Authors: E. Pineda, M.H. Aliabadi

Abstract: This paper presents the development of a new boundary element formulation
for analysis of fracture problems in creeping materials. For the creep crack analysis the Dual
Boundary Element Method (DBEM), which contains two independent integral equations, was
formulated. The implementation of creep strain in the formulation is achieved through domain
integrals in both boundary integral equations. The domain, where the creep phenomena takes
place, is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep
analysis is applied to metals with secondary creep behaviour. This is con
ned to standard power
law creep equations. Constant applied loads are used to demonstrate time e¤ects. Numerical
results are compared with solutions obtained from the Finite Element Method (FEM) and
others reported in the literature.

109

Authors: M. Wünsche, Jan Sladek, Vladimir Sladek, S. Hrcek

Abstract: In this paper, the symmetric Galerkin boundary element method (SGBEM) will be developed and applied for boundary value problems with layered and fiber reinforced piezoelectric representative volume elements (RVE) and real macroscopic structures. Mechanical and electric loadings are considered to determine the effective material properties. For this purpose, the resulting boundary value problem is formulated as boundary integral equations (BIEs). The Galerkin method is applied for the spatial discretization of the boundary to solve the BIEs numerically. The required surface derivatives of the generalized displacements are computed directly with a boundary integral equation. Numerical examples will be presented and discussed to show the efficiency of the present SGBEM and the influence of the fiber variation on the effective material properties.

9

Authors: Andrey Petrov, Sergey Aizikovich, Leonid A. Igumnov

Abstract: Problems of wave propagation in poroelastic bodies and media are considered. The behavior of the poroelastic medium is described by Biot theory for partially saturated material. Mathematical model is written in term of five basic functions – elastic skeleton displacements, pore water pressure and pore air pressure. Boundary element method (BEM) is used with step method of numerical inversion of Laplace transform to obtain the solution. Research is based on direct boundary integral equation of three-dimensional isotropic linear theory of poroelasticity. Green’s matrices and, based on it, boundary integral equations are written for basic differential equations in partial derivatives. Discrete analogue are obtained by applying the collocation method to a regularized boundary integral equation. To approximate the boundary consider its decomposition to a set of quadrangular and triangular 8-node biquadratic elements, where triangular elements are treated as singular quadrangular. Every element is mapped to a reference one. Interpolation nodes for boundary unknowns are a subset of geometrical boundary-element grid nodes. Local approximation follows the Goldshteyn’s generalized displacement-stress matched model: generalized boundary displacements are approximated by bilinear elements whereas generalized tractions are approximated by constant. Integrals in discretized boundary integral equations are calculated using Gaussian quadrature in combination with singularity decreasing and eliminating algorithms.

158

Authors: Michael Wünsche, Jan Sladek, Vladimir Sladek, Ch. Zhang, M. Repka

Abstract: Time-harmonic crack analysis in two-dimensional piezoelectric functionally graded materials (FGMs) is presented in this paper. A frequency-domain boundary element method (BEM) is developed for this purpose. Since fundamental solutions for piezoelectric FGMs are not available, a boundary-domain integral formulation is derived. This requires only the frequency-domain fundamental solutions for homogeneous piezoelectric materials. The radial integration method is adopted to compute the resulting domain integrals. The collocation method is used for the spatial discretization of the frequency-domain boundary integral equations. Adjacent the crack-tips square-root elements are implemented to capture the local square-root-behavior of the generalized crack-opening-displacements properly. Special regularization techniques based on a suitable change of variables are used to deal with the singular boundary integrals. Numerical examples will be presented and discussed to show the influences of the material gradation and the dynamic loading on the intensity factors.

149