are derived using a parametric co-ordinate formulation. Expansion functions with a constant curl, defined over parallelograms and triangles, which can be used in moments-based investigations of electromagnetic wave interactions with surfaces and apertures, are then obtained. Finally, two basis functions, which have appeared in the literature and have been used to solve field problems associated with rectangular apertures and arbitrary surfaces, are identified as special cases of these expansion functions.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620180508
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    Plastic analysis of torsion of a prismatic beam (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 927-944 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element formulation for stress analysis of a twisting beam is developed. The formulation is effective for a prismatic beam with solid section as well as a thin-walled beam, and can be applied both to a pure-torsion problem and a warping-torsion problem. The formulation is of a great advantage to an elastic-plastic torsion problem. The formulation does not stand on the assumption of a thin-walled structure, and therefore torsional rigidity of the section can be evaluated exactly without using the so-called Saint-Venant's torsional constant. Torsional rigidity is, in this paper, evaluated directly by a warping function of the section. Warping function is evaluated numerically due to shape of the section, due to progress of plastic region and due to effect of finite displacement (finite rotation, small strain). Pure-torsion and warping-torsion of a rectangular beam and an H-beam, which have an elastic-plastic material property, are analysed, and the extension to the finite displacement problem is discussed. Many numerical examples are provided in order to check the accuracy of the formulation.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620180609
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    Announcements (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 955-957 
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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.1620180614
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    Static analysis of shallow shells of arbitrary shape - a new approach (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 967-979 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient and economical numerical technique for the analysis of shallow shells-of arbitrary shape is presented. The technique is based upon the method of constant-deflection contours combined with the well-known finite element method. In the proposed method the elemental stiffness matrix is derived from a system of two consistent partial differential equations for two scalar functions using Galerkin's method. Several representative examples are included to indicate the effectiveness of the method.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620180703
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    A block equation solver for large unsymmetric matrices arising in the boundary integral equation method (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 997-1017 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented. The solver uses Gaussian elimination. The advantages of the solver over many existing eliminational or iterational methods are that it ignores many of the large groups of zeros that occur in piecewise homogeneous work, and also restrains growth of the number of non-zero matrix entries. Memory requirements and computation times therefore are reduced for many piecewise homogeneous problems.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620180705
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    Universal finite element matrices for tetrahedra (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1055-1061 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods are described for forming element matrices for a wide variety of operators on tetrahedral finite elements, in a manner similar to that previously employed for line segments and triangles. This technique models the differentiation and product-embedding operators as rectangular matrices, and produces finite element matrices by replacing all required analytic operations by their finite matrix analogues. The method is illustrated by deriving the conventional matrix representation for Laplace's equation. Computer programs are available, which generate universal finite element matrices for use in various applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180709
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    The optimum size of quarter-point crack tip elements (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1101-1103 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Ingraffea and Manu1 and Lynn and Ingraffea2 have shown that the size of the quarter-point elements can affect the computed elastic stress intensity factor. The nature of the effect is such that, all other details remaining constant, there is a particular crack tip element size which minimizes the error in the computed stress intensity factor. Here, size of element means the radial edge length. The reasons for this size dependence are discussed below. It will be seen that the discussion is in terms of the need to simultaneously represent the singular and finite stress terms in a given problem. The discussion has relevance to other formulations of crack tip elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180713
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    Another kind of numerical instabilities of the integral approach to the interior boundary-value problem for the two-dimensional Helmholtz equation (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1115-1130 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a previous paper it has been proved by the author that the integral equations arising from the application of Green's formula to the Helmholtz equation in a limited domain can show a certain type of numerical instability, if a real Green's function is used. It has been also proved that such instabilities cannot arise if a complex Green's function is employed.However, it has been found in this latter case also that numerical instabilities can occur. This has been proved and thoroughly analysed for a circular domain, and a technique of avoiding these instabilities has been devised.Furthermore, when this technique is followed, very accurate results can be obtained, regardless of wavenumber used. Thus, only three or four segments are sufficient to describe a wavelength, contrary to what until now has been obtained, i.e. that at least six segments are always necessary. This last result has been shown to be valid also for geometries other than the circular one.
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    URL: http://dx.doi.org/10.1002/nme.1620180802
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    Yale sparse matrix package I: The symmetric codes (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1145-1151 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180804
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    Second-order design sensitivity analysis of mechanical system dynamics (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1699-1717 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Dependence of dynamic response of nonlinear mechanical systems on design variables is analysed. An adjoint variable method is used to derive first- and second-order derivatives of measures of dynamic response with respect to design variables. A computational algorithm is presented for numerical calculation of first and second design derivatives. A simple oscillator example is solved analytically and by the adjoint variable method, with identical results. A burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically. It is shown that quadratic appriximations of dynamic response, using results of second-order design sensitivity analysis, can be substantially better than conventional linear approximations.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620181109
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    Engineering applications of computational hydraulics, Volume 1, ‘Homage to Alexandre preissmann’, edited by M. B. Abbott and J. A. Cunge, Pitman. No. of pages: 262. Price: £27.50. ISBN 0 273 08512 3 (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1739-1739 
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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.1620181113
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    Masthead (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982) 
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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.1620181201
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    Considerations of core storage arising from the finite element analysis of radiation diffusion-transport benchmark problems (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1745-1764 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Problems involving the diffusion and transport (angular dependence considered) of neutron radiation are frequently encountered in radiation physics and nuclear engineering. Neutron diffusion problems require substantial computer storage arising from the energy and spatial dependence, while in the case of transport problems the angular dependence of the neutron flux and of the neutron scattering process gives rise to a further considerable increase in storage. In the present work, a method has been developed which greatly eases the bandwidth problem in the solution of large systems of linear equations and algorithms have been developed to assemble and solve such systems of equations in one and two dimensions. The formalism used is the variational method and, for simplicity, linear interpolating functions have been used to derive a symmetric banded system of equations. Finite element algorithms have been implemented in the codes FEED1 and FEED2, which treat one and two space dimensions, respectively. Three benchmark problems are analysed in this paper and results are compared with finite difference discrete ordinate method solutions. It is shown that the finite element method provides fast and accurate solutions to neutron diffusion and transport problems.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620181202
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    Numerical operational methods for time-dependent linear problems (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1829-1854 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general and systematic discussion on the use of the operational method of Laplace transform for numerically solving complex time-dependent linear problems is presented. Application of Laplace transform with respect to time on the governing differential equations as well as the boundary and initial conditions of the problem reduces it to one independent of time, which is solved in the transform domain by any convenient numerical technique, such as the finite element method, the finite difference method or the boundary integral equation method. Finally, the time domain solution is obtained by a numerical inversion of the transformed solution. Eight existing methods of numerical inversion of the Laplace transform are systematically discussed with respect to their use, range of applicability, accuracy and computational efficiency on the basis of some framework vibration problems. Other applications of the Laplace transform method in conjunction with the finite element method or the boundary integral equation method in the areas of earthquake dynamic response of frameworks, thermaliy induced beam vibrations, forced vibrations of cylindrical shells, dynamic stress concentrations around holes in plates and viscoelastic stress analysis are also briefly described to demonstrate the generality and advantages of the method against other known methods.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620181207
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