摘要:

AbstractIn the present paper an incremental procedure is formulated for first‐order elastoplastic analysis of plane frame structures discretized into a finite number of beam elements and described by piecewise linear elastic‐perfectly plastic constitutive laws, under the assumption of both reversible and irreversible behaviour of material and using piecewise linear yield conditions at any desired degree of discretization in the space of the active stress resultants (axial force, shear force and bending moment).The proposed method, by using the independent elastic‐plastic kinematical compatibility equations, restrains the problem sizes within not more than twice the number of the redundant unknowns in the complete elastic frame, regardless of the degree of discretization of the piecewise linear yield conditions, still maintaining the advantage exhibited by the Mathematical Programming methods of requiring only one factorization of the matrix governing the problem when no local unloading occurs. Furthermore, the outlined algorithm allows the additional computational effort to be restrained in the case of local unloading, inasmuch as it requires a new factorization to be performed of a part of the matrix governing the problem, whose size is small with respect to the total size of the m

ISSN:0029-5981    

DOI:10.1002/nme.1620260402

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractCombinations of the Ritz–Galerkin and finite element methods are applied to solving singularity problems of homogeneous, elliptic equations. The Ritz‐Galerkin method is used in the subdomains where there exist singular points; and the finite element method is still used in the rest of the solution domains. More general coupling techniques than those of Reference 6 along the common boundary of subdomains are discussed. Numerical experiments using these kinds of coupling techniques are provided for the first time. It is interesting that the calculated results of Motz's problem have shown the simplified hybrid strategy in Reference 6 to be optimal for both error bounds and stability of numerical solutions, among all general coupling techniq

ISSN:0029-5981    

DOI:10.1002/nme.1620260403

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractExpansions in terms of beam functions and Chebyshev polynomials are used to compute solutions to the primary two‐point boundary value problem within a spectral collocation formulation. The performance of the methods is analysed in terms of accuracy and robustness relative to the level of non‐linearity. Accurate results are obtained with Chebyshev polynomials and the performance of these trial functions is insensitive to the level of non‐linearity whereas the behaviour of the beam functions shows great sensitivity to the level of non‐linearity. The use of Newton's method to solve the mixed linear‐non‐linear system for the Chebyshev coefficients is successful for highly non‐linear problems without the need for parameter

ISSN:0029-5981    

DOI:10.1002/nme.1620260404

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe paper describes the basic ideas of Monte Carlo annealing algorithms for structural optimization with discrete design parameters. The algorithm generates randomly a set of design parameters, with probability depending on the objective function and given by the Boltzmann–Gibbs distribution. In this model the search for the global minimum is simulated by a relaxation process of the statistical mechanical system with the Hamiltonian proportional to the objective function. The rate of the convergence of the method and its dependence upon the annealing probability are discussed. Numerical implementation of the method for the weight optimization of the ten‐bar planar cantilever truss is presented. The results of numerical simulation are compared with those obtained by the dual methods. The principal conjecture is that the method is fairly efficient and has great potential for applicaton in engineering des

ISSN:0029-5981    

DOI:10.1002/nme.1620260405

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractComparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw‐Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numericall

ISSN:0029-5981    

DOI:10.1002/nme.1620260406

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe two matrix equations obtained from the mixed finite element method are uncoupled through the use of the QR decomposition. The procedure obtains the basis for the null space which is composed of solutions to the homogeneous flux‐equilibrium equation. The result is that, even for statically indeterminate problems, stresses can be obtained without solving for the displacement field. Furthermore, the stress field can be decomposed directly into contributions from applied forces and from prescribed displacements. The appearance of kinetic modes can easily be monitored. The possibility of utilizing non‐conventional basis functions for use in conjunction with the QR decomposition is explored briefly. Simple examples are given to illustrate the theoretical resu

ISSN:0029-5981    

DOI:10.1002/nme.1620260407

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractHouseholder's method for tridiagonalizing a real symmetric matrix, a major step in evaluating eigenvalues of the matrix, is modified into a parallel algorithm for a concurrent machine of message passing type. Each processor of the concurrent machine has its own CPU, communications control and local memory. Messages are passed through connections between processors. Although the basic algorithm is inherently serial, the computations can be spread over all processors by scattering different rows of the matrix into processors, hence the term “Scattered Row Decomposition”. The steps in the serial and the parallel algorithms are identified. Expressions for efficiency and speedup are given in terms of problem and machine parameters. For a concurrent machine of ring type interconnection, a selected representative problem of large order exhibits efficiency approaching 66 per c

ISSN:0029-5981    

DOI:10.1002/nme.1620260408

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe backward mapping approach for computation of global domains of attraction of asymptotically stable non‐critical equilibrium points of dynamical systems is presented. A basis for the proposed approach is an extension of Lyapunov's direct method due to LaSalle and Lefschetz. An iterative process that converges to the global domain of attraction of an asymptotically stable equilibrium point is formulated. The method applies to both continuous time and discrete time multidimensional systems. It is shown that the backward mapping approach proposed by C. S. Hsu for spiral equilibrium points of second order discrete time systems is a particular case of the algorithm presented here. The proposed method can be used for autonomous systems as well as for systems with periodic coefficients. When applied to discrete time formulation of dynamical systems, the method can be used to determine the regions of stability of periodic solutions. The paper concludes with a number of illustrative examples that demonstrate the usefulness of the proposed approac

ISSN:0029-5981    

DOI:10.1002/nme.1620260409

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractAn advanced implementation of the boundary element technique for the periodic and transient dynamic analyses of two‐dimensional elastic or visco elastic solids of arbitrary shape and connectivity is presented. For transient dynamic analysis the problem is first solved in the Laplace transform space and then the time domain solutions are obtained by numerical inversion of transformed domain solutions.The present analysis is capable of treating very large, multi‐domain problems by substructuring and satisfying the equilibrium and compatibilities at the interfaces. With the help of this substructuring capability, problems related to the layered media and soil–structure interaction can all be analysed. This paper also introduces a new type of element called ‘Enclosing Element’, which has been developed and used to model the infinitely extending boundaries of a half‐space or a layered medium. A number of numerical examples are presented, and through comparisons with available analytical and numerical results, the accuracy, stability and efficiency of the present analysis are

ISSN:0029-5981    

DOI:10.1002/nme.1620260410

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractAn analysis of thin plates byC0elements is presented. The fundamental part of it is the formulation of a set of constraints that relate the rotational degrees of freedom to the translational degrees of freedom and which are weaker than the usual Kirchhoff constraints. A penalty term associated with these constraints is then introduced instead of the usual expression for the shear strain energy. It is shown that the approach is effective for both quadrilateral and triangular elements.

ISSN:0029-5981    

DOI:10.1002/nme.1620260411

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY