Fully-coupled piezoelectric assumed-strain least-squares nonlinear shell. (October 2018)

• Record Type: Journal Article
• Authors: Areias, P.; Rabczuk, T.; César de Sá, J.; Mota Soares, C.A.
• Is Part Of: Thin-walled structures. Volume 131(2018)
• Page Start: 631
• Page End: 645
• Publication Date: 2018-10
• Subjects: Piezoelectricity -- Finite strains -- PVDF -- Zero poling stress -- Orthotropy -- Geometrically exact shells; Thin-walled structures -- Periodicals; 690.1
• DOI: 10.1016/j.tws.2018.07.041
• Languages: English
• ISSNs: 0263-8231

Abstract

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. Abstract : Highlights: Full finite-strain quadrilateral shell with 8 degree-of-freedom at each node. Assumed contravariant stresses, determined by least-square fitting. Condensation of assumed-strain parameters. Appropriate for PVDF modeling. Illustration of piezo actuators with finite strains.