Isogeometric analysis for accurate 3D stress recovery of thick laminated composite plates using higher-order shear deformation theory

Accurate stress prediction in laminated composite plates plays a crucial role in the reliable design of such structures. However, achieving 3D stress predictions with a high accuracy-to-cost ratio remains challenging. Although plate models are more efficient compared to 3D solids, they are unable to capture out-of-plane stresses directly. Additionally, for thick plates, classical and first-order shear deformation plate theories fail to accurately predict stress distributions. To address this significant challenge for thick composite plates, the present paper proposes an equilibrium-based 3D stress recovery method, combining Higher-Order Shear Deformation Theory (HSDT) with Isogeometric Analysis (IGA). HSDT can model nonlinear transverse shear deformations without the need for shear correction factors, thereby improving the accuracy of stress predictions. The proposed method first solves for the deflections using a Galerkin isogeometric formulation, followed by the computation of the required in-plane stress derivatives. It then directly enforces the strong-form stress equilibrium to capture the out-of-plane stresses. IGA's smooth, high-order basis functions enable the precise reconstruction of out-of-plane stresses in laminated structures with complex anisotropic couplings. Numerical validations against analytical solutions and three-dimensional finite element results demonstrate the accuracy and efficiency of the proposed method across various laminate configurations.