Composite shell finite elements with arbitrary displacement fields along the thickness

This article presents a novel methodology for constructing shell theories with fully customizable kinematic fields specifically designed for multi-layered composite shells. The proposed framework introduces the independent expansion functions for each displacement component, enabling component-specific theory refinement. This approach significantly extends the capabilities of existing shell theory formulations while maintaining computational efficiency. The present work employs an enhanced version of the Carrera unified formulation (CUF) to characterize through-thickness kinematics. The proposed framework utilizes a combination of Taylor and Lagrange polynomial expansions to construct structurally efficient shell theories. The formulation employs the finite element method for mid-surface discretization using Lagrange-type elements. To mitigate locking phenomena, the framework incorporates the mixed interpolation of tensorial components (MITC) technique. Plates and cylindrical shells are studied here. The current numerical results are validated against established reference solutions from the literature. Comprehensive accuracy assessments are performed for both displacement fields and stress distributions. These analyses reveal a strong dependence of optimal model selection on key problem parameters.