Weak‐form element differential method for solving mechanics and heat conduction problems with abruptly changed boundary conditions

Summary 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 n...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 121; no. 16; pp. 3722 - 3741
Main Authors: Zheng, Yong‐Tong, Gao, Xiao‐Wei, Lv, Jun, Peng, Hai‐Feng
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 30.08.2020
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Subjects:
Accuracy
Boundary conditions
Conduction heating
Conductive heat transfer
element differential method
Finite element method
heat conduction
Mathematical analysis
Nodes
Numerical methods
Numerical stability
Problem solving
Robustness (mathematics)
solid mechanics
strong‐weak‐form method
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:Summary 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.
Bibliography:Funding information
National Natural Science Foundation of China, 11672061; 11702054; 11772083
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6379