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  • 1970-1974  (489)
  • 1965-1969  (32)
  • Engineering  (521)
  • 101
    Electronic Resource
    Electronic Resource
    Shape function subroutine for an isoparametric thin plate element (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 431-440 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070403
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  • 102
    Electronic Resource
    Electronic Resource
    Multiangular elements in plate bending (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 545-551 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of bending a thin plate is solved by the finite element method. Using a differential equation of the plate element equilibrium determines the potential energy by contour values of displacements and their first derivatives. In the equilibrium state they have to be such that the potential energy reaches its minimum. The suggested calculation algorithm enables the use of multiangular elements of arbitrary shape instead of integration in the area of this element in which curvilinear integrals appear along the element contour. Elaborated also is the program for calculation by computer and verified usability of the method for various elements based on the example of the square plate.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070412
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  • 103
    Electronic Resource
    Electronic Resource
    Semigroup schemes for dynamic problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 556-560 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified method for obtaining explicit approximate solution schemes for dynamic problems is presented. These schemes are based on the theory of semigroups of operators and can furnish approximate solutions which have an arbitrarily small truncation error. The physical problem considered is that of elastodynamics although the method is clearly not limited to this setting.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070415
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  • 104
    Electronic Resource
    Electronic Resource
    An inhomogeneous, tapered finite element (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 568-570 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070419
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  • 105
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    A discussion of papers by D. B. Spalding and A. K. Runchal (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 560-563 
    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.1620070416
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  • 106
    Electronic Resource
    Electronic Resource
    Degeneration of brick-type isoparametric elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 579-581 
    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.1620070423
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  • 107
    Electronic Resource
    Electronic Resource
    Exact Mises limit loads for cylindrical shells (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 575-578 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical solutions for limit loads of pressurized cylindrical cantilever shells are given for the exact Il'yushin yield surface.It is suggested that the numerical approach can be used for more complex problems for which the exact solution based on equation (2) has not been obtained to date.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070422
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  • 108
    Electronic Resource
    Electronic Resource
    Numerical studies of viscous, incompressible flow through an orifice for arbitrary Reynolds numberFunds for the computations described in this paper were made available by the Research Committee of the Graduate School of the University of Wisconsin. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 489-496 
    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.1620060405
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  • 109
    Electronic Resource
    Electronic Resource
    Mass condensation and simultaneous iteration for vibration problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 543-552 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A relationship is developed between mass condensation and simultaneous iteration when used to determine the natural frequencies and vibration modes of large structural systems. A significant factor in the comparison between the methods is the extra versatility and reliability of simultaneous iteration.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060410
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  • 110
    Electronic Resource
    Electronic Resource
    Spline interpolation techniques for variational methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 565-576 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Interpolation techniques are reviewed in the context of the approximation of the solution of boundary value problems. From the variational formulation, the approximation error norm is related to the interpolation error norm.Among global interpolation techniques, bicubic splines and spline-blended are reviewed; among local, Hermite's and ‘serendipity’ polynomials. The corresponding interpolation error norms are computed numerically on two test functions. The methods are compared for accuracy and for number of operations required in the solution of boundary value problems. The conclusion is that spline interpolation is most convenient for regular hyper-elements, while high precision finite elements become convenient for very fine or irregular partition.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060412
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  • 111
    Electronic Resource
    Electronic Resource
    A mixed finite element model for use in potential flow problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 467-473 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized variational principle is presented, which leads to a modified finite element approach for three-dimensional field problems. Both, potential function and velocity field, are approximated by expansions which are continuous across the inter-element boundaries. The rapid convergence of this mixed model is shown by two examples.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060403
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  • 112
    Electronic Resource
    Electronic Resource
    Computer program for solution of large, sparse, unsymmetric systems of linear equations (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 497-509 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computer program for the in-core solution of large, sparse, unsymmetric systems of linear equations is presented in this paper. The program employs elimination techniques for solution of systems of linear equations. A limited number of zeros is stored and trivial arithmetic is by-passed to preserve computer storage and to reduce the time required for solution. Several techniques for selecting the pivotal elements are discussed and their effect on accuracy and computational time are examined.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060406
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  • 113
    Electronic Resource
    Electronic Resource
    Impulsively started viscous flow past a finite flat plate with and without an applied magnetic field (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 521-527 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical methods are used to investigate the two-dimensional motion of a viscous incompressible fluid impulsively started past a flat plate of finite breadth at zero incidence to the uniform motion of the fluid at large distances from the plate. A step by step integration in time of Helmholtz's vorticity equation is used for Reynolds numbers 10-500.The magnetohydrodynamic case is also considered with the applied magnetic field at infinity parallel to the uniform stream and the non-conducting plate. Results for the Magnetic Reynolds number 50 and infinite, Viscous Reynolds number 50 and 0≤β≤2, where β is the ratio of the square of the Alfvén speed to the square of the main stream velocity, are presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060408
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  • 114
    Electronic Resource
    Electronic Resource
    Exact finite element solutions to the Helmholtz equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 529-542 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For one-, two- and three-dimensional co-ordinate systems finite element matrices for the wave or Helmholtz equation are used to produce a single difference equation holding at any point of a regular mesh. Under homogeneous Dirichlet or Neumann boundary conditions, these equations are solved exactly. The eigenfunctions are the discrete form of sine or cosine functions and the eigenvalues are shown to be in error by a term of + O(h2n) where n is the order of the polynomial approximation of the wave function. The solutions provide the means of testing computer programs against the exact solutions and allow comparison with other difference schemes.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060409
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  • 115
    Electronic Resource
    Electronic Resource
    Diagonally dominant matrices for the finite element method in hydrology (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 587-591 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method provides a powerful new instrument in the solving of problems of flow in the subsoil by means of a numerical processor. This new technique may be reinforced, without complicating its numerical aspect, by an appropriate choice of the sub-regions into which the original region is divided.In two-dimensional confined flows particular types of triangular meshes may be adopted which ensure the final matrices to be diagonally dominant both in steady-state and transient conditions, in heterogeneous and anisotropic fields. This will allow the utilization of rapidly converging iterative processes in the solution of the final linear systems with a notable saving of processing time.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060414
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  • 116
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    A new relaxation method for obtaining the lowest eigenvalue and eigenvector of a matrix equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 511-519 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The matrix eigenvalue problem Hui = λi ui is considered. It is shown that when a new approximate vector v(n+1) to u1 (the eigenvector of the lowest eigenvalue) is computed from the present one v(n) by the relation v(n+1) = (1- αH + βH2) v(n) or v(n+1) = (1- αH + βH2 - γH3) v(n), the convergence rate is at least double that of the gradient method which corresponds to set β = γ = 0. Moreover, by choosing parameters α, β, or γ properly, one can get about three to five times faster convergence rate than that of the latter method, for H having very small γ2-γ1 and very large λN (the largest eigenvalue), further modifications are suggested. The relation with the Richardson method is also discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060407
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  • 117
    Electronic Resource
    Electronic Resource
    Sector elements for matrix displacement analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 553-563 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three sector elements, two for plane stress problems (PSL and PSN) and one for plate bending problems (BSN), have been developed. Of the three elements, two are based on the natural mode technique. The elements have been applied to typical problems to test their performance.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060411
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  • 118
    Electronic Resource
    Electronic Resource
    A finite element weighted residual solution to one-dimensional field problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 577-585 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The one-dimensional diffusion-convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two-dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060413
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  • 119
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    A simplified numerical scheme for calculating the flow of a chemically reacting gas (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 595-598 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060416
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  • 120
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    Reply to preceding discussion (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 602-602 
    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.1620060419
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  • 121
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    Erratum (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 242-242 
    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.1620070302
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  • 122
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    A higher-order triangular finite element for the solution of field problems in orthotropic media (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 287-295 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a triangular finite element for the solution of two-dimensional field problems in orthotropic media. The element has nine degrees of freedom, these being the potential and its two derivatives at each node.The ‘stiffness’ matrix is derived analytically so that no further integration is required when computations are performed using the element.The results obtained using the element are compared with the exact mathematical solution of both a temperature distribution and a torsion problem.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070306
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  • 123
    Electronic Resource
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    Transient shell response by numerical time integration (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 273-286 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In using the finite element method to compute a transient response, two choices must be made. First, some form of mass matrix must be decided upon. Either the consistent mass matrix prescribed by the finite element method can be employed or some form of diagonal mass matrix may be introduced. Secondly, some particular time integration procedure must be adopted. The procedures available divide themselves into two classes: the conditionally stable explicit schemes and the unconditionally or conditionally stable implicit schemes. The choices should be guided by both economy and accuracy. Using exact discrete solutions compared to the exact solutions of the differential equations, the results of these choices are displayed. Concrete examples of well-matched methods, as well as ill-matched methods, are identified and demonstrated. In particular, the diagonal mass matrix and the explicit central difference time integration method are shown to be a good combination in terms of accuracy and economy.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070305
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  • 124
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    Evaluation of some numerical schemes for consolidation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 243-254 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Five finite difference and two finite element schemes for solution of the one-dimensional consolidation problem are compared and evaluated from the viewpoints of convergence, accuracy, stability and computational efforts. An example problem involving laboratory experiments is also solved by using various schemes. Conclusions are drawn regarding relative suitability of these schemes for practical applications.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070303
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  • 125
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    On convergence of Newton's method for load flow problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 325-336 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Kantorovich theorem is virtually the only known sufficiency condition for convergence of Newton's method on a set of non-linear equations. The theorem gives very conservative bounds and is difficult to apply. In this paper the power system load flow problem is solved by Newton's method, and a sufficiency condition for the convergence of the iterations on this particular problem is given. The criterion relates to a condition number defined on the Jacobian matrix associated with the non-linear equations. Computational feasibility is considered and the merits of its use are discussed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070309
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  • 126
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    Finite element analysis of Supersonic panel flutter (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 379-394 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070313
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  • 127
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    Normal gradient boundary condition in finite difference calculations (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 395-400 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An outline is given of a method for dealing with curved boundaries in finite difference calculations (relaxation or other similar techniques) where the gradient normal to the boundary is specified. Fluid flow calculations using the velocity potential are typical of such problems and the flow round a circular cylinder is computed as an example. The method makes no approximation which is not made in the usual finite difference techniques, therefore accuracy at the boundary is as good as in the remainder of the field.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070314
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  • 128
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    Rate of convergence for the iterative approach in elastic-plastic analysis of continua (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 497-508 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In connection with the finite element method, the iterative approach has been commonly used for the analysis of elastic-plastic continua. The rate of convergence of iteration is investigated in the present paper; it depends largely upon the ratio of tangent modulus to Young's modulus, accuracy of the first guess for the exact solution and occurrence of unloading. In the case of finite displacements the rate of convergence is closely related to the stability characteristics of the continua in the sense of Shanley.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070408
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  • 129
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    On a combined sturm sequence and inverse iteration technique for eigenproblem solution of spinning structuresThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 509-518 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an efficient numerical algorithm for the accurate computation of specific eigenvalues and related vectors of spinning structures. The Sturm sequence technique is first applied to isolate the required roots, which are then individually located by an inverse iteration technique adopting an efficient matrix formulation specially developed for this purpose. The associated digital computer procedure is numerically stable, which also fully exploits the banded form of relevant matrices. Furthermore, the algorithm proves to be much faster than other related existing procedures.A computer program, based on the current algorithm, has been developed in FORTRAN V for the JPL UNIVAC 1108 computer. Numerical results for representative structures, computed by the program, are also presented in detail. Extensive applications of the program are envisaged in the attitude control of spacecraft and in the natural frequency analysis of spinning structures, discretized by the finite element method.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620070409
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  • 130
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    Author's reply to a recent discussion1. Solution of eigenvalue problems by sturm sequence methodK. K. Gupta, ‘Solution of eigenvalue problems by Sturm sequence method’, Int. J. num. Meth. Engng, 4, 379-404 (1972). (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 553-554 
    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.1620070413
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  • 131
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    A variable step incremental procedure (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 563-566 
    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.1620070417
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  • 132
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    A more efficient front solution: Allocating assembly locations by longevity considerations (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 570-573 
    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.1620070420
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  • 133
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    On finite element integration in natural co-ordinates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 574-575 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Integration formulas for polynomial expressions in terms of natural co-ordinates are extensively quoted without proof in standard references on finite element theory. A derivation of these relations is presented and their application is extended to non-integral exponents.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620070421
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  • 134
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    On an integration method for solving boundary value problem (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 7 (1973), S. 566-568 
    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.1620070418
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  • 135
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973) 
    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.1620050301
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  • 136
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    Stochastic shakedown analysis of concrete slabs (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 303-309 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of lower bound plastic analysis of axisymmetric slabs for shakedown conditions is described which permits inclusion of stochastic parameters. All solutions are obtained numerically using a mathematical programming approach. Results are for concreteslabs.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050302
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  • 137
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    Computational procedures for the maximum likelihood parameters of the gamma and beta distributions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 327-336 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A computational procedure is presented for calculating the maximum likelihood sampled parameters for the gamma and beta distributions. The procedure employed is both computationally efficient and easy to use. In order to facilitate immediate application, a self-contained FORTRAN IV computer code has been included to carry out the necessary operations.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050304
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  • 138
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    A finite element, linear programming methods for the limit analysis of thin plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 311-325 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite elements having linear moment distributions and use of linearized yield criteria allow one to determine lower bounds to the collapse load of thin plates as solutions of linear programs.The method is quite general and rigorously meets the requirement of the lower bound theorem of limit analysis for concentrated or line load distributions. Ways of treating distributed surface loads are also discussed and tested.Actual bounds are computed for a variety of plate problems governed by Tresca yield criterion and compared with previous solution obtained from higher order stress elements and non-linear optimization techniques. The comparison shows that the present method can yield accurate bounds with considerably shorter computer times and relatively small number of elements. Additional tests show that numerical convergence to the limit loads is assured by suitable refinement of the mesh pattern.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050303
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  • 139
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    Design parameter variation and structural response (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 337-349 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general power series method is developed to aid in obtaining changes in the response variable due to changes in design parameters. The approach is considered for eigenvalue problems and systems of simultaneous equations which may represent static, dynamic and stability response problems. Particular emphasis is placed upon the eigenvalue problem and techniques for improving the calculations form the power series are suggested utilizing modified Rayleigh quotient expressions. Each of the methods proposed is treated computationally by the formulation of a finite element solution of column elastic stability. Investigations of solution accuracy versus percentage variation in element stiffness, whether the method underestimates or overestimates the changes, and the required number of eigenvalue solutions are presented.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050305
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  • 140
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    A finite element tensor approach to plate buckling and postbuckling (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 351-365 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A practical finite element method is presented for geometrically non-linear (von Kármán) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stage of non-linearity.Several different triangular elements are used in explicitly the required tensors. Buckling and post-buckling solutions are outlined and demonstrated by numerical examples.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050306
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  • 141
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    The finite element method in domains with curved boundaries (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 367-373 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For boundary value problems of the second order in two variables, there are proposed elements suitable for use along the curved part of the boundary. Numerical results show a considerable improvement of accuracy.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050307
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  • 142
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    The quadratic programming approach to the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 375-381 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element approximation technique is described in which the potential energy function is minimized subject to liner constraints. The constraints require satisfaction of all kinematic boundary conditions and interelement continuity conditions. An example, indicating the efficiency of the proposed method, is presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050308
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  • 143
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    Comparison between sparse stiffness matrix and sub-structure methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 383-394 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Recent publications have emphasized the advantages of the sparseness of the over-all stiffness matrix of a structure. An alternative to setting up the over-all stiffness matrix is to use sub-structures. The main purpose of this paper is to show that there is equivalence between these two approaches when rows are not interchanged. It follows that a sparse matrix method can never be more efficient than the sub-structure method, if a suitable choice of sub-structures is assumed. However when identical sub-structures are contained within a structure the repetition can be utilized by the sub-structure method. In such cases the sub-structure method will often be quicker than the best sparse matrix solution.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050309
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  • 144
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    Flow of compressible fluid in porous elastic media (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 419-442 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation for flow of fluid in a porous elastic media has been derived from a Gurtin type variational principle. Biot's field equations for porous media have been used in which the constitutive relations include the compressibility of the fluid. It has been shown that by proper choice of the form of the compressibility of the fluid as a function of the state variables, this option of the formulation can be used to treat the partially saturated soil. The method is general with respect to geometry, boundary conditions and material properties. Finally, the results of a series of examples have been presented and compared with exact results to demonstrate accuracy and applicability.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050311
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  • 145
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    Free vibration analysis of spinning structural systems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 395-418 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents an efficient digital computer procedure, along with the complete listing of the associated computer program, which may be conveniently utilized for the accurate solution of a wide range of practical eigenvalue problems. Important applications of the present work are envisaged in the natural frequency analysis of spinning structures discretized by the finite element technique, and in the determination of transfer function associated with the dynamic blocks of control systems of spacecraft utilizing gas jets or reaction wheels for attitude control, as well as of spin-stabilized and dual-spin-stabilized satellites.The validity of the Sturm sequence property is first established for the related matrix formulation involving Hermitian and real symmetric, positive-definite matrices, both being usually of highly banded configuration. A numerically stable algorithm based on the Sturm sequence method is then developed which fully exploits the banded form of the associated matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be extremely fast and economical in comparison to other existing methods of such analysis. Numerical results are presented for spinning bent cantilever beam and the solar arrays of SKYLAB, the earth-orbiting space station proposed by NASA.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050310
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  • 146
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    The treatment of natural boundary conditions in the finite element and finite difference methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 443-446 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To isolate the relative accuracy in the numerical approximation of the natural boundary conditions, a plane- stress example is presented for which the field equations using finite element and finite difference methods are identical. For this example, and by implication a wider class of problem, it is demonstrated that by using conventional practice in both methods the implicit representation of the natural boundary conditions in the finite element gives rise to a lower numerical accuracy than that in the less convenient explicit satisfaction of these boundary conditions in finite difference method.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050312
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  • 147
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    A compact Fortran sequence for limit analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 446-449 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This note presents a FORTRAN sequence for solving a particular case of the ‘bounded variables’ problem.1 It is this problem, rather than the standard linear programming problem, which appears when systematic matrix methods are applied to the rigid-plastic collapse analysis of a plane frame or truss The method uses considerably less storage than a standard simplex approach, and produces the collapse mode as a by-product of the calculation. The sequence is part of a complete program for the plastic collapse analysis of frameworks, details of which may be obtained from the author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050313
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  • 148
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    Announcement (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 452-452 
    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.1620050315
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  • 149
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973) 
    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.1620050401
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  • 150
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    An iterative procedure for the oscillatory laminar boundary layer (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 449-452 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of small sinusoidal oscillations imposed on a stagnation point flow is considered. This leads to an ordinary differential equation which, in the high frequency limit, has a simple solution. An iterative method (involving a linear integral operator) is developed, starting from this basic solution. This scheme, performed numerically, is ‘under-relaxed’ and this renders it applicable to as wide a frequency range as possible: convergence criteria are discussed in terms of the relaxation parameter. The streamwise velocity profiles computed are compared with those given by an independent method.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050314
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  • 151
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    Finite element stress field solution of the problem of saint venant torsion (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 455-458 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some finite element solutions for the Saint Venant torsion problem accounting for orthotropy, inhomogeneity and multiply connected sections are presented. The Prandtl stress function formulation is used. The stresses, torsional stiffness and warping function are calculated. On the basis of various approximations using higher order elements the choice of ‘the best’ element is discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050402
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  • 152
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    Pure moment loading of axisymmetric finite element models (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 459-463 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of loading axisymmetric finite element models by application of a uniform circumferentially distributed moment is presented herein. Operationally, this is accomplished by changing the radius of curvature of some reference point in the axisymmetric model. The radius change gives rise to hoop strains, which are used in an ‘initial strain’ method to actually load the model. The resulting pure axisymmetric moment is computed by integrating the hoop stresses thus generated over a cross-sectional cut through the axisymmetric model. For non-linear problems, the procedure just described can be performed incrementally. Several numerical examples are presented herein to illustrate the method, such as bending of a curved bar, sharp folding of a thin sheet and bending of a toroidal tube until the cross-section is flattened.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050403
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  • 153
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    Axisymmetric triangular finite elements for the scalar helmholtz equation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 481-497 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element method for solving Laplace's, Poisson's and Helmholtz's equations in the axisymmetric case is developed. Complete polynomial functions of arbitrarily high order are used as basis functions. Each triangular element is described by a matrix equation involving cotangents of the vertex angles, the vertex co-ordinates and the triangle area, as well as certain universal numeric matrices. The method of obtaining these matrices is given in detail. The matrices depend only on the polynomial order; values of all matrices to sixth order inclusive have been computed. Important properties of the matrices are discussed and simple example problems are presented.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050405
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  • 154
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    Rolling and impact on a linearly viscoelastic slabPresented at the 6th U.S. National Congress of Applied Mechanics, 15-19 June 1970, Boston, Massachusetts. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 465-479 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of viscoelastic contact stress analysis introduced in an earlier paper10 is developed further to treat two problems: the steady-state rolling of a cylinder and axisymmetric impact of a sphere. The procedure is equally applicable to a medium of infinite depth (half-space) or to a slab of finite thickness. The analysis is based on the computation of a set of viscoeiastic influence coefficients. To find the pressure distribution on the instantaneous contact surface, point matching is used. In the rolling problem, a study is made of such phenomena as critical speed and the effect of medium thickness through a comparison with existing results. The impact problem is solved in an iterative scheme of successive approximations. An example is presented for the study of typical impact parameters.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050404
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    Inversion of prony series characterization for viscoelastic stress analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 499-502 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is common in numerical viscoelastic stress analysis to represent the material functions as Prony series.1 Often series representations for creep function representations are available (for example, see Reference 2) and the stress analysis method requires a relaxation function representation. This paper describes an efficient and reliable method to numerically perform the inversion. An example is given for the inversion and a subsequent re-inversion indicates the accuracy of the method.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050406
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  • 156
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    Numerical solution of mixed boundary value problems using numerical green's functions (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 517-521 
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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 for obtaining the Green's functions for Poisson's equation with mixed boundary conditions is presented. The Green's functions thus obtained are then employed to rapidly obtain numerical solutions of the above equation by matrix multiplication, with subsequent considerable savings in machine time.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050408
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  • 157
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    On the generalization of stress function procedure for dynamic analysis of plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 523-542 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Southwell's stress functions, hitherto used for static analysis of plate flexure problems, are generalized for use in the dynamic analysis of plates. Four finite element models for plate analysis are formed using stress functions. These are used in the numerical calculation of the natural frequencies for some plate problems and the results are compared with alternative solutions.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050409
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    Experiment versus analysis: Computational techniques for the description of static material responseThis work was supported by the United States Atomic Energy Commission. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 503-515 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical basis is presented for the determination of material properties from arbitrarily shaped experimental specimens. The experimental method is derived from an application of numerical boundary value problem solutions to the specimen stress analysis and from the application of a least squares criterion to the comparison of analytical and experimental deformations.Material properties are determined mathematically from the solution to a non-linear set of equations, in which the non-linearity is a function of the specimen type, number of data points and the quality of recorded data. Several solution techniques, based on either direct iteration or function minimization are examined in terms of the parameters affecting convergence.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050407
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  • 159
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    Large deflection analysis of plates and shallow shells using the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 543-556 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The finite element method is applied to stability and large deflection analysis of plates and shallow shells. Based on the von Karman strain expressions for plates and the Marguerre shallow shell theory, equilibrium and incremental equations for a non-linear analysis by finite elements is developed. Great emphasis is placed on the specific matrix formulation, thereby obtaining a highly efficient method that is well suited to modern electronic computer analysis. A doubly curved, non-linear quadrilateral element is developed. The versatility and efficiency of the present method is illustrated by several examples including large deflection and post shear-buckling behaviour of plates and snap-through of shallow shells.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620050410
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    Realization of two-dimensional state space digital filters (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 565-571 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a realization procedure for two-dimensional digital filters. The novel procedure evolves from a state space description of the analog filter function and a method of discretization. Examples are presented to illustrate the method proposed. A discussion of small computer implementation of the two-dimensional digital filter is also included.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050412
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    Convergence of the solution for the far scattered field of a conducting cylinder of arbitrary cross-sectionThe research for this paper was supported by the Department of Electrical Engineering at the University of Manitoba. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 557-564 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Convergence of the solution for the far scattered field of a conducting cylinder of arbitrary cross-section is investigated by studying the scattering of a transverse magnetic field by a conducting triangular prism. It is shown that the convergence of the solution depends mainly on the physical size of the cross-section and not on the form of the current distribution on the prism.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050411
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    A self-adjusting grid for finite-difference programsThis research was conducted under the McDonnell Douglas Independent Research and Development Program. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 585-587 
    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.1620050414
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    A comparison of first and second order axially symmetric finite elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 573-583 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An attempt is made to evaluate the relative merits of first and second order triangular elements in axially symmetric elastostatic stress analysis. The presented results should be of value to those requiring comparison data. Typical stresses, displacements and computer times are presented for three specific numerical examples. Where available, the elasticity solution is used to evaluate the accuracy of computed results. Comparisons indicate that for the same nodal point configuration, the second order solutions are generally better than the corresponding first order solutions, even though the latter involve many more elements. Furthermore, the second order elements may lead to improved results even when fewer nodal points are used. Finally, computer times seem to be higher for the first order solutions and the numerical effort required to obtain comparable accuracy is much greater for the first order solutions.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050413
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    A further modification to Ahmad's shell element (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 588-589 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620050415
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    On the inverse of matrices with nearly equal elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 589-591 
    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.1620050416
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    Advances in computational methods in structural mechanics and design, J. T. Oden, R. W. Clough and Y. Yamamoto, Editors, University of Alabama at Huntsville Press, 1972. No. of pages: 789. price: $10.00 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 591-592 
    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.1620050417
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    Iterative methods for non-linear optimization problems, S. L. S. Jacoby, J. S. Kowalik and J. T. Pizzo, Prentice-Hall, Englewood Cliffs, New Jersey, 1972. No. of pages: 274. Price $14.00 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 5 (1973), S. 592-592 
    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.1620050418
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973) 
    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.1620060101
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  • 169
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    Unsteady MHD duct flow by the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 1-10 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we are concerned with applying the finite element method to seek an approximate numerical solution to a class of unsteady magnetohydrodynamic flow in ducts with arbitrary cross-section. A consistent discrete model for the MHD flow equation with a small magnetic Reynolds number has been developed via the concept of finite elements. A numerical example of MHD flow in a rectangular duct is given, and its results of velocity profiles are compared with the results obtained by other methods.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060102
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    Bending and vibration of multilayer sandwich beams and plates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 11-24 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element displacement analysis of multilayer sandwich beams and plates, each with n stiff layers and n-1 weak cores, is presented. Each layer of the sandwich structure may have individual orthotropic properties of its own and the bending rigidities of the stiff layers are taken into account while direct stresses in cores are neglected in the analysis. The condition of common shear angle for all cores, which has been used by several authors is not implied in the formulation.Several examples on bending problems have been solved using lower-order elements and the accuracy of the results has been shown to be excellent. Two higher-order elements have also been developed but have not been found to yield much better results.The free vibration problems of multilayer sandwich structures have also been solved, and good accuracy is demonstrated.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060103
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    Study in particle percolation: Computer program (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 25-32 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A description of a computer program giving the path of a percolating smooth spherical particle through a three-dimensional cluster of stationary spheres, under the influence of a gravitational field is presented.The history of the moving particle starting with an arbitrary velocity and position is followed. The coefficient of restitution for the spheres is an input variable. When the gravitational force approaches zero and the coefficient of restitution is unity, the computer program can also be utilized for the treatment of radiative heat transfer and for Knudsen diffusion in packed beds.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060104
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    A finite element method for block adjustment problems of photogrammetry (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 33-38 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown that the finite element method can be used advantageously in generating the normal equations of a given photogrammetric network for block adjustments. In this method aerial (or spatial) photographs of a block are processed one at a time, in any random order, to generate the portion of the coefficient matrix between the main diagonal and the variable band and the right hand vector of the normal equations, related with the adjustments to the control points. Any known information related with the adjustments may be imposed, and an internal control point relabelling scheme may be used during the assembly process, in order to minimize the actual computer storage area and the solution time requirements. The paper shows the analogies between the linear equilibrium problems of structural mechanics, and the block adjustment problems of photogrammetry, in order to enable the students of both fields to use the same computer software. In this context, plate-point adjustment matrices and plate-point load vectors for the adjustment problem (corresponding to the element stiffness matrices and the element load vectors of equilibrium problems) are defined and explicit expressions are given.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060105
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    A finite element method for non-self-adjoint problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 39-54 
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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 a general theory and application of the finite element method for some special class of non-self-adjoint problems. The formulation employed here is based on the Galerkin method for linear boundary value and eigenvalue problems described by the partial differential equations of elliptic type, and it can be regarded as an extension of the usual displacement method formulated by the use of the principle of minimum potential energy. In order to illustrate its validity and feasibility, the method is applied to the problems of the two-group neutron diffusion equations and of the stability of a non-conservative system.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060106
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    Note on an approximate method for computing consistent conjugate stresses in elastic finite elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 55-61 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A technique is described wherein improved stresses can be computed in finite element models based on displacement approximations. The method is based on the idea of consistent stress approximations and it approximates such stresses using the notion of a domain of influence of the stress intensity at a nodal point. Considerable improvement in accuracy of the stresses is obtained with little difficulty.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060107
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    Stresses in a partly yielded notched bar - An assessment of three alternative programs (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 63-73 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The results of three finite element stress analysis programs are compared for the problem of the elasto-plastic bending of a notched beam under plane strain conditions. Both Tresca and von Mises yield criteria are considered and the numerical results are compared with an available analytical solution based on slip-line field theory. The general conclusion is drawn that finite element methods can be used with confidence in elasto-plastic stress analysis.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060108
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    Use of the least squares criterion in the finite element formulation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 75-88 
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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 a new method of formulating the finite element relationships based on the least squares criterion. To overcome the high degree of inter-element continuity, a method of reducing the original governing differential equation to a set of equivalent system of first-order differential equations is proposed. The validity of the method is demonstrated by means of several numerical examples. In particular, application of the method to problems with unknown variational functionals is considered.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060109
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    Finite element solution algorithm for viscous incompressible fluid dynamics (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 89-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical solution algorithm employing the finite element concept of solid mechanics is derived for the transient laminar two-dimensional flow of an incompressible viscous fluid. Through dependent variable transformation, the problem is uniformly recast into the solution of a quasi-linear elliptic boundary value-problem, for which the finite element solution theory is established. The algorithm is uniquely user-oriented in accepting the generalized elliptic boundary condition specification of any non-coordinate-surface solution do main closure segment and on employing an arbitrarily irregular computational latticc. Numerical results are presented for several problems in internal flow illustrating solution accuracy, convergence, versatility and the ability to predict imbedded regions of recirculating flow.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060110
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    A numerical method for the analysis of longitudinal elastic-plastic stress wave propagation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 103-115 
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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 for the analysis of one-dimensional propagation of elastic-plastic stress waves in cylindrical bars is proposed. The method is based on the division of the bar into elements of finite length and the solution of the equations of motion for these elements.Numerical results are presented for semi-infinite bars and a finite bar fixed at one end.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060111
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    The analysis of dislocation systems by the finite element method (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 117-128 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the stress field due to any prescribed continuous distribution of dislocations can be determined. The finite element method is employed giving wide freedom with regard to boundary geometry and material properties. The presentation is limited to situations which conform to either the standard plane or anti-plane conditions. Some results are obtained for simple dislocation configurations and compared with theoretical expressions available. Solutions are then obtained to problems in which the material behaves elasto-plastically, a limiting shear stress criterion being employed. Finally the analysis of discrete edge dislocations by use of the slab analogy is presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060112
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    Numerical integration of uncoupled equations of motion using recursive digital filtering (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 137-140 
    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.1620060114
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    Solution of quadratic matrix equations for free vibration analysis of structuresThis paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 129-135 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures.The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures: a cantilever beam and a semicircular arch.
    Additional Material: 3 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060113
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    On the automatic selection of independent displacement variables in general purpose finite element codes (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 141-145 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of generation of surplus displacement variables in general purpose finite element codes, using the displacement method, is discussed. A method of automatic selection of independent variables is proposed which eliminates abortive computer runs from this source and saves engineer data preparation. Extensions of the algorithm are outlined and the uniqueness of solution demonstrated by an example.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620060115
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    Discussion of a paperK. K. Gupta, ‘Solution of eigenvalue problems by the Sturm sequence method’, Int. J. num. Meth. Engng, 4, 379-404 (1972). By K. K. GUPTA (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 145-146 
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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.1620060116
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    A note on certain incompatible elements (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 146-147 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060117
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    Comments on a paperS. Singh and G. M. Ramaswamy, ‘A sector element for thin plate flexure’, Int. J. num. Meth. Engng. 4, 133-142 (1972). (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 148-149 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060118
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    Mathematical foundations for design : Civil engineering systems, Robert M. Stark and Robert L. Nicholls, McGraw-Hill, New York, 1972. No. of pages: 566. Price: £7.90 (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 151-151 
    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.1620060120
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    Letter to the editor (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 152-152 
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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.1620060121
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    Proceedings of the symposium on applications of the finite element method (FEM) in geotechnical engineering, 1-4 MAY 1972, edited by C. S. Desai. U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., 1972. No. of pages: xvii + 1227. Price: $20.00 (hard bound). Available from: Director, U.S. Army Engineer Waterways Experiment Station, WESTR, P.O. Box 631, Vicksburg, Miss. 39180 U.S.A. (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 149-151 
    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.1620060119
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    Masthead (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973) 
    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.1620060201
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  • 190
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    Finite elements for field problems in cylindrical co-ordinates (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 169-178 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with the extension of the finite element method as applied to the solution of the Laplace or wave equation to cylindrical co-ordinate systems. The base matrices required for solving problems governed by these equations are derived for circular polar, elliptic cylinder and parabolic cylinder co-ordinates. The matrices allow problems whose boundaries are described as co-ordinate surfaces in cylinder co-ordinates to be attacked directly by the finite element method. The subject is discussed from the point of view of one interested in electromagnetic wave propagation in uniform waveguide structures.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060203
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  • 191
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    Finite element method applied to analysis of flow over a spillway crest (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 179-189 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical analysis of fluid flow over a spillway is treated in the present paper. A variational principle is introduced for a flow with a free surface boundary under gravity, where the stream function and the profile of the free boundary are independent quantities subjected to variation. A new iteration method is formulated by the combined use of the variational principle and the finite element method. A numerical example based on the iterative method is illustrated. Results thus obtained show good agreement with those obtained from an empirical formula.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060204
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  • 192
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    Point matching computation of transverse resonances (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 155-168 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Point matching (collocation) methods are reviewed and the conditions under which they break down are examined. The detailed treatment applies to complex-valued solutions of the two-dimensional Helmholtz equation with either Neumann or Dirichlet boundary conditions. Point matching methods (when they are valid) can have very real computational advantages. It is shown, by a combination of analysis and computational example, how to estimate whether the cross-section of any particular resonant system is suitable for the application of an existing point matching method. An extended point matching method is introduced to handle cases for which previous methods fail. The method is illustrated with several computational examples. The discussion is specifically concerned with electromagnetic wave guides, but the results can be applied to a wide range of physical systems.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060202
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  • 193
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    On the unity of the constant strain/constant moment finite element methods (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 191-200 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper is an attempt to unify the finite element methods of ‘first’ order in plate stretching and plate bending, i.e. those assuming in each element constant strains in stretching or constant moments in bending. Reference is made to the stretching-bending analogy between the method of Turner, Clough, Martin and Topp and the method of Elias. By another analogy property a plate stretching method which is the dual to the constant moment method of Herrmann (and Hellan) is derived. The transformation of variables which carries the last pair of dual methods identically into the first pair is finally demonstrated.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060205
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  • 194
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    Direct numerical solution of three-dimensional equations containing elliptic operators (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 201-212 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A direct three-dimensional elliptic solver is presented for application in a wide class of numerical methods for solving partial differential equations in physics and engineering. The derived algorithm and FORTRAN code implement Buzbee, Golub and Nielson's proposed extension of Buneman's Cyclic-Reduction Poisson solver to three dimensions. Both a ‘most direct’ cyclic reduction and a revised method (to eliminate roundoff error difficulties) are derived. Tests on an IBM 360/67 computer, using various optional combinations of subroutines, showed significant differences in accuracy and computing time, with the optimum subroutine combination depending on mesh size.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060206
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  • 195
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    Solution methods for eigenvalue problems in structural mechanics (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 213-226 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A survey of probably the most efficient solution methods currently in use for the problems Kφ = ω2Mφ and KΨ = λKGΨ is presented. In the eigenvalue problems the stiffness matrices K and KG and the mass matrix M can be full or banded; the mass matrix can be diagonal with zero diagonal elements. The choice is between the well-known QR method, a generalized Jacobi iteration, a new determinant search technique and an automated sub-space iteration. The system size, the bandwidth and the number of required eigenvalues and eigenvectors determine which method should be used on a particular problem. The numerical advantages of each solution technique, operation counts and storage requirements are given to establish guidelines for the selection of the appropriate algorithm. A large number of typical solution times are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060207
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  • 196
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    An integrated force method for discrete analysis (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 237-251 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integrated force method is developed for the analysis of discrete structures in which all the element forces are taken as the independent variables instead of the conventional way of treating the redundants as the prime unknowns. Computationally the integrated force method is superior to the standard force method. The analogy between Beltrami-Michell formulation for continuous problems and the present formulation for discrete structures is presented. Illustrative examples for the determination of forces and displacements are presented for pin-connected and rigid-connected frame structures for various load conditions.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060209
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  • 197
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    A convergent method for cyclic plasticity analysis with application to nuclear components (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 227-236 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for elastic-plastic analysis of pressure vessels subject to cyclic mechanical and thermal loading is proposed. The method is shown to lead to a highly convergent solution when applied in conjunction with Prager's complete kinematic hardening rule. The plastic strain increments are written in terms of the total strains, thus leading to a consistent formulation when the analysis is done by an incremental iterative process.The proposed method is applied to the analysis of a long cylinder in the state of generalized plane strain and subject to cyclic loading. Cyclic plasticity and creep are considered in one of the problems analysed. The finite difference method is used in the solution of the compatibility and equilibrium equations. It is shown that the computation time using the proposed method is very small compared to other techniques.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060208
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  • 198
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    The orthogonal projection method for the numerical solution of a field problem (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 287-296 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method, based on the orthogonal projection method of Hilbert space, is given. Two approximate solutions, which bound the exact solution from above and below, are described. The error of the approximate solution is calculated directly. An example of a calculation of temperature field in a nuclear reactor shell is presented.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060213
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  • 199
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    A direct integral equation method for the potential flow about arbitrary bodies (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 253-264 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The velocity on the surface of an arbitrary three-dimensional body in the potential flow of an ideal fluid is determined by means of an integral equation method. The equations to be solved are a pair of singular integral equations of the second kind, the unknowns being the desired velocity components. The integral equations are approximated by a set of linear equations, which are solved numerically. For ellipsoids the results are compared with the analytic solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060210
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  • 200
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    Criteria for finite element discretization of shells of revolution (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 265-274 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is described whereby an efficient finite element discretization scheme for a shell of revolution can be predetermined and subsequently refined for successive analyses by considering the following criteria: 1.Stress intensification in the vicinity of a concentrated action.2.Variation in the strain energy intensity function. Several case problems have been studied to validate the procedure.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060211
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