Fully-coupled piezoelectric assumed-strain least-squares nonlinear shell

Abstract

Relevance of finite strain shell piezoelectric analysis is significant due to the general use of polyvinylidene fluoride (PVDF). A finite-strain geometrically exact shell model for the analysis of piezoelectric laminated structures is introduced. An assumed-strain formulation is employed, with least-squares fitting of contravariant linear stress fields. This allows the condensation of internal degrees-of-freedom corresponding to the assumed strains. The resulting piezoelectric shell has 8 degrees-of-freedom in each node, with 3 position/displacement degrees-of-freedom, 3 rotation parameters and the upper and lower electrostatic potential at the nodes. This contrasts with available formulations where only one electric degree-of-freedom is considered. A total of 32 degrees-of-freedom in each 4-node element are used. In term of implementation, we use a generalized strain and generalized stress formulation to reproduce the conventional finite element organization. Six examples are presented, with transversely isotropic and orthotropic cases, including finite strains and asymmetric plies. Results show a remarkably good agreement with the sources and we achieve higher values of actuation.