摘要:

AbstractThe odd—even permutation and associated unitary transformations for reordering the matrix coefficientAis employed as a means of breaking the strong seriality which is characteristic of closely coupled systems. The nested dissection technique is also reviewed, and the equivalence between reorderingAand dissecting its network is established. The effect of transformingAwith odd—even permutation on its topology and the topology of its Cholesky factors is discussed. This leads to the construction of directed graphs showing the computational steps required for factoringA, their precedence relationships and their sequential and concurrent assignment to the available processors. Expressions for the speed‐up and efficiency of usingNprocessors in parallel relative to the sequential use of a single processor are derived from the directed graph. Similar expressions are also derived when the number of available processors is fewer than req

ISSN:0029-5981    

DOI:10.1002/nme.1620231203

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper describes the basic ideas of sequential quadratic programming (SQP) algorithms for design optimization. There are two fundamental differences between the various algorithms: (i) the difinition of the QP subproblem solved at each iteration, and (ii) the descent function used during step size determination. The performances of the algorithms can change dramatically depending on how the two steps are executed. Numerical implementation details of various computational steps are discussed. Three programs based on SQP algorithms are used to solve 17 structural design problems having 7 to 96 design variables and 10 to 1051 performance constraints besides design variable bounds. Based on the performance of these programs, efficient procedures to execute various steps of the SQP methods are determined. It is concluded that the potential constraint strategy, where only a subset of the constraints is used to define the QP subproblem, is essential for large scale engineering design applications. With this strategy the SQP methods are quite robust and have great potential for routine application in engineering design.

ISSN:0029-5981    

DOI:10.1002/nme.1620231204

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA matrix formulation of structural analysis, known as the integrated force method (IFM) is an attempt to establish an approach in which internal forces are the unknowns. Gradients of such behaviour constraints as stress, displacement and frequency can be obtained in closed form via the IFM. Closed form reanalysis formulae can also be generated. Computational experiments reported here show that reanalysis and gradient generation can be performed efficiently by this approach.

ISSN:0029-5981    

DOI:10.1002/nme.1620231205

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA linear finite element formulation for the analysis of multi‐layered shells comprised of linear elastic and viscoelastic layers is presented. The elastic and viscoelastic layers may occupy arbitrary locations and the formulation is appropriate for thick and thin shells. The concept of a multi‐director field defined over a reference surface is employed for the description of the initial geometry and motion of the multi‐layered shell. The kinematical theory incorporated in the three‐dimensional variational formulation describes, within individual layers, the effects of transverse shear and transverse normal strain to arbitrary orders in the layer thickness co‐ordinate. These kinematics have ‘local support’ over a layer and prove to be convenient and accurate in application. All stresses are computed through three‐dimensional constitutive equations and the usual ‘zero normal stress’ shell hypothesis is not employed. Layer material properties are assumed to be isotropic, although this is not a restriction of the formulation. Sufficiently general constitutive equations for the viscoelastic layers are presented in rate form and an accurate and efficient product algorithm is introduced for their temporal integration. Finite element formulations using both resultant and continuum approaches are developed and compared. Observations and suggestions on the use of reduced/selective integration in the presence of high‐order kinematics are made and a number of numerical examples are presented to illustrate the capabili

ISSN:0029-5981    

DOI:10.1002/nme.1620231206

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractShallowly curved beam elements, including shear deformation and rotary inertia effects, are derived from Hamilton's variational principle. Different degree polynomials, labelled ‘anisoparametric’, are used to interpolate the kinematic variables, instead of uniform interpolations as in the conventional isoparametric procedure. This approach yields a correct representation of the bending strain and, importantly, the membrane and transverse shear strains. Consequently, the severe shortcomings of the exactly integrated isoparametric elements, characterized by excessively stiff solutions in the thin regime (a phenomenon often referred to as membrane and shear locking), are overcome. Uniform (isoparametric‐like) nodal patterns are achieved by explicitly enforcing higher‐degree penalty modes in the membrane and shear strains. This procedure preserves the compatibility of the kinematic field and the capability of the element to move rigidly without straining. Exact quadratures are used on all element matrices, producing a correct rank stiffness matrix, a consistent load vector and a consistent mass matrix. The elements suffer no limitations over the entire theoretical range of the slenderness ratio. For further enhancement and, particularly, in coarse‐mesh situations, an effective relaxation of penalty constraints at the local element level is introduced. This technique ensures a well‐conditioned stiffness matrix. Although the element penalty constraints are relaxed, the corresponding global structure constraints are enforced as is required by the analytic theory. Particular attention is given to the simplest element—a two‐node, six degree‐of‐freedom beam in which all strains are constant. Solutions to static and free vibration arch and ring problems are presented, demonstrating the exceptional modelling capabilit

ISSN:0029-5981    

DOI:10.1002/nme.1620231207

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA simple technique for time and space adaptation in one‐dimensional evolutionary partial differential equations, suggested by Sanz‐Serna and Christie,1is tested. It is found that the equidistribution ofh i2u″(xi) greatly improves on the equidistribution of arc‐length used by those authors. The time‐step control is found to perform poorly in the integration of rough solutions and the reasons for this behaviour a

ISSN:0029-5981    

DOI:10.1002/nme.1620231208

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractAn expression is derived for the potential at an arbitrary point due to a general polynomial distribution of source over a curved triangular domain. The expression is important for the numerical solution of electromagnetic field problems and generalizes the cases of linear and uniform distributions solved previously.

ISSN:0029-5981    

DOI:10.1002/nme.1620231209

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThis paper presents a general finite difference equation for the determination of beam bending moments. The scope of its application to the solution of cable‐assisted bridge problems is discussed. Its derivation and relation to previous difference formulations is explained. It is found that some previous formulations can be conveniently represented by the proposed general difference equation through the variation of a general difference coefficient. The accuracy of the proposed equation is illustrated with numerical example

ISSN:0029-5981    

DOI:10.1002/nme.1620231210

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractThe use of the TLM method for modelling thermal diffusion in bodies of complex geometries is described. Both regular and irregular orthogonal meshes are used. Results are compared with those obtained using finite element analysis.

ISSN:0029-5981    

DOI:10.1002/nme.1620231211

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY

摘要:

AbstractA modification of the dynamic relaxation method is proposed which facilitates static analysis of non‐linear problems. Continuous loading in time is adopted instead of the ordinary step function of time. Inertia and damping forces arising during the loading process are kept at a minimum using an optimum load time history. This results from the stationary condition of an appropriate functional. The equation of motion is included as a subsidiary condition. Continuous load—deflection curves can be obtained. An incremental solution is avoided. Application of the method is extremely simple. Existing programs based on explicit time integration schemes can be easily adapted for it. Sample solutions are presen

ISSN:0029-5981    

DOI:10.1002/nme.1620231212

出版商:John Wiley&Sons, Ltd    

年代:1986

数据来源: WILEY