Three-dimensional stress analyses of complex laminated shells with a variable-kinematics continuum shell element

Abstract

This paper presents a new variable-kinematics continuum shell (VKCS) element that can be used to model laminated shell structures with arbitrary geometry in a finite element (FE) setting. The novelty is in the implementation of variable-kinematics capability in a continuum shell formulation, using Carrera’s Unified Formulation (CUF). The resultant model has completely general geometric and kinematic descriptions. In the formulation, the geometrical representation is based on a numerical isoparametric map with no simplifying assumptions on the shell geometry; whereas the element displacement fields are written in terms of the Fundamental Nuclei according to CUF. In the variable-kinematics framework, the levels of hp– and p–refinements in the through-thickness and in-plane domains are free parameters that can be varied independently. By parametrically varying in-plane mesh densities and model kinematics, model settings with good trade-offs in computational cost and desired level of accuracy can be identified. In addition to the existing literature benchmarks, we include new 3D stress benchmarks for laminated shells with complex geometrical features, such as spatially varying curvatures, non-orthogonal coordinate lines and variable thicknesses. The higher-order models yield asymptotically correct three-dimensional stresses, even in regions near singularities, without requiring numerical artefacts nor stress recovery procedures. In terms of computational efficiency, the model variants utilising high p-level require fewer total degrees of freedom (dofs) compared with linear 3D finite element method (FEM) for convergence of the 3D stress field. In terms of wider applications, the compact formulation can allow for the same computer code and model mesh to be used across a wide range of analyses for complex shell structures that requires different model fidelity, with minimal inputs from the user.