摘要:

AbstractAn analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper. Reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well‐known trapezoidal and midpoint rules to fit the present context. Other integration schemes such as the radial return, mean normal and closest point procedures are particular cases of this general formulation. The meaning of first and second‐order accuracy in the presence of the plastic consistency condition is examined in detail, and the criteria derived are used to identify two second‐order accurate members of the proposed algorithms. A general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed. With the aid of this methodology, the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule. Finally, numerical examples are presented that illustrate the performance of the algor

ISSN:0029-5981    

DOI:10.1002/nme.1620210902

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractAn efficient method for solving algebraic equations is given. The linear equations are solved only once and iterations are performed on the non linear equations. If an initial approximation to a desired root is available, then it is utilized in the solution process. Results of some computational experiments are given.

ISSN:0029-5981    

DOI:10.1002/nme.1620210903

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

ISSN:0029-5981    

DOI:10.1002/nme.1620210904

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractVarious mathematical programming methods for structural optimization are studied. In a companion paper, these methods have been studied based on certain theoretical considerations. In this paper, the methods are studied based on solving a set of test problems. The methods that are studied include recursive QP, feasible directions, gradient projection, SUMT and multiplier methods. Various computer codes have been developed, and are studied together with some existing programs such as CONMIN and OPTDYN. The test problems considered have 3–47 design variables and 3–252 constraints. The evaluation criteria consist of studying the accuracy, reliability and efficiency of a code. It turns out that globally convergent algorithms (multiplier methods, in particular) are very reliable but not efficient. Primal algorithms (like CONMIN), which are not proved to be globally convergent, are efficient but not relia

ISSN:0029-5981    

DOI:10.1002/nme.1620210905

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe solution to a two‐dimensional problem using the boundary element method requires the evaluation of a line integral over the boundary. The integrand ot this line integral is a product of a known Green's function and an unknown function. A large number of Green's functions for two‐dimensional problems can be represented by a linear combination of four singular functions. By approximating the unknown function by a linear combination of known polynomials, integrals are generated whose integrand is a product of the polynomiais and one of the four singular functions. To evaluate these integrals analytically, the boundary is approximated by a sum of straight‐line segments. Recursive formulae are established which reduce the generality and the complexity of the integrands to simple expressions. Analytical forms for these simple expressions are found and are used for initiating the algo

ISSN:0029-5981    

DOI:10.1002/nme.1620210906

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThis paper presents a method of analysing the distribution of a two‐dimensional electromagnetic field in a conducting medium of known cross‐section carrying sinusoidal current and of unknown numerical values of boundary conditions on conductors surfaces. The method combines the finite element and separation of variables methods. An example is given of application of the method to calculation of impedance and electrodynamic forces of two thick, full and round conductors carrying oppositely directed sinusoidal currents. On the basis of numerical computation, graphs of resistance, reactance and electrodynamic forces are plot

ISSN:0029-5981    

DOI:10.1002/nme.1620210907

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA finite element technique of analysing the hydrodynamic pressure, resulting from the vibration of a structure submerged in an unbounded fluid domain, is presented. A suitable boundary condition is proposed for the surface where the unbounded fluid domain is truncated. Pressure is assumed to be the nodal unknown and the fluid is treated as being incompressible and inviscid. The proposed method is computationally very efficient and its implementation in a finite element program is quite straightforward. The efficiency of the method is demonstrated by analysing some two‐dimensional problem

ISSN:0029-5981    

DOI:10.1002/nme.1620210908

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA one‐dimensional exterior electromagnetic scattering problem is formulated using a differential equation approach followed by a finite element discretization. By interpreting the resulting linear algebraic equations as node voltage equations for a transmission line, a boundary element is obtained which satisfies the requirement of no wave reflection at the edge of the finite element region. Numerical results which show the elimination of non‐physical standing waves from the scattered field are presented and discus

ISSN:0029-5981    

DOI:10.1002/nme.1620210909

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA local elliptic projection is introduced to provide improved local approximations to the finite element solution of boundary‐value problems. The approach yields a composite global approximation that is more accurate and provides a good starting value for iterative solution methods. The procedure is particularly effective when used in conjunction with adaptive mesh refinement, as illustrated in numerical studies involving two‐point problems of boundary‐layer and interior‐lay

ISSN:0029-5981    

DOI:10.1002/nme.1620210910

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractDifferent mechanical formulations are employed for calculation of the large deformations occurring in metal forming processes. Eulerian and updated Lagrangian descriptions, valid for viscoplastic materials, are presented. In view of the numerical tests which were carried out, the Eulerian formulation, associated with an implicit integration scheme which proved to be numerically accurate and reliable, is shown to be preferable.

ISSN:0029-5981    

DOI:10.1002/nme.1620210911

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY