Details
| Original language | English |
|---|---|
| Pages (from-to) | 695-727 |
| Number of pages | 33 |
| Journal | Applied Mathematical Modelling |
| Volume | 66 |
| Early online date | 14 Oct 2018 |
| Publication status | Published - Feb 2019 |
| Externally published | Yes |
Abstract
Many rectangular plate elements developed in the history of finite element method (FEM) have displayed excellent numerical properties, yet their applications have been limited due to inability to conform to the arbitrary geometry of plates and shells. Numerical manifold method (NMM), considered to be a generalization of FEM, can easily solve this issue by viewing a mesh made up of rectangular elements as mathematical cover. In this study, ACM element (Adini and Clough element from A. Adini, R.W. Clough, Analysis of plate bending by the finite element method, University of California, 1960), a typical rectangular plate element is first integrated in the framework of NMM. Then, vibration analysis of arbitrary shaped thin plates is conducted employing the tailored NMM. Using the definition of integral of scalar functions on manifolds, we developed a mathematically rigorous mass lumping scheme for creating a symmetric and positive definite lumped mass matrix that is easy to inverse. A series of numerical experiments have been studied and analyzed, including free and forced vibration of thin plates with various shapes, validating the proposed mass lumping scheme can supersede the consistent mass formulation in those cases.
Keywords
- Forced vibration, Free vibration, Kirchhoff's plates, Lumped mass matrix, Numerical manifold method, Vibration analysis
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Applied Mathematical Modelling, Vol. 66, 02.2019, p. 695-727.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Numerical manifold method for vibration analysis of Kirchhoff's plates of arbitrary geometry
AU - Guo, Hongwei
AU - Zheng, Hong
AU - Zhuang, Xiaoying
N1 - Funding information: This study is supported by the National Natural Science Foundation of China , under the Grant Nos. 11172313 and 51538001 .
PY - 2019/2
Y1 - 2019/2
N2 - Many rectangular plate elements developed in the history of finite element method (FEM) have displayed excellent numerical properties, yet their applications have been limited due to inability to conform to the arbitrary geometry of plates and shells. Numerical manifold method (NMM), considered to be a generalization of FEM, can easily solve this issue by viewing a mesh made up of rectangular elements as mathematical cover. In this study, ACM element (Adini and Clough element from A. Adini, R.W. Clough, Analysis of plate bending by the finite element method, University of California, 1960), a typical rectangular plate element is first integrated in the framework of NMM. Then, vibration analysis of arbitrary shaped thin plates is conducted employing the tailored NMM. Using the definition of integral of scalar functions on manifolds, we developed a mathematically rigorous mass lumping scheme for creating a symmetric and positive definite lumped mass matrix that is easy to inverse. A series of numerical experiments have been studied and analyzed, including free and forced vibration of thin plates with various shapes, validating the proposed mass lumping scheme can supersede the consistent mass formulation in those cases.
AB - Many rectangular plate elements developed in the history of finite element method (FEM) have displayed excellent numerical properties, yet their applications have been limited due to inability to conform to the arbitrary geometry of plates and shells. Numerical manifold method (NMM), considered to be a generalization of FEM, can easily solve this issue by viewing a mesh made up of rectangular elements as mathematical cover. In this study, ACM element (Adini and Clough element from A. Adini, R.W. Clough, Analysis of plate bending by the finite element method, University of California, 1960), a typical rectangular plate element is first integrated in the framework of NMM. Then, vibration analysis of arbitrary shaped thin plates is conducted employing the tailored NMM. Using the definition of integral of scalar functions on manifolds, we developed a mathematically rigorous mass lumping scheme for creating a symmetric and positive definite lumped mass matrix that is easy to inverse. A series of numerical experiments have been studied and analyzed, including free and forced vibration of thin plates with various shapes, validating the proposed mass lumping scheme can supersede the consistent mass formulation in those cases.
KW - Forced vibration
KW - Free vibration
KW - Kirchhoff's plates
KW - Lumped mass matrix
KW - Numerical manifold method
KW - Vibration analysis
UR - http://www.scopus.com/inward/record.url?scp=85055274798&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2018.10.006
DO - 10.1016/j.apm.2018.10.006
M3 - Article
AN - SCOPUS:85055274798
VL - 66
SP - 695
EP - 727
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
SN - 0307-904X
ER -