Coupled Thermo-Electro-Mechanical Analysis of Smart Plates Embedding Composite and Piezoelectric Layers

Abstract

This article considers the static analysis of multilayered piezoelectric plates subjected to mechanical pressures and to field loads such as electric potential and temperature. The Principle of Virtual Displacements has been extended to thermo-electro-mechanical cases by including the virtual internal electric and thermal works and by writing the opportune constitutive relations. The governing equations are given in terms of three main primary variables (displacements, electric potential and temperature) and they are solved in a closed-form solution. The primary variables are expanded in the thickness direction in both Equivalent Single Layer (ESL) and Layer-Wise (LW) form with higher orders of expansion. The models proposed enable to obtain a quasi-3D description of the static thermo-electro-mechanical analysis of multilayered plates and to analyze the effects of each physical field involved. The limitations of classical theories for such analyses have also been discussed.

Keywords:

• Field loads
• Layer wise approach
• Multifield effects
• Multilayered plates
• Piezoelectric layers
• Refined models

Notes

Comparison between classical, refined and three-dimensional models for the thickness ratio a/h = 5. The non-dimensional values are the maximum amplitudes in the plane.

Comparison between classical, refined and three-dimensional models for the thickness ratio. The non-dimensional values are the maximum amplitudes in the plane.

Comparison between classical, refined and three-dimensional models for the thickness ratio. The non-dimensional values are the maximum amplitudes in the plane

Comparison between classical, refined and three-dimensional models for the thickness ratio. The dimensional values are the maximum amplitudes in the plane. Displacements are in 10⁻¹² m, stresses are in 10⁻¹ Pa and electric potential is in V.

The non-dimensional values are in particular points in the plane. Cylindrical loads which mean that the only dimension a affects the results.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.

Thermo-electro-mechanical variables evaluated by means of classical and refined two-dimensional models. The dimensional values are the maximum amplitudes in the plane.