Static and dynamic fracture analysis in thin piezoelectric laminas by the boundary element method

摘要

A boundary element method (BEM) is developed to study the static and dynamic fracture problems in a thin piezoelectric structure. The method uses quadrature formula and the collocation method for the temporal and spatial discretization. A quadratic quarter-point element is implemented at the crack tip. The strongly singular and hypersingular integrals are evaluated by a regularization technique based on a suitable variable change. The nearly singular integrals arisen in thin structures are dealt with in two ways. One is based on a nonlinear coordinate transformation for curve-quadratic element, and the other is based on an analytical integration method for straight quadratic element. A displacement extrapolation technique is used to determine the intensity factors (IFs) including the stress intensity factors (SIFs) and electrical displacement intensity factor (EDIF). Numerical examples are presented to verify the effectiveness and stability of present BEM in a thin piezoelectric structure.