#### Vol. 15, No. 3, 2020

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Bending of nonconforming thin plates based on the first-order manifold method

### Xin Qu, Fangfang Diao, Xingqian Xu and Wei Li

Vol. 15 (2020), No. 3, 325–344
##### Abstract

As the convergence, good numerical accuracy and high computing efficiency of nonconforming elements cannot be achieved simultaneously using the finite element method (FEM) or the current numerical manifold method (NMM), the first-order NMM was developed to analyze the bending of thin plates. The first-order Taylor expansion was selected to construct the local displacement function, which endowed the generalized degrees of freedom with physical meanings and decreased the rank deficiency. Additionally, the new relations between the global and local rotation functions in the first-order approximation were derived by adopting two sets of rotation functions, $\left\{{𝜃}_{xi},{𝜃}_{yi}\right\}$ and $\left\{{𝜃}_{x}^{\phantom{\rule{0.33em}{0ex}}i},{𝜃}_{y}^{\phantom{\rule{0.33em}{0ex}}i}\right\}$. Regular meshes were selected to improve the convergence performance. With the penalized formulation fitted to the NMM for Kirchhoff’s thin plate problems, a unified scheme was proposed to deal with irregular and regular boundaries of the domain. The typical examples indicated that the numerical solutions achieved using the first-order NMM rapidly converged to the analytical solutions, and the accuracy of such numerical solutions was vastly superior to that achieved using the FEM and the zero-order NMM.

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