V. Sladek

Effects of material gradients on transient dynamic mode-III stress intensity factors in a FGM

Abstract This paper presents a transient dynamic crack analysis for a functionally graded material (FGM) by using a hypersingular time-domain boundary integral equation method. The spatial variations of the material parameters of the FGM are described by an exponential law. A numerical solution procedure is developed for solving the hypersingular time-domain traction BIE. To avoid the use of time-dependent Green’s functions which are not available for general FGM, a convolution quadrature formula is adopted for approximating the temporal convolution, while a Galerkin method is applied for the spatial discretization of the hypersingular time-domain traction BIE. Numerical results for the transient dynamic stress intensity factors for a finite crack in an infinite and linear elastic FGM subjected to an impact anti-plane crack-face loading are presented and discussed. The effects of the material gradients of the FGM on the transient dynamic stress intensity factors and their dynamic overshoot over the corresponding static stress intensity factors are analyzed.

Boundary integral equation method in thermoelasticity: part II crack analysis

Abstract The boundary integral equation formulation of thermoelasticity problems from part I is applied to crack problems in both finite and infinite thermoelastic bodies. For a flat crack in an infinite body the normal and tangential crack opening displacement are decoupled. Transient and steady state problems of thermoelasticity, as well as stationary problems, are considered.

Three dimensional crack analysis for an anisotropic body

An integral equation formulation for three dimensional anisotropic elastostatic boundary value problems is presented. Both the finite and infinite anisotropic body with a crack are considered. The boundary integral equation can be solved numerically for the unknown surface tractions and displacements in a well-posed boundary value problem. Once all boundary quantities are known, the field solution is given by a Somigliana type integral formula. Isotropic elastostatic boundary value problems are included as a special case of this general formulation.

Contour integrals for mixed-mode crack analysis: effect of nonsingular terms

Abstract An integral formulation for computing the nonsingular stresses (NSS) in a cracked body under mixed-mode static and dynamic loads is presented. The reciprocity theorems are applied to find the integral formula. The auxiliary fields are selected to eliminate the singular terms in the asymptotic expansion of the stresses near the crack tip. For elastodynamic crack problems, the integral representation of the NSS is presented in both the time and Laplace transform domain. Required variables along the integration path and region enclosed by the integration contour are obtained from the boundary element analysis. Influence of the NSS on predicting the crack growth direction is investigated for cracks under mixed-mode load conditions.

Three-dimensional curved crack in an elastic body

Abstract The boundary integral equations, which give the relation between the crack opening displacement and traction on the surface of a crack embedded in an infinite isotropic elastic body are formulated. The integral equations are transformed into spherical and cylindrical coordinates in the cases of cracks curved in the shape of spherical and cylindrical surfaces respectively, so that these boundary integral equations may be converted into a system of algebraic equations by the boundary element method. The dependence of stress-intensity factors on the curvature of crack has been numerically calculated for the spherical crack with circular contour under a constant load.

Boundary integral equation method in thermoelasticity part III: uncoupled thermoelasticity

Abstract This paper presents conversion of the volume integral of temperature gradients to a surface integral in the integral formulation of boundary value problems of uncoupled thermoelasticity. Particular classes of problems such as thermal stresses, quasi-static problems of uncoupled thermoelasticity, and stationary problems of thermoelasticity are considered. The improved formulation makes numerical computation more accurate and less formidable. The integral formulations in uncoupled thermoelasticity are given in the Laplace transform domain as well as in the time domain.

Evaluations of the T-stress for interface cracks by the boundary element method

Abstract The path independent M -integral is applied to computation of the T -stress for interface cracks between dissimilar materials. The unique relation between the M -integral and T -stress is found for a properly selected auxiliary solution. The problem of a semi-infinite interface crack between dissimilar materials loaded by a point force applied to the crack tip in a direction parallel to the interface suits such an auxiliary solution. A new subregion boundary element method is applied to solve the given bimaterial interface crack problem. Numerical results for centre-cracked plate, single-edged notch and double-edged notch specimens are included.

Meshless LBIE formulations for simply supported and clamped plates under dynamic load

Simply supported and clamped thin elastic plates under dynamic loads are analyzed. Both harmonic and impact loads are considered. Viscous damping is taken into account. The governing partial differential equation (PDE) of fourth order is decomposed into two coupled PDEs of second order for the deflection and its Laplacian. Both equations contain time-dependent variables. The Laplace transform is used to eliminate the time dependence of the variables. Unknown Laplace transforms are computed from the local boundary integral equations. The meshless approximation based on the moving least square method is employed for the implementation. Time-dependent values are obtained by the Durbin inversion technique.

A local BIEM for analysis of transient heat conduction with nonlinear source terms in FGMs

The diffusion equation with nonlinear heat source intensity in functionally graded materials (FGMs) is considered. In FGMs the thermal material properties are dependent on spatial coordinates. For transient or steady-state heat problems in FGMs the conventional boundary integral equation method or boundary element method cannot be applied due to the lack of a fundamental solution. In this paper, a local boundary integral equation method is proposed to analyse a temperature distribution in a nonhomogeneous body under a microwave heating. To eliminate time variable in the heat equation, the Laplace transform technique is used. The boundary-domain integral formulation with a simple fundamental solution corresponding to the Laplace operator is related to all subdomains which cover the analysed domain. If such integral equations are considered on small subdomains with a simple geometry (circle), domain integrals can be easily evaluated. Physical fields (temperature, heat flux) on the local boundary and in the interior of the subdomain are approximated by the moving least-square. The method is completely element free.

A boundary integral equation method for dynamic crack problems

Abstract A vector boundary integral equation formulation is presented for two-dimensional problems of elastodynamics. The BIE on which numerical work is based is written in a form entirely free of Cauchy principal value integrals. This method is used for computation of dynamic stress intensity factors for cracks in plane strain problems, when a finite body is subjected to dynamic loading with Heaviside-function time dependence.