A maxwell-consistent variational framework for piezoelectric laminates: from single plates to multilayer structures

Abstract This paper develops a variational modeling framework for voltage-actuated piezoelectric plates and multilayer laminates under full electromagnetic coupling. By applying Hamilton’s principle to a continuum setting, the formulation retains full electromagnetic coupling through Maxwell’s equations, capturing both electric and magnetic field effects. This enables consistent reductions to quasi-static and electrostatic regimes without sacrificing physical fidelity. Unlike traditional models