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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| Vydané v: | International journal for numerical methods in engineering Ročník 121; číslo 16; s. 3722 - 3741 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Hoboken, USA
John Wiley & Sons, Inc
30.08.2020
Wiley Subscription Services, Inc |
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| Abstract | 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. |
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| AbstractList | 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. 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. 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. |
| Author | Gao, Xiao‐Wei Lv, Jun Peng, Hai‐Feng Zheng, Yong‐Tong |
| Author_xml | – sequence: 1 givenname: Yong‐Tong orcidid: 0000-0001-5690-1340 surname: Zheng fullname: Zheng, Yong‐Tong organization: Dalian University of Technology – sequence: 2 givenname: Xiao‐Wei orcidid: 0000-0001-5818-4058 surname: Gao fullname: Gao, Xiao‐Wei organization: Dalian University of Technology – sequence: 3 givenname: Jun surname: Lv fullname: Lv, Jun organization: Dalian University of Technology – sequence: 4 givenname: Hai‐Feng orcidid: 0000-0003-3657-2564 surname: Peng fullname: Peng, Hai‐Feng email: hfpeng@dlut.edu.cn organization: Dalian University of Technology |
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| Cites_doi | 10.1016/j.ijheatmasstransfer.2017.08.039 10.1007/b13382 10.1016/j.jcp.2008.03.027 10.1016/j.cma.2018.06.021 10.1006/jcph.1998.6165 10.1016/j.enganabound.2005.05.011 10.1002/nme.4693 10.1016/j.ijheatmasstransfer.2018.05.100 10.1007/978-3-642-48860-3 10.1017/CBO9780511605345 10.1007/s00466-004-0610-0 10.1016/0045-7949(72)90020-X 10.1002/nme.1602 10.1007/s00466-019-01799-9 10.1016/j.ijmecsci.2018.12.032 10.1002/nme.715 10.1002/nme.5193 10.1002/nme.5604 10.1080/10407790.2018.1461491 10.1016/S0045-7825(96)01078-X 10.1016/j.apm.2018.11.036 10.1016/j.ijheatmasstransfer.2018.07.155 10.1016/j.jcp.2010.11.023 10.1016/j.camwa.2019.05.026 10.1002/nme.1733 10.1016/j.enganabound.2015.01.011 10.1007/s11012-014-0014-y 10.1016/j.enganabound.2014.05.006 10.1016/0045-7949(80)90149-2 10.1016/j.cma.2015.01.006 |
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Element differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher... Element differential method (EDM), as a newly proposed numerical method, has been applied to solve many engineering problems because it has higher... |
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| SubjectTerms | 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 |
| Title | Weak‐form element differential method for solving mechanics and heat conduction problems with abruptly changed boundary conditions |
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