Application of novel refined mixed finite elementmethod in the analysis of composite laminated beams

Abstract

This paper shows the application of refined finite element model developed by authors, which incorporate all the elastic equation that are, equilibrium equation, constitutive equation and kinematic equation to be satisfied explicitly at nodes. The present method considers the equilibrium equation for the refinement of the approximation function. Authors used the concept of mixed finite element model by choosing stress and displacement as the primary variable, along with the equilibrium equation as a refinement on approximation function. Ramtekkar [1] in his model restrict the arbitrary choosing of stress function by selecting the stress variation from displacement derived space, by imposing the elastic relations on the variation and then used the Minimum Potential Energy Principle to obtain the governing differential equation. In present work, authors satisfy the equilibrium equation at nodes also by considering the body forces as variables in the formulation which enables the model to satisfy the equilibrium equation explicitly at the node. The formulation is validated by the elastic beam problem solved by Pagano [2] for all three cases. Results obtained are very accurate and also shows faster convergence over the Ramtekkar [1] model.