Abstract Shear locking is a critical challenge in the finite element analysis of plates based on First-Order Shear Deformation Theory (FSDT). The Bergan–Wang (BW) formulation offers a simple and effective alternative by using a single independent variable w for bending, eliminating the need for reduced integration or assumed strain fields and performing equally well in thin and thick plate regimes. In this study, a novel quadrilateral element (Q4BW) is developed by combining the BW single-variable bending kinematics with the von Kármán strain field and thermo-mechanical coupling, enabling the geometrically nonlinear analysis of symmetric laminated composite plates under thermal loads. The governing equations are derived from the principle of virtual work and solved with the iterative Newton–Raphson method. The element is validated through patch test, linear bending, thermal buckling, and postbuckling analyses for plates with simply supported and clamped edges, using both temperature-independent and temperature-dependent material properties. Results are benchmarked against analytical solutions, 3D elasticity, higher order elements and established locking-free elements. The Q4BW element exhibits excellent accuracy across all thickness ratios, is strictly free of shear locking, and accurately traces nonlinear postbuckling paths. Its simple three-independent-degree-of-freedom formulation makes it a robust and efficient tool for advanced composite plate analysis.
Mahmoud et al. (Fri,) studied this question.