摘要:

AbstractThe Possibility of the application of the finite element method to some problems of nonlinear optics is investigated in this paper. The self‐action of a light beam in a nonlinear medium is considered. The general approach to the cretion of conservative computation schemes is presented, based on varitional principles. Definite schemes, which are applicable for the problem of thermal self‐action, are described in detail both in the case of cylindrical and or rectangular co‐ordinates. The accuracy and convergence of the models are analysed. The results of computation of the self‐action problems in motionless and moving media are pr

ISSN:0029-5981    

DOI:10.1002/nme.1620141102

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractDynamic response of strip footings resting on a soil medium, idealized as an elastic halfspace, is obtained using the finite element discretization technique with constant strain rectangular elements consisting of 4CST elements. Boundary stresses have been computed using a combination of Rayleigh wave absorbing boundaries (RAB) and standard vicous boundaries (SVB). The influences of contact pressure distributions at the footing—soil interface, mass and frequency ratios on the dynamic response of a strip footing are studied. Effects of embedment, static surcharge, nonhomogeneity and nonlinear constitutive relations are shown. Results are compared with the existing solution and are presented graphicall

ISSN:0029-5981    

DOI:10.1002/nme.1620141103

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractAn algorithm is described which appears to give an efficient solution of nonlinear finite element equations. It is a quisi‐Nowton method, and we compare it with some of the alternatives. Initial tests of its application to both material and geometric nonlinearities are discusse

ISSN:0029-5981    

DOI:10.1002/nme.1620141104

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractTwo properties of hybrid element method for diffraction and radiation of water waves are examined. For long waves in shallow water the method is shown to give a unique solution for all frequencies. Thus, unlike several other known methods, there are no irregular frequencies for which the approximating matrix equation is singluar. For a sea of arbitrary depth, it is shown that all known global identities such as reciprocity and energy theorems are preserved by the discrete solution. Thus, satisfaction of these identities by the numerical solution is only a necessary but by no means sufficient condition for accuracy.

ISSN:0029-5981    

DOI:10.1002/nme.1620141105

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractSeveral examples are presented to illustrate how standard finite differnce schemes for the wave eqation (e.g. Lax–Wendroff, Leafrog, etc.) can be developed from finite element analysis. The development of the diffrence schemes from the element schemes is made possible by using Galerkin's method on both the spacial and temporal dimension

ISSN:0029-5981    

DOI:10.1002/nme.1620141106

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe concept of fictitious external loading being in exact equilibrium with the internal stresses in a structure is introduced. It is employed in conjunction with the principle of virtual work in an effort to examine certain details of the finite element displacement method in an alternative way.

ISSN:0029-5981    

DOI:10.1002/nme.1620141107

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe use of local mesh refinements for the generation of meshes for the finite element or finite difference methods is studied. A class of rectangular meshes which admit restricted local refinements, referred to as irregular rectangular meshes, is introduced and its representation discussed. Properties of algorithms for mesh refinements are discussed from the viewpoints of termination with a mesh in the specified class, memory utilization, symmetry and fragmentation of the mesh.

ISSN:0029-5981    

DOI:10.1002/nme.1620141108

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractTransform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi‐dimensional cas

ISSN:0029-5981    

DOI:10.1002/nme.1620141109

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe stiffness‐derivative method of Parks1for calculating the linear elastic crack tip stress intensity factor for any symmetric crack configuration and a particular loading is extended to calculate the weight function vector field2,3which serves as a Green's function for the stress intensity factor. The method, which combines the observations of Rice3on the weight function and of Zienkiewicz4on the differential stiffness method, permits very efficient determination of the weight function, requiring only one additional back‐substitution on the already‐factored stiffness matrix. Thus, the stress intensity factor for arbitrary loading of this configuration can subsequently be determined by quadrature alone. The promising extension of the method to three‐dimensional configurations is outlined.While this manuscript was under review, the authors became aware of the recent work of Vanderglas,21in which the same approach as ours is used to extend the stiffness derivative method. The present work was then voluntarily revised in order to address further certain aspects of the topic of shape function perturbation, which Vandergla

ISSN:0029-5981    

DOI:10.1002/nme.1620141110

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY

摘要:

AbstractThe superconvergent property of the discrete solution to certain one‐dimensional problems is examined in the context of the weighted residual difference equations and their conservation properties. The difference equations are shown to satisfy the differential equation exactly at nodes and reproduce the derivatives at boundary nodes. The exact values for the first derivative at interior nodes follow from the conservation property when applied locall

ISSN:0029-5981    

DOI:10.1002/nme.1620141111

出版商:John Wiley&Sons, Ltd    

年代:1979

数据来源: WILEY