Finite rotation exact geometry solid‐shell element for laminated composite structures through extended SaS formulation and 3D analytical integration

Abstract

SummaryA nonlinear exact geometry hybrid‐mixed four‐node solid‐shell element using the sampling surfaces (SaS) formulation is developed for the analysis of the second Piola‐Kirchhoff stress that extends the authors' finite element (Int J Numer Methods Eng. 2019;117:498‐522) to laminated composite shells. The SaS formulation 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 of these surfaces as basic shell unknowns. The external surfaces and interfaces are also included into a set of SaS. The proposed hybrid‐mixed solid‐shell element is based on the Hu‐Washizu variational principle and is completely free of shear and membrane locking. The tangent stiffness matrix is evaluated by efficient three‐dimensional (3D) analytical integration. As a result, the developed exact geometry solid‐shell element exhibits a superior performance in the case of coarse meshes and allows the use of load increments, which are much larger than possible with existing displacement‐based solid‐shell elements. It could be useful for the 3D stress analysis of thick and thin doubly curved laminated composite shells because the SaS formulation gives the possibility to obtain the 3D solutions with a prescribed accuracy.