In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms are presented for the computation of a ncar-crack-tip field parameter, the vector J,-integral, and its variation along thc front of an arbitrary three-dimensional crack in a structural component. Account is taken of possible non-elastic strains present in the structure; in this case the near-tip J,-values may be significantly different from the far-field values J,, especially under non-proportional loading.

A complete form of stress and electric displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic piezoelectric media, is derived by using the complex function theory. New definitions of real-valued stress and electric displacement intensity factors for the interfacial crack are proposed. These definitions are extensions of those for cracks in homogeneous piezoelectric media. Closed form solutions of the stress and electric displacement intensity factors for a semi-infinite crack as well as for a finite crack at the interface between two dissimilar piezoelectric media are also obtained by using the mutual integral.

A family of new 4-noded membrane elements with drilling degrees of freedom and unsymmetric assumed stresses is presented; it is derived from a mixed variational principle originally formulated for finite strain analysis and already used in the literature to develop a purely kinematic membrane model. The performance of these elements, investigated through some well established benchmark problems, is found to be fairly good and their accuracy is comparable with that given by models with a larger number of nodal parameters

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The necessity of a special treatment of the numerical integration of the boundary integrals with singular kernels is revealed for meshless implementation of the local boundary integral equations in linear elasticity. Combining the direct limit approach for Cauchy principal value integrals with an optimal transformation of the integration variable, the singular integrands are recasted into smooth functions, which can be integrated by standard quadratures of the numerical integration with suf®cient accuracy. The proposed technique exhibits numerical stability in contrast to the direct integration by standard Gauss quadrature. IntroductionA lot of attention has been paid during the past decade to meshless implementations of both the formulations based originally on variational principles (weak form) (Belytschko et al., 1996) and/or boundary integral equations (Zhu et al., 1998;Mukherjee and Mukherjee, 1997).Recall that, by using an approach based on the BIE, the dimension of the integration region is reduced by one as compared with the dimension of the domain in which a boundary value problem is solved. Beside this most evident attractive property of the BIE formulations one could bring other advantages, such as good conditioning and high accuracy, resulting from the use of singular kernels. Sometimes the appearance of singular integrals has been considered as a handicap of the BIE formulations because of the relative complexity of accurate numerical integration. The problem of singularities has been resolved successfully in boundary element implementations of the BIE formulations (see e.g., Sladek and Sladek, 1998) when the boundary densities are approximated within ®nite size elements polynomially. Having known the boundary densities in a closed form, one can regularize the integrands involving singular kernels before utilizing quadratures for numerical integration (Tanaka et al., 1994). Nevertheless, the question of singularities is to be reconsidered in meshless implementations of the BIE. Now, instead of the de®nition of ®nite size elements by grouping nodal points on the boundary, the nodal points are spread throughout the whole domain including its boundary. When the coupling among the nodal points is satis®ed via the moving least-squares (MLS) approximation of physical ®elds (such as potential, displacements), the boundary densities are not known in a closed form any more, because the shape functions are evaluated only digitally at any required point. Thus, the peak-like factors in singular kernels cannot be smoothed by cancellation of divergent terms with vanishing ones in boundary densities before the numerical integration. The proposed method consists in the use of direct limit approach and utilization of an optimal transformation of the integration variable. The smoothed integrands can be integrated with suf®cient accuracy even by using standard quadratures of numerical integration.Section 2 summarizes the important equations of the local BIE formulation for solution of boundary value problems of linear ...

Abstract-Results of an elastic-plastic finite element analysis of crack closure effects under mode I Spectrum loading are presented. Various factors that cause crack growth acceleration or retardation under low-to-high, high-to-low, and single overload cyclic loadings are discussed.