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  • 1
    Electronic Resource
    Electronic Resource
    Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 85-98 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Triangular and prismatic quadratic isoparametric elements, formed by collapsing one side and placing the mid-side node near the crack tip at the quarter point, are shown to embody the (1/√r) singularity of elastic fracture mechanics and the (1/r) singularity of perfect plasticity. The procedure of performing the fracture analysis for the case of small scale yielding is discussed, and the finite element results are compared with theoretical results.The proposed elements have wide application in the fracture analysis of structures where ductile fracture is investigated. They permit a determination of the relationship between crack tip field parameters, loading, and geometry. And for a given fracture criterion can be applied to the prediction of fracture in structures such as pressure vessels under in service conditions.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110109
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  • 2
    Electronic Resource
    Electronic Resource
    Solution of a complex quadratic eigenvalue problem (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 99-106 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A complex quadratic eigenvalue problem of order n (n = 20, 30, 40,…) encountered in an investigation of pipe flow was reduced to that of computing the eigenvalues of either a real or a complex matrix of order 2n, depending on the linearization technique used. To get satisfactory results using the CDC 6000 series computer, double-precision versions of certain widely used and highly regarded eigenvalue subroutines were required. Although the modified subroutines used for the real matrix computations required less core than those used for the complex matrix, the calculation time was not significantly faster than that for the complex matrix. The use of ‘balancing’ subroutines merits further investigation.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110110
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  • 3
    Electronic Resource
    Electronic Resource
    Integration of triangular finite elements containing corrective rational functions (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 107-114 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Rational corrective functions are often supplemented to complete polynomials in order to create conforming triangular finite elements for plate bending. Although such elements containing complete polynomials of degree 3 or 4 have long been known, conforming triangular elements for plate bending, which contain complete polynomials of arbitrary degree p ≤ 5 and new corrective rational functions, have been given only recently.Integration of rational functions usually requires numerical quadrature. It is shown here that these new corrective rational functions fall into two classes. For those in one class, explicit closed form integration formulas are available. For those in the other class, integration can be performed very efficiently by summing series whose general term is O(kd) for large k, where d ≤ 5. These formulas also apply to the older third and fourth order elements.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110111
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  • 4
    Electronic Resource
    Electronic Resource
    An ‘upwind’ finite element scheme for two-dimensional convective transport equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 131-143 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110113
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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    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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  • 9
    Electronic Resource
    Electronic Resource
    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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  • 10
    Electronic Resource
    Electronic Resource
    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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  • 11
    Electronic Resource
    Electronic Resource
    An attenuation-free upwind difference formula for analogue computation of charge flow in semiconductorsThis work was supported by GEC Telecommunications Limited. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 439-445 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first order partial differential equations of charge flow are commonly differenced in the space co-ordinate, with a view to analogue computation of the resulting ordinary differential equations in time. Defects of orthodox difference formulae are identified. In particular: (a) reversed waves and stability problems arise from central differences and (b) first order errors and a ‘pseudo-viscous’ dispersion effect with accompanying false attenuation results from upwind differences. These difficulties are particularly serious in view of the coarse differencing required for practical analogue computation. A much superior formula is presented which is entirely free of attenuation and is easily implemented. Various other desirable features are reported.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110305
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  • 12
    Electronic Resource
    Electronic Resource
    A mathematical programming method for the inelastic analysis of reinforced concrete frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1137-1154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110709
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  • 13
    Electronic Resource
    Electronic Resource
    Drying-induced stresses in porous bodies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1175-1184 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110711
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  • 14
    Electronic Resource
    Electronic Resource
    Nodal grafting for crack propagation studies (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1185-1187 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, efficient method for propagating cracks through a finite element mesh is presented: nodes, borrowed from other points in the mesh, are ‘grafted’ along the advancing crack front. The method requires neither an increase in bandwidth nor a mesh regeneration. It can be easily implemented in any existing program using iso(sub)parametric elements of at least quadratic order.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110712
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  • 15
    Electronic Resource
    Electronic Resource
    A heuristic for root isolationThis work was supported by the National Science Foundation under grant ENG75-10234. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 598-603 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A heuristic for isolating the real roots of an equation involving a continuous function over a specified region is presented. Root isolation strategies are well known for polynomial and rational functions; however, there have been no really effective root isolation strategies for transcendental functions. For a transcendental function and a given interval, there has been no way to decide the existence of roots within the interval unless the function changed sign at the endpoints or unless evaluations were performed within the interval. This paper presents a new decision procedure using only interval endpoints. The methodology developed does not guarantee to detect real roots in an interval; however, the technique will effectively indicate real roots in a given interval unless the behaviour of the function is quite erratic.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110316
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  • 16
    Electronic Resource
    Electronic Resource
    Comment on ‘optimal stress locations in finite element models’ (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 604-604 
    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.1620110317
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  • 17
    Electronic Resource
    Electronic Resource
    Optimization of non-unimodal systems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1235-1250 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two direct search algorithms for the optimization of non-unimodal systems are presented. One method is interior in nature by using boundary relaxation with pseudo one-dimensional search in the feasible region; the other one is an exterior method which allows the violation of constraints followed by the use of a penalty function to drive the search back into the feasible region. These two methods are usually capable of leaving local optima to reach a better solution if such exists. The application of the proposed approaches to several non-unimodal systems shows that they are better than the existing methods. The proposed methods are also attractive because of the ease of programming and the high probability of reaching the global optimum.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110805
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  • 18
    Electronic Resource
    Electronic Resource
    Computer program for solution of large, sparse, unsymmetric systems of linear equations (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1251-1259 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program is presented for in-core solution of a large, sparse, unsymmetric, unbanded system of linear equations. The program employs two partially packed arrays (one for storing non-zero elements, and one for column identifications). Used as the pivotal row is the row with the minimum number of non-zero elements. To avoid instability, the pivot is the largest absolute element in the pivotal row. The method was tested on a system of equations encountered in field application of the three-dimensional Galerkin finite element solution of flow and mass transport through porous media. Performance is compared with that of available alternatives.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110806
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  • 19
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110807
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  • 20
    Electronic Resource
    Electronic Resource
    A hybrid stiffness matrix for orthotropic sandwich plates with thick faces (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1291-1306 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A stiffness matrix is derived for a rectangular orthotropic sandwich plate element with thick faces by the assumed stress hybrid approach.It will be demonstrated that an independent polynomial can be used for the internal forces of the sandwich plate by the membrane theory (assumption of thin faces) and also for the additional moments and shear forces of the faces.The boundary displacements are approached solutions of the homogeneous differential equation of a sandwich beam.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110809
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  • 21
    Electronic Resource
    Electronic Resource
    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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110811
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  • 22
    Electronic Resource
    Electronic Resource
    A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1340-1342 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation. By using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110813
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  • 23
    Electronic Resource
    Electronic Resource
    Announcement & call for papers (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1344-1344 
    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.1620110816
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  • 24
    Electronic Resource
    Electronic Resource
    Substructured macro elements based on locally blended interpolation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1405-1421 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we describe a new class of locally refined macro finite elements which are especially amenable to the use of substructuring techniques for the efficient solution of the resulting idealization. The tools and guidelines illustrated by the examples of modelling crack tips, point load singularities and singularities at re-entrant corners should enable an analyst to construct other such blended macro elements specifically tailored to his particular class of problems. The use of such substructured macro elements in finite element calculations permits substantial reduction in the manual effort of data preparation and the computational cost of numerical solution.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110906
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  • 25
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    A numerical method for two-dimensional Navier-Stokes equation by multi-point finite differences (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1439-1454 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical scheme with a high degree of accuracy has been developed for the full Navier-Stokes equations. The method utilizes the multi-mesh points for space and time derivatives in order to improve the truncation error. Whereas the existing numerical method employing the finite difference scheme, e.g. the explicit, pure implicit, Crank-Nicolson, and DuFort-Frankel schemes, has the truncation errors of the order (Δx)2, Δx being the spatial mesh length, the one for the present method is generally of the order (Δx)3. A numerical example is shown for a natural convection flow in a square box and the results are compared with those of Cormack et al. One order of magnitude reduction of the computing time for a constant degree of accuracy was attained for the two-dimensional problems. Furthermore, a two order of magnitude reduction is to be expected when the method is applied for the three-dimensional Navier-Stokes equations.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110908
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  • 26
    Electronic Resource
    Electronic Resource
    The numerical solution from measurement data of linear integral equations of the first kind (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 729-740 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem considered in this paper is the solution of the Volterra integral equation of the first kind for the input function where we are given the impulse response or kernel and discrete, noise contaminated, observed values of the output function. The present method, introduced here, is based on assuming a multipolynomial form for the input function. Using the integral equation and the least squares method, the coefficients of all the terms in these polynomials are found simultaneously, in order to avoid bias toward any subset of the data. The solution is obtained in such a way that successive polynomials are continuous in function value and derivative at the points of juncture. Thus a smoothed estimate of the input function is generated. The development of the algorithm is presented and applied to two illustrative problems. Possible improvements and extensions of the method are also discussed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110409
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  • 27
    Electronic Resource
    Electronic Resource
    Masthead (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977) 
    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.1620111001
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    Analyse numérique des inéquations variationelles (in French), R. Glowinski, J. L. Lions and R. Trémolieres, Dunod, Paris, 1976. No. of pages: 558. price: 390FF (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1486-1486 
    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.1620110914
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    The influence of the choice of connectors in the finite element methodPresented at the ‘Meeting on Mathematical Aspects of Finite Element methods’, 10-12 December, 1975 in Rome. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1491-1505 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The patch test is interpreted from a variational point of view. This leads to the conclusion that non-conforming (or non-stress diffusive) displacement (stress) models can be considered as special hybrid models. A simple choice of mixed connectors is proposed that satisfy a priori the patch test for any assumed displacement or stress field. Finally some numerical examples are given of finite elements that do not pass the patch test but still exhibit convergence in practical applications.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620111002
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    A simple and efficient finite element for plate bending (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1529-1543 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and efficient finite element is introduced for plate bending applications. Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is surprisingly accurate.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111005
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  • 31
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620111008
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  • 32
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    Numerical integration on a triangle (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 797-815 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Approximations, with any arbitrary degree, of integrals on a triangle are obtained as a product (different from Stroud's conical product formulas) of one-dimensional Gauss-Jacobi formulas.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110504
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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.
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    URL: http://dx.doi.org/10.1002/nme.1620110503
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  • 34
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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.
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    URL: http://dx.doi.org/10.1002/nme.1620110505
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  • 35
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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 
    Details
    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.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110707
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  • 36
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    Efficient numerical treatment of periodic systems with application to stability problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1117-1136 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two efficient numerical methods for dealing with the stability of linear periodic systems are presented. Both methods combine the use of multivariable Floquet-Liapunov theory with an efficient numerical scheme for computing the transition matrix at the end of one period. The numerical properties of these methods are illustrated by applying them to the simple parametric excitation problem of a fixed end column. The practical value of these methods is shown by applying them to some helicopter rotor blade aeroelastic and structural dynamics problems. It is concluded that these methods are numerically efficient, general and practical for dealing with the stability of large periodic systems.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110708
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  • 37
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110710
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  • 38
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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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  • 39
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    A block iterative LU solver for weakly coupled linear systems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 897-900 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110511
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  • 40
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110510
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    A note on a simple thick finite strip (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 905-907 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110513
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    Analysis of power type singularities using finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1225-1233 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation is described for problems with solution functions known to have local rλ variation (s), 0〈λ〈1, and thus singular gradients. Special 3-node triangular elements encircle the singularity and focus to share a common node at the singular point. The shape function of each triangle has the appropriate r λ mode and a smooth angular mode expressed in element natural co-ordinates. As with standard elements, the unknowns are the nodal values of the function. Even if the precise angular form of the asymptotic solution is known, the formulation makes no attempt to embed it, but instead piecewise approximates it. This allows assembly of the element coefficient matrix using standard procedures without nodeless variables and bandwidth complications.The conditions of continuity, low order solution capability, and accurate numerical integration of the singularity element are discussed with a view towards establishing the general range of applicability of the formulation. Numerical applications to the elastic fracture mechanics problems of composite bondline cracking and crack branching are discussed.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110804
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    Diffraction and refraction of surface waves using finite and infinite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1271-1290 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The wave problem is introduced and a derivation of Berkhoff's surface wave theory is outlined. Appropriate boundary conditions are described, for finite and infinite boundaries. These equations are then presented in a variational form, which is used as a basis for finite and infinite elements. The elements are used to solve a wide range of unbounded surface wave problems. Comparisons are given with other methods. It is concluded that infinite elements are a competitive method for the solution of such problems.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110808
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    A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1307-1328 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission-line modelling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank-Nicolson routine may be expressed as the exact solution of certain transmission-line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110810
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    A reply to the letter by Holzer (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1343-1343 
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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.1620110814
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    Finite element techniques for fluid flow, J. J. Connor and C. A. Brebbia, Newnes-Butterworth, London/Boston, 1976. No. of pages: 310. Price: $10·00 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1343-1343 
    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.1620110815
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    More about ‘artificial’ softening of finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1334-1339 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is proposed for making overly stiff elements more flexible. The central idea is quite simple and is illustrated by application to a sample element, whose behaviour is greatly improved. The effort needed to soften an element is very small if its stiffness matrix is naturally produced with reference to generalized co-ordinates before a final transformation to nodal displacement degrees-of-freedom.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110812
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    Masthead (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977) 
    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.1620110901
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    Static analysis of diaphragm-supported cylindrical shells using a curved finite strip (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1347-1364 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two versions are presented of a tranversely-curved finite strip for the static analysis of circular cylindrical shells. The strip is a refined displacement model with sixteen transverse degrees-of-freedom arranged either at two or at four nodal lines. The analysis is specialized for cylinders with diaphragm supports at the ends - via the employment of simple trigonometric series in the longitudinal direction - but extension to other end conditions is straightforward in principle. Detailed results of applications of the curved strip are presented.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110902
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    Application of least square collocation technique in finite element and finite strip formulation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1391-1404 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach in the formulation of finite elements using the concepts of least squares in conjunction with collocation is developed. No numerical integration is required in the stiffness formulation and the resulting matrix has the advantage of being always symmetrical. This approach has also been applied to the finite strip method and provides a means for rapid and accurate analysis of high order partial differential equations. The accuracy and versatility of the method are demonstrated by several examples.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110905
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    A theoretical study of thermal stress relief in thin shells of revolution (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1423-1437 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is given for examining the effect of uniformly heating thin shells of revolution which have an initial stress state. It is assumed that the yield strength decreases with temperature so that significant plastic flow takes place. The note includes a detailed study of this annealing effect on a finite length cylinder which has been given an initial state of stress by removing a longitudinal strip from it and rejoining the edges. The spread of the plastic regions with increasing temperature is followed and it is shown that the peak stress following a heating and cooling cycle is about 10-20 per cent in excess of the yield strength of the material at the peak temperature attained.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110907
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    Error in eccentric beam formulation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1473-1477 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: When the stiffness matrix of a beam element is transformed linearly to account for eccentricity with respect to the plate it is attached to, an incompatibility in the axial displacement field is introduced. The nature of the error so introduced is discussed.
    Additional Material: 4 Ill.
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    On the approximation of convection problems in fluid dynamics (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1477-1483 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is well-known that oscillatory result when cerntral difference of finite element approximations are suoght for convective and boundary layer flows unless the grid length is sufficiently small. A priori limits on the grid spacing, bleow which the solutions are oscullation freee, are derived form one-dimensional idenlizations of these problems and result form boundaryb layer theiry.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110911
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110607
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110606
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110608
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    On isoparametric vs linear strain triangular elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1041-1043 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110610
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    Ways to improve the bending response of finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1029-1039 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Four new ways to relieve the excessive bending stiffness of linear elements are described, and incorporated into plane elements. All satisfy the ‘patch test’. The new elements are compared with existing elements in test problems. Application to three-dimensional problems is proposed.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110609
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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 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110611
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    A modification of the alpha constant technique (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1053-1054 
    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.1620110613
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    Masthead (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977) 
    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.1620111201
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    A data structure for finite element analysis (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1779-1799 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The philosophy of a simple data structure for handling data for finite element analyses is described. The technique is advocated as an efficient way of handling finite element data and of communicating between programs using the data.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111203
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  • 63
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    Lagrange polynomials of a complex variable for two-dimensional interpolation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1801-1808 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We recognize that established techniques permit two-dimensional interpolation to be accomplished efficiently as well as accurately when the grid of points, on which the data is available, is regular. Existing methods suitable for irregular grids are computationally protracted. We show that by using Lagrange polynomials of a complex variable we can interpolate, almost as conveniently as in one dimension, from an irregular grid onto particular points lying on parallel lines. Standard one-dimensional interpolation schemes can then be used to complete the two-dimensional interpolation. We discuss how, in any particular instance, the order of the Lagrange polynomials is chosen, and we present the results of a computational test of our method.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620111204
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    Contouring on isoparametric surfaces (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1893-1897 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111211
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    Advanced Engineering Mathematics, A. J. Bajpai, L. R. Mustoe and D. Walker, Wiley, London, 1977. No. of pages 578. Price £11·50, $22·00, paper £4·75, $10·00 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1898-1898 
    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.1620111212
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  • 66
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    Finite elements in water resources, (Edited by W. G. Gray, G. F. Pinder and C. A. Brebbia), Pentech Press, London, 1977. No. of pages 1024. price £22·50, $45·00 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1898-1898 
    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.1620111213
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    The finite element solution of dissipative electromagnetic surface waveguides (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 11-25 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method is developed for investigating the propagation of high frequency electromagnetic waves along closed or open (surface) waveguides containing dissipative materials and having a cross section of arbitrary shape. The complex propagation constants and associated complex electromagnetic fields are determined as a function of frequency for possible modes of propagation. The method is verified by applying it to structures of simple shape for which analytical results may be calculated for comparison. Waveguides considered include a waveguide filled with dissipative material, a dissipative dielectric rod, a dielectric coated wire and a conducting wire.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110104
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    Displacement incrementation in non-linear structural analysis by the self-correcting method (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 3-10 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The prediction of non-linear structural behaviour by the finite element method wherein buckling does not occur has received considerable attention and, with it, reasonable success has been achieved. However, the post-buckling problem has been less actively pursued probably because of the inherent numerical difficulties encountered. This Technical Note reviews very briefly the numerical methods currently being used for pre- and post-buckling analysis and presents a self-correcting approach based on load and displacement incrementation which is shown to be efficient, reliable, and easy to program. Numerical solutions are presented which demonstrate the effectiveness of the method.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110103
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    Simplex elements of C0 continuity with varying polynomial degrees (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 27-38 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A hierarchical approach is used to construct the simplex elements which permits easy merging of elements of different orders. The explicit interpolation functions and the algorithm of using such elements are presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110105
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    Optimal structural design under dynamic loads (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 39-52 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an algorithm for optimal design of elastic structures, subjected to dynamic loads. Finite element, modal analysis and a generalized steepest descent method are employed in developing a computational algorithm. Structural weight is minimized subject to constraints on displacement, stress, structural frequency, and member size. Optimum results for several example problems are presented and compared with those available in the literature.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110106
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    Infinite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 53-64 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A series of shape functions analogous to Lagrange polynomials, but including an exponential decay term, are suggested as appropriate for elements which extend to infinity. The shape functions are applied to a number of examples, mainly of viscous flow, where the domain extends to infinity. Both explicitly integrated and numerically integrated elements are described. The technique is applicable to many problems where the domain is supposed to extend to infinity.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110107
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    Large displacement, transient analysis of space frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 65-84 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation is presented for the transient analysis of space frames in large displacement, small strain problems. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and deformable elements are treated by a co-rotational (rigid-convected) description. Deformable elements may be connected either to nodes directly or through rigid bodies. The equations of motion are integrated by an explicit procedure. Sample results are presented on the snap-through of an arch-type structure and an idealization of a vehicle-barrier impact.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110108
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    On special isoparametric elements for linear elastic fracturemechanics: A discussion of papers by E. D. Henshell (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 200-203 
    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.1620110122
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    Calculation of stress intensity factors in three dimensions by finite element methods (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 211-229 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods are used to calculate the stress intensity factors for three-dimensional geometries containing a number of depths of crack subjected to various loads. Special elements are used at the tip to represent the variation of the displacement with respect to the square root of the distance from the tip. The stress intensity factors are determined by comparison of the displacements in the special elements, by a method of virtual crack extensions, and, in one case, by an integral around the tip. With meshes containing between 50 and 100 quadratic isoparametric elements, results accurate to within 1 per cent or 4 per cent (depending on case) of known solutions are demonstrated.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110202
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    The coupling of the finite element method and boundary solution proceduresExtended version of a paper presented to ‘World Congress on Finite Element Methods in Structural Mechanics’ Bournemouth, October 12-17, 1975. (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 355-375 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems - structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110210
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    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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    Masthead (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977) 
    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.1620110301
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    Compact representation of triangular finite elements for Poisson's equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 419-430 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The energy expression associated with Poisson's equation is written, for triangular domains, in a form invariant to translation and rotation. The element matrices derived from this depend only on the intrinsic parameters of the element, say the three sides. Considerable savings in storage can be achieved by storing the global stiffness matrix in terms of these element matrices.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110303
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    A homework exercise in finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 411-417 
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    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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    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 
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    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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    A numerical method of solving Fredholm integral equations applied to current distribution and inductance in parallel conductors (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 447-467 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: If the resistance of a conductor is negligible compared with the reactance and if radiation effects are ignored the inductance and current distribution may be obtained by using perfectly-conducting models. In this paper the distribution of current in a system of infinitely-long, perfectly-conducting straight conductors of arbitrary cross-section is shown to satisfy an integral equation of Fredholm type and a general digital procedure for solving this equation, and hence for determining inductance, is given.The relative advantages of stepped, piecewise-linear and piecewise quadratic approximations to the current distribution are studied using arrangements of strip conductors and of isolated rectangular conductors having known current distributions. The advantageous effect of varying the width of the sections used in the computation is also established. It is shown that inductance estimates accurate to within 0·1 per cent can be obtained with a relatively small number of sections and that for a large number of sections the inductance converges on the theoretical value. The paper also examines current distribution and inductance for ‘go-and return’ systems of rectangular conductors, as well as for two paralleled conductors with remote return, and compares the inductances obtained with previous derivations.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110306
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    Structural instability and natural vibration analysis of thin arbitrary shells by use of the Semiloof element (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 481-498 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: At present the Semiloof element is probably one of the most efficient available for the solution of thin shells of arbitrary geometry. Experience in static situations indicates that accurate results can be obtained for non-trivial geometric and loading configurations with relatively coarse meshes. Variable thickness shells or discontinuous thicknesses can be accommodated and no difficulties are encountered in modelling sharp corners or multiple junctions in structures. The element is basically non-conforming but some measure of C1 continuity is provided by the introduction of normal rotation variables at Loof nodes on the element boundary. This paper examines the element behaviour when applied to elastic instability and vibration situations. An eigenvalue solution scheme based on Sturm sequences is presented which does not require the usual elimination of a percentage of the total nodal variables by static condensation. Finally the method is assessed by the solution of several numerical examples.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620110308
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    Periodic Galerkin finite element method of unsteady periodic flow of viscous fluid (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1093-1105 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element analysis of unsteady flow of two-dimensional incompressible viscous fluid is presented employing stream function as a field variable. The Galerkin approach is applied in the procedure of discretizing in time. Using trigonometric series as the interpolation function, the non-linear algebraic simultaneous equation system is derived. Several numerical examples show the adaptability of the formulation.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110706
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    On the treatment of ‘infinite’ boundaries in the finite element method (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1194-1197 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110714
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    Computational methods and problems in aeronautical engineering, Proceedings of a Conference held at University of Manchester, Sept. 1974. Published Academic Press, 1976. £12 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1198-1198 
    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.1620110716
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    Finite element methods in flow problems, Second International Symposium, Proceedings Conference held at Santa Margharita Ligure, Italy, June 1976. Published by ICCAD, c/o 1st Scienze delle Costruzioni, Via Montallegro 1, 16145 Genova, Italy. $25 (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1198-1198 
    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.1620110717
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    Erratum (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1202-1202 
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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.1620110802
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  • 88
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    Electronic Resource
    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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  • 89
    Electronic Resource
    Electronic Resource
    Eccentrically loaded sandwich panels (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1365-1378 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the design of eccentrically loaded sandwich panels in civil engineering structures. A theoretical analysis taking into account the non-linear stress-strain properties of the materials and the influence of shear deformations is proposed. A computer program based on the described algorithm is used to solve a numerical example. It is found that the Newton-Raphson procedure both in the solution of strains at individual sections and in the step by step procedure over the whole structure converges rapidly. Thus the method is suitable for the evaluation of the critical load due to strength failure or loss of stability.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110903
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  • 90
    Electronic Resource
    Electronic Resource
    The computation of some slipline field solutions for asymmetric extrusion (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1379-1389 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two families of slipline field solutions for extrusion through unsymmetrical square dies, which have hitherto only been suggested qualitatively are computed and their ranges of validity determined. The solutions are of ‘indirect type’ and have been obtained using a technique by which the integral operators are approximated by matrices. The determination of the slipline angles and other field parameters corresponding to any given geometry requires the solution of a set of non-linear algebraic equations. This is accomplished using a non-linear optimization procedure.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110904
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  • 91
    Electronic Resource
    Electronic Resource
    Isoparametric, finite element, variational solution of integral equations for three-dimensional fields (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1455-1471 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved numerical method, based on a variational approach with isoparametric finite elements, is presented for the solution of the boundary integral equation formulation of three-dimensional fields. The technique provides higher-order approximation of the unknown function over a bounding surface described by two-parameter, non-planar elements. The integral equation is discretized through the Rayleigh-Ritz procedure. Convergence to the solution for operators having a positive-definite component is guaranteed. Kernel singularities are treated by removing them from the relevant integrals and dealing with them analytically. A successive element iterative process, which produces the solution of the large dense matrix of the complete structure, is described. The discretization and equation solution take place one element at a time resulting in storage and computational savings. Results obtained for classical test models, involving scalar electrostatic potential and vector elastostatic displacement fields, demonstrate the technique for the solution of the Fredholm integral equation of the first kind. Solution of the Fredholm equation of the second kind is to be reported subsequently.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110909
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  • 92
    Electronic Resource
    Electronic Resource
    Letter to the editor (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1484-1485 
    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.1620110912
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  • 93
    Electronic Resource
    Electronic Resource
    An alternating direction method for multi-dimensional parabolic free surface problems (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 741-752 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A locally one-dimensional method (fractional step or alternating direction method) is used to approximate multi-dimensional free surface problems for the diffusion equation by a sequence of one-dimensional problems. These are solved with the method of lines and invariant imbedding.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110410
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  • 94
    Electronic Resource
    Electronic Resource
    On an eigensystem routine due to K. K. Gupta (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 759-764 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An eigensystem subroutine ‘EASI’ due to K. K. Gupta is critically discussed. Some faults are pointed out and remedial measures which have been adopted in practice are presented. The result is a consistently reliable convergent algorithm which has solved narrow bandwidth problems of order up to 1000 × 1000.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110413
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  • 95
    Electronic Resource
    Electronic Resource
    A modified prefrontal routine (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 765-766 
    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.1620110414
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  • 96
    Electronic Resource
    Electronic Resource
    First Cesaro sums for high order finite elements near singularities (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 753-755 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: High order finite elements often exhibit an oscillatory behaviour near stress singularities which appears similar to the Gibbs phenomenon in the theory of Fourier series. It is known that under certain conditions the average of successive partial sums (the first Cesaro sum) of a Fourier series exhibiting the Gibbs phenomenon will converge monotonically to the function being approximated. An analogous device introduced for high order finite element approximations near a stress singularity successfully smooths the oscillations of the computed stress.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110411
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  • 97
    Electronic Resource
    Electronic Resource
    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 
    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.1620110412
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  • 98
    Electronic Resource
    Electronic Resource
    Finite element post-buckling analysis for frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 833-849 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Presented in this paper is a direct method of analysis of the elastic non-linear behaviour of frames. Emphasis is given to the method's capability of tracing the post-buckling path from a bifurcation point although the method can also trace the non-linear behaviour of frames with eccentricities. The method is proposed as an alternative to the main methods currently in use, the perturbation method and the incremental method. Conditions for equilibrium and stability are developed from a variational approach to the total potential. A finite element approximation is made and an efficient solution technique for the resulting non-linear equations is developed.Results for three frames are given demonstrating good agreement with solutions generated from other approaches.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110506
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  • 99
    Electronic Resource
    Electronic Resource
    Flexible finite-difference stencils from isoparametric finite elements (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1653-1665 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new finite-difference technique for the numerical solution of boundary value problems for partial differential equations in two space variables is described. Isoparametric finite elements are used in a finite-difference context to derive difference approximations to space derivatives on a locally curvilinear grid. The result is a generalization of a classical finite-difference stencil which is ‘flexible’ in that it is adaptable to variable meshes, such as those arising from regions with curved boundaries. Numerical results presented for a test problem (potential flow past a circle) using a 9 × 10 grid agree with the analytic solution to within one per cent.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111103
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  • 100
    Electronic Resource
    Electronic Resource
    A finite element Laplace transform solution technique for the wave equation (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1719-1732 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described for the solution of the wave equation with time dependent boundary conditions. The finite element solution accompanied by the numerical Laplace inversion process seems to be an efficient procedure to treat such problems. The programming involved is straightforward in the sense that numerical Laplace inversion routines can be directly used as a time integration procedure after obtaining standard finite element differential equation solutions in the transformed domain.Some results are presented for one- and two- dimensional applications, such as wave propagation in longitudinal bars and wave propagation in harbours.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620111107
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