摘要:

AbstractWe present a new approach for the fast, efficient solution of large systems of non‐linear equations arising from the finite element discretization. The proposed non‐linear solver builds on the advantages of the popular methods of solution that are currently being employed, while eliminating most of their undesirable features. It combines the well‐known BFGS method with the FAS version of the multigrid method, introduced by Brandt,1to form a fast, efficient solution method for non‐linear problems. We present numerical performance studies that are indicative of the convergence properties as well as the stability of the new

ISSN:0029-5981    

DOI:10.1002/nme.1620381002

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA methodology for simulating the growth of long through cracks in the skin of pressurized aircraft fuselage structures is described. Crack trajectories are allowed to be arbitrary and are computed as part of the simulation. The interaction between the mechanical loads acting on the superstructure and the local structural response near the crack tips is accounted for by employing a hierarchical modelling strategy. The structural response for each cracked configuration is obtained using a geometrically non‐linear shell finite element analysis procedure. Four stress intensity factors, two for membrane behaviour and two for bending using Kirchhoff plate theory, are computed using an extension of the modified crack closure integral method. Crack trajectories are determined by applying the maximum tangential stress criterion. Crack growth results in localized mesh deletion, and the deletion regions are remeshed automatically using a newly developed all‐quadrilateral meshing algorithm. The effectiveness of the methodology, and its applicability to performing practical analyses of realistic structures, is demonstrated by simulating curvilinear crack growth in a fuselage panel that is representative of a typical narrow‐body aircraft. The predicted crack trajectory and fatigue life compare well with measurements of these same quantities from a full‐scale pressurized pan

ISSN:0029-5981    

DOI:10.1002/nme.1620381003

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA hybrid finite element approach is proposed for the mechanical response of two‐dimensional heterogeneous materials with linearly elastic matrix and randomly dispersed rigid circular inclusions of arbitrary sizes. In conventional finite element methods, many elements must be used to represent one inclusion. In this work, each inclusion is embedded inside a polygonal element and only one element is required to represent one inclusion.In numerically approximating stress and displacement distributions around the inclusion, classical elasticity solutions for a multiply‐connected region are employed. A modified hybrid functional is used as the basis of the element formulation where the displacement boundary conditions of the element are automatically considered in a variational sense.The accuracy and efficiency of the proposed method are demonstrated by two boundary value problems. In one example, the results based on the proposed method with only 64 hybrid elements (450 degrees of freedom) are shown to be almost identical to those based on the traditional method with 2928 conventional elements (5526 degrees of freed

ISSN:0029-5981    

DOI:10.1002/nme.1620381004

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one‐dimensional (1‐D) bar problems for both small and large deformation as well as three 2‐D large deformation non‐linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability w

ISSN:0029-5981    

DOI:10.1002/nme.1620381005

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe present paper deals with the study and effective implementation for Stress Intensity Factor computation of a mixed boundary element approach based on the standard displacement integral equation and the hypersingular traction integral equation. Expressions for the evaluation of the hypersingular integrals along general curved quadratic line elements are presented. The integration is carried out by transformation of the hypersingular integrals into regular integrals, which are evaluated by standard quadratures, and simple singular integrals, which are integrated analytically. The generality of the method allows for the modelling of curved cracks and the use of straight line quarter‐point elements. The Stress Intensity Factors can be computed very accurately from the Crack Opening Displacement at collocation points extremely close to the crack tip. Several examples with different crack geometries are analyzed. The computed results show that the proposed approach for Stress Intensity Factors evaluation is simple, produces very accurate solutions and has little dependence on the size of the elements near the crack ti

ISSN:0029-5981    

DOI:10.1002/nme.1620381006

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThis paper describes an incomplete factorization method for computing a preconditioning matrix for the conjugate gradient method. The incomplete factorization satisfies the stability requirement that the incomplete factor remains positive definite throughout the factorization. When selecting a preconditioner for the conjugate gradient method, the number of non‐zero entries to be retained in the incomplete factor should be limited so that the amount of computations involving the preconditioning matrix is minimized. This paper introduces a method to generate an effective preconditioning matrix within a predefined space. Numerical results are presented to demonstrate the effectiveness of the incomplete factor as a preconditioner for the conjugate gradient method for solving large‐scale structural engineering probl

ISSN:0029-5981    

DOI:10.1002/nme.1620381007

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe objective of this paper is to conduct reliability‐based structural optimization in a multidisciplinary environment. An efficient reliability analysis is developed by expanding the limit functions in terms of intermediate design variables. The design constraints are approximated using multivariate splines in searching for the optimum. The reduction in computational cost realized in safety index calculation and optimization are demonstrated through several structural problems. This paper presents safety index computation, analytical sensitivity analysis of reliability constraints and optimization using truss, frame and plate example

ISSN:0029-5981    

DOI:10.1002/nme.1620381008

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractAn efficient dual boundary element technique for the analysis of a two‐dimensional finite body with multiple cracks is established. In addition to the displacement integral equation derived for the outer boundary, since the relative displacement of the crack surfaces is adopted in the formulation, only the traction integral equation is established on one of the crack surfaces. For each crack, a virtual boundary is devised and connected to one of the crack surfaces to construct a closed integral path. The rigid body translation for the domain enclosed by the closed integral path is then employed for evaluating the hypersingular integral. To solve the dual displacement/traction integral equations simultaneously, the constant and quadratic isoparametric elements are taken to discretize the closed integral paths/crack surfaces and the outer boundary, respectively. The present method has distinct computational advantages in solving a fracture problem which has arbitrary numbers, distributions, orientations and shapes of cracks by a few boundary elements. Several examples are analysed and the computed results are in excellent agreement with other analytical or numerical solution

ISSN:0029-5981    

DOI:10.1002/nme.1620381009

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractA Finite Volume (FV) procedure is described for solving the elastic solid mechanics equations in three dimensions on an unstructured mesh, for bodies undergoing thermal or mechanical loads. The FV procedure is developed in parallel with the conventional FE Galerkin procedure so that the differences in each approach may be clearly distinguished. The matrix form of the FV procedure is described, and is implemented in parallel with the FE procedure, both for two‐dimensional quadrilateral and three‐dimensional brick meshes. The FV and FE procedures are then compared against a range of benchmark problems that test the basic capability of the FV technique. It is shown to be approximately as accurate as the FE procedure on similar meshes, though its system matrix set‐up time is twice as long for a node by node set‐up pr

ISSN:0029-5981    

DOI:10.1002/nme.1620381010

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620381011

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY