Four-field interactions in the structural analysis of multilayered smart plates and shells

The present work develops refined fully coupled thermo-electro-magneto-mechanical models for the linear and stationary analysis of advanced multilayered structures. The modern industries go to the direction of innovative multilayered configurations that use conventional and unconventional materials such as composite laminates, sandwich structures, piezoelectric and piezomagnetic materials. These so-called smart structures are subjected to sever mechanical, electric, magnetic and thermal loads. Unconventional materials, e.g., piezoelectric and piezomagnetic ones, introduce also a response in terms of electric or magnetic potential when the structures are subjected to mechanical or thermal loads. All these features lead to the concept of multifield problems, where four different physical fields (mechanical, thermal, electric and magnetic field) interact between them with different weight and importance. The refined multifield models here proposed, in the framework of analytical solutions, are able to include directly the intensive physical variables of the problem in the governing equations (displacements, temperature, electric potential and magnetic potential) and to obtain the extensive variables from constitutive relations (e.g., stresses, electric field, magnetic field, heat flux, electric displacements). All these variables give a comprehensive analysis of the investigated structures and they permit to improve the design. The refined multifield models are two-dimensional models for the analysis of plate and shell structures, they are here developed in the framework of the Carrera’s Unified Formulation that allows both equivalent single layer (ESL) and layer wise (LW) approaches to be considered with high orders of expansion through the thickness. Classical models (such those based on Kirchhoff or Reissner-Mindlin hypotheses) are obtained as particular cases of refined ESL models. Assessments and benchmarks are proposed in order to evaluate the response of multilayered structures when subjected to mechanical pressure and to field loads (temperature, electric and magnetic potential are field loads that are applied through the thickness). Analytical closed-form results demonstrate the inadequacy of classical theories, originally developed for conventional structures, and the importance of refined LW models. An appropriate extension of the Principle of Virtual Displacements to the thermo-electro-magneto-mechanical problems and multifield constitutive equations allows the coupling between the different physical fields to be quantified in the fully coupled governing equations.