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<p>We present and analyze a new hybridizable discontinuous Galerkin method for the Reissner–Mindlin plate bending problem. Our method is based on the formulation utilizing Helmholtz Decomposition. Then the system is decomposed into three problems: two trivial Poisson problems and a perturbed saddle-point problem. We apply HDG scheme for these three problems. This scheme yields the optimal convergence rate which is uniform with respect to the plate thickness on general polygonal meshes. Implementation is provided to illustrate the efficient of our new method. Numerical methods show that our method is truly locking-free on general polygonal meshes.</p>

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Locking-Free HDG Methods for Reissner–Mindlin Plates Equations on Polygonal Meshes

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Gang Chen,
  • Lu Zhang,
  • Shangyou Zhang

摘要

We present and analyze a new hybridizable discontinuous Galerkin method for the Reissner–Mindlin plate bending problem. Our method is based on the formulation utilizing Helmholtz Decomposition. Then the system is decomposed into three problems: two trivial Poisson problems and a perturbed saddle-point problem. We apply HDG scheme for these three problems. This scheme yields the optimal convergence rate which is uniform with respect to the plate thickness on general polygonal meshes. Implementation is provided to illustrate the efficient of our new method. Numerical methods show that our method is truly locking-free on general polygonal meshes.