Title of Paper:Weak-form element differential method for solving mechanics and heat conduction problems with abruptly changed boundary conditions

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Date of Publication:2020-08-30

Journal:INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

Included Journals:SCIE

Volume:121

Issue:16

Page Number:3722-3741

ISSN No.:0029-5981

Key Words:element differential method; finite element method; heat conduction; solid mechanics; strong-weak-form method

Abstract:Element differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher computational efficiency and it is more stable than other strong-form methods. However, due to the utilization of strong-form equations for all nodes, EDM become not so accurate when solving problems with abruptly changed boundary conditions. To overcome this weakness, in this article, the weak-form formulations are introduced to replace the original formulations of element internal nodes in EDM, which produce a new strong-weak-form method, named as weak-form element differential method (WEDM). WEDM has advantages in both the computational accuracy and the numerical stability when dealing with the abruptly changed boundary conditions. Moreover, it can even achieve higher accuracy than finite element method (FEM) in some cases. In this article, the computational accuracy of EDM, FEM, and WEDM are compared and analyzed. Meanwhile, several examples are performed to verify the robustness and efficiency of the proposed WEDM.