摘要:

AbstractWe investigate the Cauchy problem for hyperbolic equations for which the frequencies of the main Fourier components in the solution are located in a given frequency interval. Difference formulae for the spatial derivatives are constructed that are tuned to the given intervals of frequencies. Numerical examples illustrating these special discretizations are given both for linear and non‐linear problem

ISSN:0029-5981    

DOI:10.1002/nme.1620230802

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the effect of material properties, boundary friction, and inertia on the flow and strain patterns in material undergoing large plane strain compression. Experimental results are presented for both the rapid compression of Plasticine and the quasi‐static compression of aluminium. In addition, a finite element code for rigid‐plastic material behaviour is discussed, and approximate procedures are described for both in‐plane and platen friction. Provision in the code was also made for strain hardening and strain rate sensitive material properties, and inertia effects. Comparison of the finite element and experimental results showed good agreement. Finite element calculations revealed that in‐plane friction had a very significant effect on the strain patterns observed in the Plasticine experiments. Finite element calculations also showed that strain hardening was of fundamental importance in determining the strain patterns that were observed to occur in the quasi‐static compression of

ISSN:0029-5981    

DOI:10.1002/nme.1620230803

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractAn algorithm and a standard subroutine are developed for the evaluation of singular integrals over arbitrary two‐dimensional domains. The integrand is a product of a Green's function with another function having a weak singularity at the boundary of the domain. Formulae are derived for an accurate estimation of the integral in the neighbourhood of the singularities. The integral over the rest of the domain is evaluated by a library subroutine. The software developed is applied to a study of some contact problems of the theory of elasticity for non‐classical doma

ISSN:0029-5981    

DOI:10.1002/nme.1620230804

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe numerical solution ofnnon‐linear algebraic equations withnunknowns, when any or all of the variables are subjected to constraints, is discussed. Distinction is made between physical and absolute constraints. It is shown, using a set of test problems, that solution of constrained equations does require a special approach. It is found that the step length restricted Newton's method performs best for problems with absolute constraints. Physical constraints can be best handled using a continuation method or penalty function

ISSN:0029-5981    

DOI:10.1002/nme.1620230805

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractIt is shown that standard finite‐element discretizations of second‐order differential equations (i.e. Galerkin and subdomain methods) using conforming linear elements may fail to approximate the original equation locally if the finite‐element grid is irregular or if subdomains are chosen improperly. This failure of local approximation can lead to spurious computational results when subdomain methods are used, but these difficulties can be averted by a judicious choice of subdomains. The conditions which the subdomains must satisfy in order for local approximation to hold are derived and used to construct an algorithm for choosing them properly. The relation of these local results to the global convergence properties of the Galerkin method is disc

ISSN:0029-5981    

DOI:10.1002/nme.1620230806

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA direct method, which uses stress and displacement modes obtained from the governing equations of a problem, is adopted for finite element formulation. It is shown that this method actually leads to a restricted hybrid stress formulation if the displacement modes are changed to ensure symmetry of the stiffness matrix. Through this direct method, however, the problem of selecting the appropriate number of stress modes in the regular hybrid stress model is bypassed. Only the minimum number of modes that are compatible with the number of nodal degrees‐of‐freedom of an element is needed in the formulation. Using more modes only leads to a combination of stress modes, and will not improve the order of performance of the element. It is shown through numerical examples that the restricted hybrid stress formulation leads to well‐balanced ele

ISSN:0029-5981    

DOI:10.1002/nme.1620230807

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA self‐adaptive mesh refinement technique is developed for boundary element solutions of the two‐dimensional Navier's equation. The method is based on error reduction and applied on the element and global level to estimate the residual error associated with each mesh. Results for several problems employing constant two‐dimensional isotropic elastostatic boundary elements are pres

ISSN:0029-5981    

DOI:10.1002/nme.1620230808

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA modified isoparametric co‐ordinate transformation is developed for the case of Lagrange cubic finite elements. This modified transformation produces significant improvements in solution accuracy while eliminating troublesome aspects of the standard isoparametric mapping. In particular, zero Jacobians in the standard transformation, which can occur in elements having non‐uniform node spacing, are completely eliminated with the new transformation. Within the analysis, the range of node locations for which the standard transformation is valid (the Jacobian does not vanish) is determined. The treatment of curved sides is discussed and illustrated. Example calculations using two‐dimensional serendipity elements show that the new transformation provides solutions that are as much as several orders of magnitude more accurate than those computed using the standard formul

ISSN:0029-5981    

DOI:10.1002/nme.1620230809

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe dynamic response of rigid strip‐foundations placed on or embedded in a homogeneous, isotropic, linear elastic half‐space under conditions of plane strain to either external forces or obliquely incident seismic waves of arbitrary time variation is numerically obtained. The above mixed boundary‐value problems are treated by the time domain boundary element method which is used in a step‐by‐step timewise fashion to provide the foundation response to a rectangular impulse. Numerical examples are presented in detail to demonstrate the use and importance of the proposed method. The method appears to be more advantageous than frequency domain techniques, because it provides the transient foundation response in a natural and direct way and can form the basis for extension to the non‐

ISSN:0029-5981    

DOI:10.1002/nme.1620230810

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe determination of the natural modes of wave propagation in an anisotropic layered medium requires the solution of a transcendental eigenvalue problem that is usually approached numerically with the aid of search techniques. Such computations require great effort. The method presented in this paper provides an alternate solution to this problem in terms of a quadratic eigenvalue problem involving tridiagonal matrices, for which the eigenvalues can be found with great speed and accuracy. The technique is then illustrated by means of an example involving a cross‐anisotropic Gibson soli

ISSN:0029-5981    

DOI:10.1002/nme.1620230811

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY