The finite element discretized symplectic method for direct computation of SIF of piezoelectric materials

A finite element discretized symplectic method is introduced to compute directly the intensity factors of cracked piezoelectric materials. After modeling by the conventional finite elements, the cracked body is divided into two regions: near and far fields. The unknowns in the far field are unchanged while the displacements, electric potentials, stresses and electric displacements in the near field are expanded in symplectic eigenfunctions and their coefficients are taken as unknowns. No new finite element is needed. The intensity factors, energy release rates and analytical expressions of the mechanical and electric fields near the crack are obtained simultaneously without any post-processing.