Jacobian weighted element differential method for solid mechanics

• Published in: Journal of computational science 2023-07, Vol.71, p.102038, Article 102038
• Main Authors: Liu, Hua-Yu, Gao, Xiao-Wei, Zhang, Gui-Yong, Yang, Kai
• Format: Article
• Language: English
• Subjects: Collocation method; Element differential method; Gradient evaluation; Green–Gauss formula; Jacobian weighting
• ISSN: 1877-7503; 1877-7511
• DOI: 10.1016/j.jocs.2023.102038

In this paper, a novel collocation method is proposed to solve the problems in solid mechanics. In the proposed method, the gradients across the element boundaries are evaluated by a weight-averaging algorithm to achieve higher order continuity. Then, the collocation method is employed to discretize the governing equations for all domain nodes, including the nodes at the interfaces of elements for which the earlier collocation methods have to use the traction-equilibrium equations. As a result of this difference, linear and serendipity elements can be used in the proposed method to reduce the total number of freedoms and easily used for very complex geometries. Moreover, the proposed method significantly improves the accuracy compared with the earlier collocation methods. The provided numerical test cases show that the method can also avoid the degeneration of accuracy when odd-order elements are employed, which further demonstrates the advantages of the proposed method. The proposed method are also leads to better convergency in nonlinear cases and iterative matrix solver. By analyzing the coefficient matrix, we found that the proposed method is better conditioned. The proposed method also yields promising advantages in transient problems for explicit time marching because of the advantage of the collocation methods. •A novel collocation method is proposed for solving problems in solid mechanics.•A weighing procedure is used to evaluate the gradient across the element boundaries.•The proposed method is much accurate and stable for two- and three-dimension problems.•The proposed method can prevent the loss of accuracy when odd-order elements are employed.