Time-Domain BEM for Dynamic Crack Problems in Thin Piezoelectric Structures

Abstract A 2-D time-domain boundary element method (BEM) is developed to study the static and dynamic fracture problems in thin piezoelectric structures under electromechanical loadings. The traditional displacement boundary integral equations (BIEs) are applied on the external boundary and the hypersingular traction BIEs are applied on the crack faces. The present time-domain BEM uses a quadrature formula for the temporal discretization to approximate the convolution integrals and a collocation method for the spatial discretization. Quadratic quarter-point elements are 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 by two ways. The first one is based on a nonlinear coordinate transformation method for curve-quadratic elements. The second method is on an analytical integration method for straight quadratic elements to avoid the nearly singularity. A displacement extrapolation technique is used to determine the dynamic intensity factors (DIFs) including the dynamic stress intensity factors (DSIFs) and dynamic electrical displacement intensity factor (DEDIF). Some examples are presented to verify the effectiveness and stability of present BEM in thin piezoelectric structures. Keywords thin piezoelectric structure, time-domain boundary element method, nearly singular integration