Finite strip analysis of cracked laminate: Stress based plane strain approach

Stress based finite strip model is developed for analysis of cracked laminate. Plane strain state is assumed and finite strip method is formulated. Total complementary potential energy is minimized and fourth order Euler Lagrange governing equations are presented. This stress based plane strain approach analyzes general lay up and loading conditions. It provides flexibility to control the number of finite strip nodal lines within each lamina hence stress behavior can be predicted across each lamina at desired location of the structure. It enhances the capability of stress based approach by differentiating stress behavior near and away from the crack tip. Boundary conditions including natural boundary conditions are imposed appropriately to solve governing Euler's equations. Results from this current semi analytical model are compared with analytical models available in literature. These are also compared with already available generalized plane strain based finite strip model for cracked laminate which evaluates displacements as unknowns by minimizing total potential energy. This work has extended the analysis of the cracked laminate by developing it with stress based finite strip approach which is applicable to any layup including non cross ply structures. Limitations of this model due to plane strain approach are discussed and results are compared with array of examples from the available literature.