Assessment of nonlinear exact geometry sampling surfaces solid‐shell elements and ANSYS solid elements for 3D stress analysis of piezoelectric shell structures

Abstract

SummaryIn this work, the finite rotation exact geometry four‐node solid‐shell element using the sampling surfaces (SaS) method is developed for the analysis of the second Piola‐Kirchhoff stresses in laminated piezoelectric shells. The SaS method is based on choosing inside the layers the arbitrary number of SaS parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the displacements and electric potentials of these surfaces as fundamental shell unknowns. The outer surfaces and interfaces are also included into a set of SaS. To circumvent shear and membrane locking, the hybrid‐mixed solid‐shell element on the basis of the Hu‐Washizu variational principle is proposed. The tangent stiffness matrix is evaluated by 3D analytical integration throughout the finite element. This novelty provides a superior performance in the case of coarse meshes. A comparison with the SOLID226 element showed that the developed exact geometry SaS solid‐shell element allows the use of load increments, which are much larger than possible with existing displacement‐based finite elements. Thus, it can be recommended for the 3D stress analysis of doubly‐curved laminated piezoelectric shells because the SaS formulation gives the opportunity to obtain the 3D solutions of electroelasticity with a prescribed accuracy.