An Extension of Variational Stress Analysis of Laminates Containing Regions with Different Material Properties in Loading Direction Using the Ply Refinement Technique

Abstract

This work extends the applicability of a recent variational model that has been used for analyzing laminates to determine the stress state in a laminate with alternating material properties in the longitudinal direction subject to tensile and bending loading. For simplicity, a plane stress problem was assumed in this study. The laminate was subdivided in the longitudinal (tensile loading) direction as in the previous analysis. In addition, the laminate was subdivided in the thickness direction by using the ply refinement technique. To introduce the ply refinement technique and to account for continuity boundary conditions between divided regions in the loading direction, the Lagrange multiplier strategy was used. Closed form expressions for the energy function derived from using the strategy led to a very concise solution for determining the approximate stresses in the laminates. As an example, a laminate with ply discontinuity was analyzed, and the resultant stress distributions were then compared to the previous variational analysis model and finite element method (FEM). Compared to the previous analysis, stress concentration at the region interfaces could be captured, and excellent agreement between FEM was demonstrated.