Multiscale thermopiezoelectric analysis of laminated plates with integrated piezoelectric fiber composites

Abstract

Abstract This study presents a comprehensive multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators. A detailed framework based on the asymptotic expansion homogenization method is developed to couple the microscale and macroscale field variables. The microscale fluctuations in temperature, mechanical displacement and electric potential are related to the macroscale temperature change, mechanical strain and electric fields through 43 distinct characteristic functions. The local thermal, mechanical and charge equilibrium equations yield a system of partial differential equations for the characteristic functions that are solved using standard finite element techniques. The homogenized thermoelectroelastic properties of a representative material element are computed using the characteristic functions and the constituent material properties. The Eshelby–Stroh formalism is used to analytically solve the three-dimensional macroscopic equilibrium equations for thick and thin laminated piezoelectric plates with arbitrary boundary conditions at the edges. Interscale transfer operators emerging from the asymptotic expansion homogenization method relate the macroscale fields to the microscale heat flux, stress and electric displacement in the individual fibers and matrix. The present multiscale analysis procedure is demonstrated by considering two model problems. In the first problem, a simply-supported sandwich plate consisting of a piezoceramic fiber composite shear actuator embedded between two graphite/epoxy layers is studied. The second problem concerns a simply-supported graphite/epoxy substrate with piezoceramic fiber composite extension actuators attached to its top and bottom surfaces. In both model problems, the responses of the laminated plates under thermal and electrical loading conditions are examined. Results are presented for the homogenized material properties, macroscale deformation, macroscale average stresses and microscale stress distributions.