Piezothermoelastic Modelling of Laminated Composite Beam with Embedded Smart Materials: A Finite Element Approach

Abstract

The finite element procedures are developed to model the piezothermoelastic behaviour of a piezoelectric laminated composite beam. Mechanical, thermal and electric fields are coupled through constitutive equations which are assumed linear within the application range. The thermodynamic potential energy is expressed by electric enthalpy for the coupled system. Minimisation of the total thermodynamic potential energy leads to a set of governing differential equations. First order shear deformation theory of laminated structures is employed in the finite element formulation. The mechanics include the contributions from elastic, thermoelestic, piezoelectric, dielectric, pyroelectric and heat conduction components. The inclusion of electric potential and temperature as state variables in finite element formulation permits a unified representation of multiple fields coupling behaviour. Extensive numerical studies are carried out to assess the performance of the element for mechanical, electrical and thermal load cases.