Energy based adaptive strategy for plates and laminates

The objective of this work is the development of a numerical solution strategy for energy-based mesh optimization based on a combined refinement strategy for laminated composite plates. In finite element computations that rely on the principle of minimum potetnial energy, the variational principle itself provides the basis of r-adaptive methods. The numerical solution can be improved by further minimizing the discrete potetnial energy with respect to material node point positions. A new adaptive scheme has been proposed and formulated for adaptive finite element analysis of laminates and plates. It involves a combination of the configurational force based r- adaption and mesh enrichment by h-refinement. These configurational forces are conjugate to the nodal motion and vanish when the potential energy is a minimum or at equilibrium. These forces are evaluated for laminates and plates by considering the weak form of the material force equilibrium. These forces assembled at nodes in a finite element discretization act as error indicators for r- adaption. The h- refinement is based on a modified patch recovery based estimator based on quantities of interest, enhanced by strain energy density ratios. Numerical study confirms that the proposed combined r - h adaption is more efficient than a purely h-adaptive approach and more flexible than a purely r-adaptive approach with better convergence characteristics.