MITC9 shell finite elements with miscellaneous through-the-thickness functions for the analysis of laminated structures

This paper focuses on developing and exploiting the potential of miscellaneous through-the-thickness approximating functions for FEM analysis of laminated composite plates/shells. Considering the theory of series expansion, Taylor series, trigonometric series, exponential functions, and miscellaneous expansions are implemented in the equivalent single layer models of Carrera Unified Formulation (CUF). Their performances in obtaining a good approximation of stress distribution through the thickness of the plate/shell are investigated by performing several static mechanical studies, and the inclusion of Murakami's zig-zag function is also evaluated. The results are compared with layer-wise theories in the framework of CUF by adopting as thickness functions both Legendre polynomials and Lagrange interpolations on Chebyshev nodes (Sampling-Surfaces method, SaS). The governing equations are derived from Principle of Virtual Displacement (PVD) and Finite Element Method (FEM) is adopted to get the numerical solutions. Nine-node 2D elements for plates and shells are employed, using Mixed Interpolation of Tonsorial Components (MITC) method to contrast the membrane and shear locking phenomenon. Simply-supported cross-ply plate and shell structures with various lay-ups and span-to-thickness ratios subjected to transverse bi-sinusoidal pressure load are analyzed. The results show that all the refined kinematic theories are able to capture the exact solution if a sufficient number of expansion (number of terms in the expansion of the displacement field) is taken, but the maximum computational cost can change for the different types of models. In some cases, combinations of different expansion theories (miscellaneous expansions) can show a significant reduction of computational costs.