Multilayered plate elements accounting for refined theories and node-dependent kinematics

Abstract

Abstract In the present work, a new class of finite elements (FEs) for the analysis of metallic and composite plates is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states present a complex distribution. On the contrary, computationally cheaper, low-order kinematic assumptions can be used in the remaining parts of the plate where a localized detailed analysis is not necessary. The primary advantage of the present variable-kinematics element and related global/local approach is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. In this paper, the novel variable-kinematics plate element is implemented by utilizing the Carrera Unified Formulation (CUF), whose main advantage consists in the possibility of keeping the order of the expansion of the state variables along the thickness of the plate as a free parameter of the model. According to CUF, Taylor polynomial expansions are used to describe the through-the-thickness unknowns to develop classical to higher-order Equivalent Single Layer (ESL) plate theories. Furthermore, the Mixed Interpolated Tensorial Components (MITC) method is employed to contrast the shear locking phenomenon. Several numerical investigations are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature.