Three-dimensional thermoelectroelastic analysis of structures with distributed piezoelectric sensors and actuators with temperature-dependent material properties

Abstract

In this paper, a geometrically exact hybrid-mixed four-node laminated solid-shell element with piezoelectric patches with temperature-dependent material properties through the sampling surfaces (SaS) formulation is developed. The SaS formulation is based on the choice of SaS, parallel to the middle surface and located at Chebyshev polynomial nodes within the layers, to introduce the temperatures, displacements and electric potentials of these surfaces as basic shell unknowns. The outer surfaces and interfaces are also included into a set of SaS. Such a choice of unknowns with the use of Lagrange polynomials in the through-thickness approximations of temperatures, temperature gradient, displacements, strains, electric potential and electric field leads to a very compact higher-order thermopiezoelectric shell formulation. To implement efficient analytical integration throughout the solid-shell element, the extended assumed natural strain method is employed for all components of the temperature gradient, strain tensor and electric field vector. The developed hybrid-mixed four-node laminated solid-shell element with piezoelectric sensors and actuators is based on the extended Hu-Washizu variational principle and shows superior performance in the case of coarse meshes. This can be useful for the three-dimensional temperature-dependent response of laminated composite shells with piezoelectric patches, since the SaS formulation allows one to obtain the numerical solutions with a prescribed accuracy, which asymptotically approach the exact solutions of thermopiezoelectricity as a number of SaS tends to infinity.