Thermal-elastic analysis of laminated plates based on the incompatible generalized partial mixed method

Abstract

Based on the generalized Hellinger-Reissner (H-R) mixed variational principle, the incompatible generalized partial mixed finite element method (IGPMFEM) is proposed in this paper for the thermomechanical stress analysis of laminated composites and sandwich plates. This method inherits the advantages of the generalized mixed element method, allowing for the simultaneous introduction of displacement and stress boundary conditions, and satisfies the discontinuity of the in-plane stresses at the material interface. Introduction of incompatible displacement mode adds higher-order terms in the polynomial expansion of the exact displacements, effectively improving the bending performance and the element accuracy. Although adding stress components would normally increase the computational effort, we address this issue by the elimination method, considering only the out-of-plane stress variables to reduce the matrix dimensions. The accuracy and effectiveness of the proposed method are evaluated by comparing the numerical results of this method with existing elasticity solutions, while the effect of stress boundary conditions is also investigated.