Papers by Keyword: Laplace Domain

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.

Abstract: In the present paper, the solution of a finite one-dimensional column with Neumann and Dirichlet boundary conditions are deduced based on the theory of mixture. The solution is obtained in the Laplace domain and the time-step method is chosen to obtain the time domain solution. The material data of Massillion sandstone are used for calculations. The column response to the dynamic loading is examined in terms of displacement, pore water pressure, and pore air pressure.

Abstract: . In this paper a variational technique is developed to calculate stress intensity factors with high accuracy using the element free Glerkin method. The stiffness and mass matrices are evaluated by regular domain integrals and the shape functions to determine displacements in the domain are calculated with radial basis function interpolation. Stress intensity factors were obtained by a boundary integral with a variation of crack length along the crack front. Based on a static reference solution, the transformed stress intensity factors in the Laplace space are obtained and Durbin inversion method is utilised in order to determine the physical values in time domain. The applications of proposed technique to two and three dimensional fracture mechanics are presented. Comparisons are made with benchmark solutions and indirect boundary element method.