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First-order VEM for Reissner-Mindlin plates

机译:用于 Reissner-Mindlin 板的一阶 VEM

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摘要

In this paper, a first-order virtual element method for Reissner-Mindlin plates is presented. A standard displacement-based variational formulation is employed, assuming transverse displacement and rotations as independent variables. In the framework of the first-order virtual element, a piecewise linear approximation is assumed for both displacement and rotations on the boundary of the element. The consistent term of the stiffness matrix is determined assuming uncoupled polynomial approximations for the generalized strains, with different polynomial degrees for bending and shear parts. In order to mitigate shear locking in the thin-plate limit while keeping the element formulation as simple as possible, a selective scheme for the stabilization term of the stiffness matrix is introduced, to indirectly enrich the approximation of the transverse displacement with respect to that of the rotations. Element performance is tested on various numerical examples involving both thin and thick plates and different polygonal meshes.
机译:该文提出了一种Reissner-Mindlin板的一阶虚元方法。采用基于标准位移的变分公式,假设横向位移和旋转为自变量。在一阶虚拟单元的框架中,假设单元边界上的位移和旋转都采用分段线性近似。刚度矩阵的一致项是假设广义应变的非耦合多项式近似确定的,弯曲和剪切部分具有不同的多项式次数。为了在保持单元公式尽可能简单的同时减轻薄板极限的剪切锁定,引入了刚度矩阵稳定项的选择方案,以间接丰富横向位移相对于旋转位移的近似值。在涉及薄板和厚板以及不同多边形网格的各种数值示例上测试了单元性能。

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