摘要:

In this paper we formulate a direct boundary element method (BEM) for plane anisotropic elasticity (i.e., the in‐plane deformation decoupled from the out‐of‐plane deformation) based on distributions of point forces and dislocation dipoles. According to a physical interpretation of Somigliana's identity the displacement field in a finite bodyRis represented by the continuous distributions of point forces and dislocation dipoles along the imaginary boundary ?R of the finite domainRembedded in an infinite body. We adopt Stroh's complex variable formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions systematically exploiting the duality relations between the point force and the dislocation solutions. Explicit formulas for the displacement and the traction formulations, obtained by analytical integration of the boundary integrals, are given. We apply these formulas to mixed mode crack problems for multiply cracked anisotropic bodies by extending the physical interpretation of Somigliana's identity to cracked bodies and representing the crack by the continuous distribution of dislocation dipoles. With the help of the conservation integrals of anisotropic elasticity, we will demonstrate the capability of the method to determine the mixed mode stress intensity factors (KIandKII) accurately.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670505

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A comprehensive integral equation based approach is presented to determine the elastic response of composite laminates under axial, bending, shear/bending and torsional loadings. The integral equations governing the laminate behavior are directly deduced from the reciprocity theorem for beam‐type structures by employing the fundamental solution of generalized plain strain anisotropic problems. Taking into account the displacement and stress continuity along the interfaces and the external boundary conditions the formulation is numerically solved by the multidomain boundary element method. The resolving system of linear algebraic equations is solved to provide the solution of the problem in terms of displacements and tractions on the boundary of each ply within the laminate. Once this boundary elastic response is determined the displacements and stresses at any point of the laminate can be computed using the appropriate boundary integral representations. The approach, based on a pointwise formulation, makes it possible to analyze laminates with the widest generalities as regards the section shape and lay‐up. Some applications are presented in order to demonstrate the accuracy and effectiveness of the method proposed.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670506

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

New complex variable, singular and hypersingular, boundary integral equations (CV‐BIE) are derived for doubly periodic plane elasticity problems. They refer to systems of blocks (grains), inclusions, holes and cracks. Their forms, convenient when adjusting conventional programs for non‐periodic systems to periodic problems, are suggested. Simple formulae are presented to calculate effective compliances in complex variables.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670507

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In the early nineties, Dvorak (1991), and Dvorak and Procházka (1996), put forward Transformation Field Analysis (TFA), which consists of expressing a linear relationship between either eigenstrains or eigenstresses and on the other hand strains and stresses in a structure. By means of these eigenparameters, mechanical and thermal phenomena in materials can be simulated. In this paper, the TFA is applied to homogenization of nonlinear composites. A very useful numerical tool, the BEM, has been applied to the solution of integral equations. A sample example shows the ability of the procedure proposed. The problem is solved on a unit cell at microscopic level, but more complicated structures of fibers on, say, reference volume elements with stochastically distributed fibers may be studied.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670508

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A nonsingular integral formulation for the Helmholtz eigenproblem is developed in this paper. This novel method contains only imaginary‐part kernels instead of complex‐part kernels in the complex‐valued BEM. Based on the imaginary‐part formulation without singular source, no singular or hypersingular integrals are present. Although this formulation avoids the computation of singular and hypersingular integrals, this approach results in spurious eigensolutions. After comparing the results from the dual formulation, the true and spurious solutions can be separated. An analytical example for the eigensolutions of a two‐dimensional circular domain is studied. The continuous system can be transformed to a discrete system with circulants. Based on the spectral properties of circulants, the true and spurious solutions for the eigenvalues, boundary modes, interior modes and multiplicities are all examined. The possible failure of Hutchinson's sorting technique of looking at modal shapes is also discussed.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670509

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This paper presents a boundary element method combined with the maximum tensile stress criterion for predicting crack initiation angles and simulating fracture propagation paths in cracked anisotropic plates under mixed mode loading. Since the calculated displacements near the crack tip by the BEM have been verified to be very accurate, a decoupling technique can be used to determine the mixed mode stress intensity factors based on the definition of the J‐integral and the relative displacements at the crack tip. Numerical examples are presented for the calculation of stress intensity factors for both isotropic and anisotropic cases. It can be found that our numerical results are in good agreement with those reported by previous authors. Fracture propagation in an anisotropic plate under mixed mode loading is simulated by an incremental crack extension with a piece‐wise linear discretization. A computer program, which can automatically generate a new mesh (required for analyzing sequentially the boundary configuration) has been developed to simulate the fracture propagation process. It was found that the numerical analysis could predict relatively well the direction of crack initiation and the path of fracture propagation.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670510

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A boundary element method based on the Cauchy integral formulae, i.e. a complex variable boundary element method (CVBEM), is proposed for the numerical solution of an antiplane crack problem involving an elastic body with shear modulus that varies continuously in space. The shear modulus assumes a certain form which is quite general to allow for multiparameter fitting of its variation. The method reduces the problem to a system of linear algebraic equations and can be readily implemented on the computer. For clarity, the CVBEM formulation is first carried out for a straight crack and then its extension to include an arbitrary curved crack is indicated.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670511

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

This article considers weakly singular, singular and hypersingular integrals which arise when the boundary integral equations (BIE) are used to solve problems in the theory of elasticity and fracture mechanics. For their regularization, an approach based on the application of the Gauss‐Ostrogradskii and the Green theorems has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals for any convex polygon, have been constructed. Such an approach may be generalized easily and applied for the calculation of multidimensional integrals with various singularities.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670512

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

A numerical algorithm for an external Dirichlet problem of the Poisson equation is considered. The domain O extending to infinity is divided into a bounded subdomain O0and the unbounded subdomain O1. The finite and the boundary element methods are applied to the boundary value problems in the bounded and the unbounded subdomains, respectively. An iterative scheme using the Dirichlet‐Neumann map on the interface ?O1is presented. The convergence of the scheme is mathematically guaranteed. A simple numerical example shows the effectiveness of our scheme.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670513

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor

摘要:

In this paper the dual boundary element formulation is developed to study crack surface contact problem with friction dynamic loads. The nonlinear three‐dimensional dynamic problem can be treated as linear problem by three assumptions. The dual boundary integral equations are given in the Laplace transform domain with the boundary varibles of displacement and traction on the external boundary and displacement discontinuities on the crack surface. Durbin's Laplace tranfrom inversion method is used and the dynamic stress intensity factors are determined by crack opening displacement. A rectangular bar containing a slant circular crack under a pressure Heaviside load is studied. The influrence of different elasticity waves on the dynamic stress intensity factorsKII(t) andKIII(t) are analysed in detail.

ISSN:0253-3839    

DOI:10.1080/02533839.1999.9670514

出版商:Taylor & Francis Group    

年代:1999

数据来源: Taylor