Energy based a-posteriori error estimation and adaptive finite element analysis of laminated composite plates

The characteristics of laminated composite plates clearly emphasize the need to have highly accurate assessment of response of localized regions in addition to determining the global response. This requires control of modelling and discretization error for the quantities of interest. A procedure to estimate discretization errors in displacement based laminated composite plate finite element models, and to guide refinement in order to achieve a specified level of accuracy is developed. The analysis is based on classical laminate and first order shear deformation theories. Linear quadrilateral elements of conforming and non-conforming type based on isoparametric formulation are used. The proposed h-refinement strategy is based on weighted average energy norm of the error in stress resultants and enhanced by strain energy density ratios. The error estimator is a node-patch based analogue of the Zienkiewicz-Zhu super convergent element patch based estimator. Uniform and adaptive refinement strategies are used. A comparison of the proposed estimator is made with the existing energy based estimators. Numerical examples are solved to demonstrate its efficiency over the conventional refinement strategy in the relative improvement of global asymptotic convergence.