A Coupled Thermo-Hygro-Mechanical-Electro Formulation for Static and Dynamic Characteristics of Piezoelectric Structures

The characteristics of multi-physics coupling in piezoelectric materials are influenced by the hygrothermal environment. Here, the thermo-hygro-mechanical-electro coupling isogeometric analysis method (THMEC-IGA) is proposed to explore the static and dynamic responses of piezoelectric structures. The inherent high-order continuity of non-uniform rational B-spline (NURBS) basis functions has higher computational accuracy than the traditional finite element method. Based on the B-spline theory, the classical piezoelectric theory and small strain theory, the constitutive equation of piezoelectric material THMEC-IGA and the displacement and electro potential shape functions are derived through the Gibbs free energy equation. The transformation method is used to accurately solve the THMEC problem, and the essential boundary conditions are appropriately applied at the control points. The subspace iteration method and Newmark method are used to solve the free vibration and transient response of the piezoelectric structures in the hygrothermal environment. The superiority of THMEC-IGA in the THMEC problem is verified using numerical examples. The advantages of THMEC-IGA in solving multi-physical field coupling problems are verified in comparison with the finite element results. The influence of empirical constants and hygrothermal changes on the mechanical properties of piezoelectric structures is studied, providing a reference for the design and analysis of piezoelectric structures.