摘要:

AbstractIn this paper, we demonstrate the use of two conceptual principles, the field‐consistency requirement and the edge‐consistency requirement, as the basis for deriving a 4‐noded quadrilateral plate bending element based on Mindlin plate theory using Jacobean transformations only. The derivation is now free of the use of such devices as strain‐interpolation points and Hrennik off strain reference lines, etc., which have been the basis for many recent formulations of this element. The shear strain constraints are now consistently defined within the element domain, and ‘tangential’ shear strains are consistently matched at element boundaries so that there is no locking even under extreme distortion—e.g. even when two nodes are collapsed so that the quadrilateral becomes a triangle. Numerical experiments show that this synthesis produces an element that should be identical to other recent formulations of this element based on tensorial transformations or on shear constraint condensation on the edges, but now given a more complete and formal

ISSN:0029-5981    

DOI:10.1002/nme.1620260803

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe numerical implementation of the Direct Boundary Element formulation for time‐domain transient analysis of three‐dimensional solids is presented in a most general and complete manner. The present formulation employs the space and time dependent fundamental solution (Stokes' solution) and Graffi's dynamic reciprocal theorem to derive the boundary integral equations in the time domain. A time‐stepping scheme is then used to solve the boundary initial value problem by marching forward in time. Higher order shape functions are used to approximate the field quantities in space as well as in time, and a combination of analytical (time‐integration) and numerical (spatial‐integration) integration is carried out to form a system of linear equations. At the end of each time step, these equations are solved to obtain the unknown field quantities at that time.Finally, the accuracy and reliability of this algorithm is demonstrated by solving a number of example problems and comparing the results against the available analytical and numerical

ISSN:0029-5981    

DOI:10.1002/nme.1620260804

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractAn efficient procedure is presented for repetitive analysis of structures, with large numbers of degrees of freedom and design variables, as they are progressively modified during the automated optimum design process. The three key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the governing finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov‐Galerkin technique. The reanalysis procedure is applied to the linear static and free vibration problems of framed structures. Changes in both the sizing and shape (configuration) design variables are considered. For static problems the similarities between the proposed procedure and the preconditioned conjugate gradient technique are identified and are exploited to provide a physical meaning for the preconditioned residual vectors. The effectiveness of the proposed procedure is demonstrated by means of numerical example

ISSN:0029-5981    

DOI:10.1002/nme.1620260805

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThe degenerated shell element is one of the most efficient elements for analysing shell structures. However, it is known to result in rather stiff models when used in thin element applications. The phenomena associated with this behaviour are known as locking phenomena.This paper analyses the machine locking mechanism developed in thin to very thin Lagrangian and serendipity elements. The machine related locking phenomenon is distinguished from the shear and membrane locking phenomena. A remedy for the pure machine locking problem is developed for the two elements. The proposed remedy is based on the technique of the modified transverse shear modulus. It is also extended to control shear locking. The proposed technique is shown to completely eliminate machine locking. Also, it is shown to effectively alleviate stiffening effects due to the presence of spurious shear strain.

ISSN:0029-5981    

DOI:10.1002/nme.1620260806

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractA new finite element for two‐layer plates with built‐in interlayer slip is developed. The new plate element is based on a new plate theory formulated using a new variational principle due to Reissner. The accuracy of the new element is investigated by applying it to the problem of a two‐layer plate with a linear slip law in cylindrical bending for which an exact elasticity solution exists. The comparison of the inplane response for several different values of interlayer shear stiffness and layer thickness ratios shows that the new element gives accurate results. The cylindrical bending of a two‐layer plate with bilinear interlayer slip law is investigated with the new element and the results obtained are compared with a plane strain analysis. Good agreement is obtained for in‐plane normal stresses and displacements. To further assess the simulation capabilities of the proposed element, a rectangular plate under concentrated load is analysed and the growth of slip failure regions

ISSN:0029-5981    

DOI:10.1002/nme.1620260807

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractIn the paper, the solution of a non‐linear structural mechanical problem is seen as a set of points along a curve in the displacement space, resulting from a continuous variation of a load parameter. The state of the structure at a specified point on the path is described by a tangent vector describing the response to a small load factor increment. For a completed, finite step, the deviation from this tangent response is described by a suggested measure. From this measure, some conclusions can be drawn concerning the iteration behaviour, guiding the iteration strategy in coming steps. Two path‐related stiffness measures are derived, giving information concerning the behaviour of the structure. Some conclusions concerning limit load points, bifurcations, etc. can be drawn from these measu

ISSN:0029-5981    

DOI:10.1002/nme.1620260808

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractPresented is a new type of a non‐local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit. The key idea, which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation, is to apply the non‐local concept only to those parameters which cause the degradation while keeping the definition of the strains local. Compared to the previously advanced fully non‐local continuum formulation, the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions. The new formulation exhibits no zero‐energy periodic modes, imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient. Two‐dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy. The formulation is applied to tunnel excavation in a soil stabilized by cement grouting, with the objective of preventing cave‐in (burst) of the tunnel sides due to compressio

ISSN:0029-5981    

DOI:10.1002/nme.1620260809

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractA ‘multiple determinant parabolic interpolation method’ is described and evaluated, principally by using a plane frame test‐bed program. It is intended primarily for solving the transcendental eigenvalue problems arising when the ‘exact’ member equations obtained by solving the governing differential equations of members are used to find the eigenvalues (i.e. critical buckling loads or undamped natural frequencies) of structures. The method has five stages which together ensure successful convergence on the required eigenvalues in all circumstances. Thus, whenever checks indicate its suitability, parabolic interpolation is used to obtain eigenvalues more rapidly than would the popular bisection alternative. The checks also ensure a wise choice of the determinant used by the interpolation. The determinants available are all usually zero at eigenvalues, and comprise the determinant of the overall stiffness matrixKnand the determinants which result, with negligible extra computation, from effectively considering all except the lastm(m=1, 2,…, n−1) freedoms to whichKncorresponds as internal substructure freedoms. Tests showed time savings compared to bisection of 31 per cent when finding non‐coincident eigenvalues to relative accuracy ϵ = 10−4, increasing to 62 per cent when ϵ = 10−8. The tests also showed time savings of about 10 per cent compared with an earlier Newtonian approach. The method requires no derivatives and its use in the widely available space frame program BUNVIS‐RG has demonstrated how easily it can replace bisection, which was used in the

ISSN:0029-5981    

DOI:10.1002/nme.1620260810

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractUsing the incremental equations of motion of a continuous medium and the total Lagrangian description, three different elements, i.e. degenerated shell element, 3‐D continuum element and solid‐shell transition element, are developed for the geometrically non‐linear analysis of laminated composite structures. Compatibility and completeness requirements are stressed in modelling shell‐type structures in order to assure the convergence of the finite element analysis. A number of laminated plate and shell examples are presented to demonstrate the validity and efficiency of various e

ISSN:0029-5981    

DOI:10.1002/nme.1620260811

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY

摘要:

AbstractThis paper is concerned with formulations of finite element models for beams, arches, plates and shells based on the principle of virtual work. The focus is on computer implementation of hierarchic sequences of finite element models suitable for numerical solution of a large variety of practical problems which may concurrently contain thin and thick plates and shells, stiffeners, and regions where three dimensional representation is required. The approximate solutions corresponding to the hierarchic sequence of models converge to the exact solution of the fully three dimensional model. The stopping criterion is based on (1) estimation of the relative error in energy norm; (2) equilibrium tests and (3) observation of the convergence of quantities of interest.

ISSN:0029-5981    

DOI:10.1002/nme.1620260812

出版商:John Wiley&Sons, Ltd    

年代:1988

数据来源: WILEY