Analytical elasticity solution for accurate prediction of localized stresses in laminated composites under patch loading

Abstract

Discontinuous patch-type loads cause highly localized stresses which can initiate failures like crack and delamination, and thus must be predicted accurately for efficient design of structures. This paper presents an iterative analytical elasticity solution for accurate stress analysis of laminated composite beams with arbitrary support conditions under a transverse patch loading. The beam is divided into segments with and without the patch loading. The governing equations are derived in the mixed form by employing the Reissner-type mixed variational principle and solved analytically for each segment using the multiterm extended Kantorovich approach. As both displacements and stresses are primary variables, the solution ensures the point-wise satisfaction of inter-layer and inter-segment continuity and boundary conditions. The accuracy of the solution is established by comparing the present numerical results with exact elasticity solutions available in literature for simply-supported edge conditions and compared with finite element solutions of Abaqus for other boundary conditions. An extensive numerical study is performed, and benchmark results are provided for various composite and sandwich laminates, thickness ratios, and boundary conditions under different cases of distributed patch load. The behavior of laminated metal-composite beams is also studied for patch loading, which reveals that thin aluminum layers on the composite beam are highly efficient and effective in reducing the stress concentration in the vicinity of patch load. The presented benchmark results will be beneficial to assess the accuracy and efficacy of different beam theories and elasticity-based approximate models for the analysis of multilayered anisotropic beams subjected to discontinuous loads.