A six node refined mixed finite element model for the analysis of fiber reinforced polymer composite beams

Abstract

A refined 6-node two-dimensional mixed finite element has been developed to analyze laminated composite using the minimum potential energy principle. This model uses four primary variables, two displacements u, w and two transverse stresses σz and τxz at each node. In the formulation process, fundamental elasticity relations, that is, displacement-strain relations, stress–strain relations, and the equilibrium equations, have been explicitly satisfied. The transverse stress terms have been invoked using the displacement-strain relation and then the stress–strain relation. The refinement in the model has been performed using the equilibrium equation in the x and z direction. This formulation is an improvement over the Desai and Ramtekkar (2002) model and contributes to the computational mechanics domain of laminates analysis. Refinement in the formulation has been performed by satisfying the equilibrium equation explicitly at the nodes. This refinement helps in getting better results with a fewer number of elements. Results obtained through the model has been compared with the elastic solution given by Pagano (1969) and the mixed finite element method by Desai and Ramtekkar (2002) model. Results show excellent agreement with the elastic solution and more economical as only 2/3rd number of the element as compared to Desai and Ramtekkar (2002) model is required for the converged results.