A novel alpha finite element method ( αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements
The paper presents an alpha finite element method ( αFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains. Three-node triangular ( αFEM-T3) and four-node tetrahedral ( αFEM-T4) elements wit...
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| Vydáno v: | Computer methods in applied mechanics and engineering Ročník 197; číslo 45; s. 3883 - 3897 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
15.08.2008
Elsevier |
| Témata: | |
| ISSN: | 0045-7825, 1879-2138 |
| On-line přístup: | Získat plný text |
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| Abstract | The paper presents an alpha finite element method (
αFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains. Three-node triangular (
αFEM-T3) and four-node tetrahedral (
αFEM-T4) elements with a scale factor
α are formulated for two-dimensional (2D) and three-dimensional (3D) problems, respectively. The essential idea of the method is the use of a scale factor
α
∈
[0,1] to obtain a combined model of the standard fully compatible model of the FEM and a quasi-equilibrium model of the node-based smoothed FEM (N-SFEM). This novel combination of the FEM and N-SFEM makes the best use of the upper bound property of the N-SFEM and the lower bound property of the standard FEM. Using meshes with the same aspect ratio, a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems. The proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation. Numerical results for 2D (using
αFEM-T3) and 3D (using
αFEM-T4) problems confirm that the present method gives the much more accurate solution comparing to both the standard FEM and the N-SFEM with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems. |
|---|---|
| AbstractList | The paper presents an alpha finite element method (
αFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains. Three-node triangular (
αFEM-T3) and four-node tetrahedral (
αFEM-T4) elements with a scale factor
α are formulated for two-dimensional (2D) and three-dimensional (3D) problems, respectively. The essential idea of the method is the use of a scale factor
α
∈
[0,1] to obtain a combined model of the standard fully compatible model of the FEM and a quasi-equilibrium model of the node-based smoothed FEM (N-SFEM). This novel combination of the FEM and N-SFEM makes the best use of the upper bound property of the N-SFEM and the lower bound property of the standard FEM. Using meshes with the same aspect ratio, a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems. The proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation. Numerical results for 2D (using
αFEM-T3) and 3D (using
αFEM-T4) problems confirm that the present method gives the much more accurate solution comparing to both the standard FEM and the N-SFEM with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems. The paper presents an alpha finite element method (alphaFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be generated automatically for arbitrarily complicated domains. Three-node triangular (alphaFEM-T3) and four-node tetrahedral (alphaFEM-T4) elements with a scale factor alpha are formulated for two-dimensional (2D) and three-dimensional (3D) problems, respectively. The essential idea of the method is the use of a scale factor alpha [0,1] to obtain a combined model of the standard fully compatible model of the FEM and a quasi-equilibrium model of the node-based smoothed FEM (N-SFEM). This novel combination of the FEM and N-SFEM makes the best use of the upper bound property of the N-SFEM and the lower bound property of the standard FEM. Using meshes with the same aspect ratio, a unified approach has been proposed to obtain a nearly exact solution in strain energy for linear problems. The proposed elements are also applied to improve the accuracy of the solution of nonlinear problems of large deformation. Numerical results for 2D (using alphaFEM-T3) and 3D (using alphaFEM-T4) problems confirm that the present method gives the much more accurate solution comparing to both the standard FEM and the N-SFEM with the same number of degrees of freedom and similar computational efforts for both linear and nonlinear problems. |
| Author | Liu, G.R. Lam, K.Y. Nguyen-Thoi, T. |
| Author_xml | – sequence: 1 givenname: G.R. surname: Liu fullname: Liu, G.R. organization: Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore – sequence: 2 givenname: T. surname: Nguyen-Thoi fullname: Nguyen-Thoi, T. email: g0500347@nus.edu.sg organization: Center for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576, Singapore – sequence: 3 givenname: K.Y. surname: Lam fullname: Lam, K.Y. organization: School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore |
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| Keywords | Finite element method (FEM) Lower bound Upper bound Alpha finite element method ( αFEM) Numerical methods Node-based smoothed finite element method (N-SFEM) High strain Strain energy Triangular finite element Tetrahedral shape Scale factor Aspect ratio Modeling Exact solution Finite element method System with n degrees of freedom Numerical methods;Finite element method (FEM);Node-based smoothed finite element method (N-SFEM);Upper bound;Lower bound;Alpha finite element method (aFEM) Non linear effect |
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αFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be... The paper presents an alpha finite element method (alphaFEM) for computing nearly exact solution in energy norm for mechanics problems using meshes that can be... |
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| SubjectTerms | Alpha finite element method ( αFEM) Computational techniques Exact sciences and technology Finite element method (FEM) Fundamental areas of phenomenology (including applications) Lower bound Mathematical methods in physics Node-based smoothed finite element method (N-SFEM) Numerical methods Physics Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Upper bound |
| Title | A novel alpha finite element method ( αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements |
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