Nonlinear analysis of laminated composite shells with piezoelectric patches under displacement‐dependent pressure loads

Abstract

In this paper, the three‐dimensional stress field in nonlinear laminated composite shells with piezoelectric patches subjected to displacement‐dependent loads is analyzed. To solve the problem, the geometrically exact (GeX) hybrid‐mixed four‐node solid‐shell element has been developed. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms are taken exactly at the element nodes. The laminated solid‐shell element formulation is based on the choice of an arbitrary number of sampling surfaces (SaS) parallel to the middle surface and located at the Chebyshev polynomial nodes within the layers, in order to introduce the displacements and electric potentials of these surfaces as unknown functions. The outer surfaces and interfaces are also included into a set of SaS. Due to analytical integration utilized to evaluate the tangent stiffness matrix, the proposed GeX piezoelectric solid‐shell element under nonconservative loading exhibits superior performance in the case of coarse meshes and allows the use of only one load step in all considered benchmark problems. Therefore, it can be recommended for the large deformation analysis of doubly curved laminated composite shells with piezoelectric patches, since the SaS formulation allows one to find three‐dimensional solutions of electroelasticity with a prescribed accuracy.