Γ-convergence of external approximations in boundary value problems involving the bi-Laplacian
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
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The paper proposes an approximation method, lumped strain method (LSM), for elastic plates based on generalized notions of the Gaussian and mean curvatures and on a relaxation of the energy functional to the space of continuous piecewise linear functions. The method adapts ideas from the theory of $\Gamma $-convergence. We restrict our attention to the case of the simply supported plate and state the proof of convergence of the method. We give an application to the rhombic plate and compare the results with those obtained by standard finite element approximations.