Complementarity, duality and symmetry in nonlinear mechanics: FINITE ELEMENT DUAL ANALYSIS IN PIEZOELECTRIC CRACK ESTIMATION

摘要

Owing to the complexity of piezoelectric crack problems, derivation of their closed-form solutions is virtually impossible and numerical solutions are largely resorted to. Hence, the upper and lower bound estimation for piezoelectric fracture parameters are of theoretical and practical values. An alternative assessment approach for electromechanical coupling cracked system is suggested in the paper. The dual path-independent integrals and the related bound theorems are presented. Consequently, the dual piezoelectric finite elements are formulated and implemented in bound analysis.