Geometrically nonlinear isogeometric analysis of smart piezoelectric FG plates considering thermal effects of piezoelectric stress and dielectric constants

Abstract

Abstract In this paper, the isogeometric analysis (IGA) integrated with a simple first-order shear deformation theory (S-FSDT) with only four variables per node is extended to study geometrically nonlinear natural frequency, nonlinear static bending and transient dynamic response of two types of smart piezoelectric functionally graded plates (PFGPs) in thermal environment. The neutral surface is introduced to avoid the stretching-bending coupling effect. The nonlinear strain-displacement relation of the plates is obtained by combining the von Karman strains with the S-FSDT. To investigate the nonlinear mechanical behavior of PFGPs in thermal environment, closer to the real situation, an augmented piezoelectric constitutive equation considering the thermal effects of piezoelectric stress and dielectric constants is used. The accuracy and effectiveness of developed approach are demonstrated through numerical experiment with comparison. We additionally investigate the variation of temperature distribution on geometrically nonlinear response of PFGPs suffering thermo-electro-mechanical load.