摘要:

AbstractWhen a homogeneous elastic continuum is modelled by a non‐uniform finite element grid, the differences in the size of adjacent finite elements can cause a spurious wave reflection which does not exist in the continuum. Extending previous studies in which the spurious wave reflection was investigated for the case of two uniform grids with a sudden element size change from one grid to the other, the present study deals with the case when the two uniform grids of different element sizes are separated by a transition zone through which the element size varies gradually, either by a geometric progression or by an arithmetic progression. The solution is carried out in complex variables and numerical plots of the results are given. When the ratio of wavelength to the largest element size is as low as 4 : 1, the spurious wave reflection is very significant, while for the ratios over 10 : 1 it is insignificant. Inserting a transition zone with gradually varying element size between the two uniform parts of the grid somewhat mitigates the phenomenon of spurious reflection, but this is significant only when the ratio of element sizes in the uniform grids is small (less than about 1·5 : 1). Varying the element size throughout the transition zone in an arithmetic progression seems slightly better than in a geometric progression. The spurious wave reflection is less pronounced for higher‐order elements, in particular for linear strain elements as compared to constant strain elements. The spurious reflection is also less severe for consistent mass than for lumped

ISSN:0029-5981    

DOI:10.1002/nme.1620190503

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA Fortran computer program is described which calculates physical quantities for a class of shell triangular elements undergoing inextensional bending. These elements are in quadratic parametric representation and may have positive, zero or negative Gaussian curvature.The exact inextensional bending solutions for the rectangular displacement components are cubic in the surface co‐ordinates and the curvature changes are relatively slowly varyin

ISSN:0029-5981    

DOI:10.1002/nme.1620190504

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractA number of numerical methods for mildly nonlinear elliptic boundary value problems on general domains is presented. The discretization procedures considered are: a fourth‐order FFT‐type method, collocation using Hermite bicubic splines and Galerkin with linear triangular as well as quadratic quadrilateral isoparametric elements. The linearized collocation and Galerkin equations are solved by various direct methods available in the ELLPACK system. A comparative study of the above equation solvers is presented for different domain geometries and compilers. The evaluation of software for the general mildly nonlinear elliptic equations is performed over 36 instances from a population of 16 parametrized problems with ‘real world’ and ‘mathematical’ behaviour. The performance data suggests that collocation is an effective method for such general problems, while Galerkin with quadratic quadrilateral isoparametric elements is uniformly superior to the one with line

ISSN:0029-5981    

DOI:10.1002/nme.1620190505

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe method of differential quadrature is demonstrated by solving the two‐dimensional Poisson equation. The results for three test problems are compared with the exact analytical solutions and the numerical solutions obtained by others for the Galerkin, the control‐volume and the five‐point finite difference methods. The method of differential quadrature leads to more accurate results for comparable levels of computational e

ISSN:0029-5981    

DOI:10.1002/nme.1620190506

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractWe have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,Available from the MacNeal‐Schwendler Corporation, Los Angeles, CA 90041, U.S.A.is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two‐ and three‐dimensional linear magneto‐statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two‐dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three‐dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary i

ISSN:0029-5981    

DOI:10.1002/nme.1620190507

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractStable difference schemes that approximate partial differential equations to any desired order are generated by means of power series. The method is demonstrated on the one‐dimensional heat equation and the stability is studied in detail. Stability analyses are then presented for parabolic linear equations with constant coefficients. A nonlinear example is presented which indicates the efficiency of the higher ordered scheme

ISSN:0029-5981    

DOI:10.1002/nme.1620190508

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractAn algorithm based on a new formulation of problem is used in generating the co‐ordinates of the meridian of the drop‐shaped tank. The stresses and moments of this form, due to the varying hydrostatic pressure head, are obtained by a finite element simulation and the usefulness of this approach is asses

ISSN:0029-5981    

DOI:10.1002/nme.1620190509

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620190510

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

摘要:

AbstractThe Davidon‐Fletcher‐Powell (DFP) algorithm for multivariable unconstrained nonlinear function minimization is implemented on a desk microcomputer—the Hindustan Computers MICRO‐2200—with a floppy disk memory extension peripheral. The program is developed using the programming keys of the system. The program is closely based on FMFP, a well‐known FORTRAN subroutine of the algorithm. Among the exercises performed are two standard nonlinear programming (NLP) test problems, namely the Rosenbrock and Wood function minimization and two SUMT (Sequential Unconstrained Minimization Technique) illustration problems in structural optimization, i.e. two‐bar and three‐bar truss weight minimization examples. Experience bears out the potential of desk calculating systems as tools in nonlinear programming algorithm research. Also, the small‐scale structural optimization capability afforded by such systems is expected to be of significance in teaching and preliminar

ISSN:0029-5981    

DOI:10.1002/nme.1620190511

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620190512

出版商:John Wiley&Sons, Ltd    

年代:1983

数据来源: WILEY