摘要:

AbstractA technique is described in which global approximations are used to improve the accuracy of the finite element method. The technique is theoretically based on two corollaries to the Lax–Milgram lemma which are presented in this paper. Basically, the technique consists of factoring the unknown function for which an approximation is desired into the product of a global approximation and a second unknown function. Finite element methods are appropriately applied to obtain an approximation to the second unknown function. The approximation to the original function then consists of the product of the specified global approximation and the approximation to the second unknown function. The advantage that finite element methods possess with respect to obtaining banded matrices is preserved in this technique. In addition, numerical examples indicate that the technique's accuracy is as much as a factor of fifty better than the accuracy obtained by directly applying a finite element method to approximate the original functio

ISSN:0029-5981    

DOI:10.1002/nme.1620211002

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA finite element formulation is developed with emphasis primarily focused on providing stress predictions for thin to moderately thick plate (shell) type structures. Plate element behaviour is specified by prescribing independently the neutral surface displacements and rotations, thusrelaxingthe Kirchhoff hypothesis. Numerical efficiency is achieved due to the simplicity of the element formulation, i.e. the approach yields a displacementdependentmulti‐layer model. In‐planelayerstresses are determined via the constitutive equations, while the transverse shear and short‐transverse normal stresses are determined via the equilibrium equations. Accurate transverse stress variations are obtained by appropriately selecting the displacement field for the element. A selective reduced integration technique is utilized in computing element stiffness matrices. Static and spectral (eigenvalue) tests are performed to demonstrate the element modelling capab

ISSN:0029-5981    

DOI:10.1002/nme.1620211003

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractIt is of interest in numerical analysis to develop symmetrical quadrature rules for integration of complete polynomial functions over a square domain with minimum computational effort. Gaussian product quadrature rules integrate such functions with maximum effort. Symmetrical quadrature rules are developed and presented for integration of complete polynomial functions up to 21st order with minimum computational effort.

ISSN:0029-5981    

DOI:10.1002/nme.1620211004

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe speeds of algorithms that are specifically designed to solve sparse matrix equations depend on the ordering of the unknowns. Because it is difficult to know what a good ordering is, many resequencing algorithms have been developed to reorder the equations in a manner that minimizes the execution time of the solver being used. There is no theoretical way of evaluating resequencing algorithms, but four widely used algorithms (Cuthill–Mckee, Gibbs–Poole–Stockmeyer, Levy, Gibbs–King) have been compared with one another on the basis of their performance on a set of benchmark test problems. This paper reports what we believe to be are minimal or near‐minimal matrix profiles and wavefronts for the benchmark problems. Comparisons of the minimal results with those produced by the widely used resequencing algorithms show that they produce profiles typically a few tens of per cent greater than minimal, but 50 per cent to 100 per cent greater on two problem types. The algorithm that produced the near‐minimal results used a simulated annealing technique, and is far too slow for

ISSN:0029-5981    

DOI:10.1002/nme.1620211005

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractAn efficient block overrelaxation algorithm is presented for the solution of the steady‐state dam seepage problem. The formulation of Alt is used in conjunction with a finite element method on a fixed mesh to obtain a finite dimensional problem which is then solved by the algorithm. Some similarities of the formulation and the residual flow method of Desai are also discussed. Numerical results are compared with results of other author

ISSN:0029-5981    

DOI:10.1002/nme.1620211006

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractIn this paper we introduce finite element methods of Petrov–Galerkin type for the approximate solution of two‐point boundary‐value problems for singularly perturbed, second‐order, ordinary, linear differential equations. We write down Petrov–Galerkin methods on a uniform mesh which have asymptotic error estimates, as the mesh size tends to zero, whose magnitude is independent of the singular perturbation parameter. This is in marked contrast to standard finite element methods which do not possess such a property on a uniform mesh. For these, typically, the error on a fixed uniform mesh blows up as the singular perturbation parameter tends to zero.This robust behaviour of these Petrov–Galerkin methods for singularly perturbed problems is achieved by choosing trial spaces of standard piecewise polynomial type, while the test spaces consist of hinged piecewise polynomials.We consider self‐adjoint and non‐self‐adjoint two‐point boundary‐value problems with Dirichlet boundary conditions. We define hinged test spaces for both types of problem. We then introduce a number of sample problems and we present numerical solutions of these sample problems using a Petrov–Galerkin method with the approp

ISSN:0029-5981    

DOI:10.1002/nme.1620211007

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA finite element modelling technique which utilizes a triangular element with 45 degrees‐of‐freedom and seven‐point integration has been tested for analysis of thin plate and shell structures. The element is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. Numerical result indicates effectiveness of the present modelling technique which features combined use of elements with kinematic modes and those without kinematic modes in an attempt to eliminate both locking and spurious kinematic modes at global structural

ISSN:0029-5981    

DOI:10.1002/nme.1620211008

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThere are many physical phenomena which can be handled by the Helmholtz equation. The equation explains certain phenomena of wave propagation. This paper presents a new finite element method to analyse surface wave motion. The characteristic point of this method is that the interpolation equation is chosen to satisfy the governing Helmholtz equation using trigonometric functions. This follows that the variational functional to be minimized can be formulated such that the integration is limited to the boundary of the element. The numerical solutions obtained are compared with analytical and experimental solutions. From these comparative studies, it is concluded that the present method provides a useful tool for the analysis of surface wave motion.

ISSN:0029-5981    

DOI:10.1002/nme.1620211009

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe detailed stress analysis of the toroidal field superconducting coil is needed to ensure its structural integrity, which includes conductor breakage, insulation breakage, sliding between two turns, or support structure failure. Such detailed‐analysis requires that each of the superconducting coil turns be modelled separately. In this paper, a curved beam finite element,13having constant radius of curvature, is considered to model a turn of a noncircular toroidal field coil. Four different coil shapes subjected to electromagnetic body forces due to toroidal magnetic fields are analysed to assess the finite element models: circular, elliptic, Princeton‐D8and compound shape9. The comparison of analytical and finite element analysis results for resultant forces, tensions and displacements suggest that the proposed approach may be extended to the detailed stress analysis of the noncircular toroidal field superconducting c

ISSN:0029-5981    

DOI:10.1002/nme.1620211010

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe problem of calculating the natural frequencies and mode shapes of rotating blades is solved by an improved finite difference procedure based on second‐order central differences. Lead‐lag, flapping and coupled bending–torsional vibration cases of untwisted blades are considered. Results obtained by using the present improved theory have been observed to be close lower bound solutions. The convergence has been found to be rapid in comparison with the classical first‐order finite difference method. While the computational space and time required by the present approach is observed to be almost the same as that required by the first‐order theory for a given mesh size, accuracies of practical interest can be obtained by using the improved finite difference procedure with a relatively smaller matrix size, in contrast to the classical finite difference procedure which requires either a larger matrix or an extrapolation procedure for improvement in

ISSN:0029-5981    

DOI:10.1002/nme.1620211011

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY