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Hu Kai, Gao Xiaowei, Xu Bingbing. Strong weak coupling form element differential method for solving solid mechanics problems. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 2050-2058. DOI: 10.6052/0459-1879-22-087
 Citation: Hu Kai, Gao Xiaowei, Xu Bingbing. Strong weak coupling form element differential method for solving solid mechanics problems. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 2050-2058. DOI: 10.6052/0459-1879-22-087

# STRONG WEAK COUPLING FORM ELEMENT DIFFERENTIAL METHOD FOR SOLVING SOLID MECHANICS PROBLEMS

• Element differential method (EDM) is a new strong-form finite element method. Compared with the weak form numerical methods, the method discretizes the governing equations directly and does not need any numerical integration. Therefore, the method has a relatively simple form, and it has high efficiency in calculating the coefficient matrix. But as a strong form method, more nodes or higher-order elements are needed to achieve a satisfactory calculation accuracy in the element differential method. At the same time, for some models containing singular points which occur on multi-material interfaces, abrupt changes in the boundary conditions, and especially at crack tips, accurate calculation results can not be obtained by the conventional element differential method. In order to overcome this weakness, a coupled method combining the element differential method and finite element method (FEM) is proposed in this paper. The main idea of the coupled method is that the finite element method is used around the singular points in the geometric model and the element differential method is selected at other parts. The strong weak coupling form not only retains the advantages of the element differential method but also ensures the accuracy of solving singular problems. At the same time, when dealing with large scale problems, the finite element method is selected for key components and the element differentiation method is used for other components. This treatment can not only obtain more accurate results but also can greatly improve the overall calculation efficiency for large scale 3D problem. In this paper, two typical examples are given, one is a two-dimensional problem with notch, and the other is a complex three-dimensional engine problem. Through the calculation and analysis of these two problems, the correctness, accuracy and efficiency of the proposed coupling method in solving two-dimensional singular problem and three-dimensional large-scale problem are proved.

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