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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| Veröffentlicht in: | Computer methods in applied mechanics and engineering Jg. 197; H. 45; S. 3883 - 3897 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
15.08.2008
Elsevier |
| Schlagworte: | |
| ISSN: | 0045-7825, 1879-2138 |
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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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| Cites_doi | 10.1002/nme.1620310502 10.1002/cnm.721 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A 10.1016/0045-7825(86)90107-6 10.1002/nme.972 10.1142/S0219876205000661 10.1002/nme.1620261205 10.1061/JSDEAG.0003877 10.1002/nme.1620170504 10.1007/s00466-006-0075-4 10.1002/cnm.967 10.1002/nme.1968 10.1016/S0045-7825(01)00281-X 10.1016/S0045-7825(03)00460-2 10.1115/1.3171737 10.1016/j.finel.2007.05.009 10.1002/nme.1620100602 10.1002/(SICI)1097-0207(19980815)42:7<1181::AID-NME402>3.0.CO;2-P 10.1142/S0219876206001132 10.1002/nme.1620200911 10.1002/nme.151 10.1002/nme.877 10.1002/(SICI)1097-0207(20000330)47:9<1549::AID-NME842>3.0.CO;2-K 10.1016/0045-7825(85)90113-6 10.1016/0045-7949(84)90197-4 10.1002/nme.1133 10.1016/0045-7825(90)90168-L 10.1016/S0045-7949(99)00095-4 10.1002/nag.1610020105 10.1002/nme.2384 |
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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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| References | Simo, Hughes (bib29) 1986; 53 Pian, Sumihara (bib37) 1984; 20 Johnson (bib23) 1987 Hughes (bib24) 1987 F. Cugnon, Automatisation des calculs elements finis dans le cadre de la methode-p, Universite de Lie, Ph.D. Thesis, 2000. Xie (bib38) 2005; 21 Allman (bib1) 1984; 19 Cook (bib31) 1974; 100 Liu, Nguyen, Dai, Lam (bib12) 2007; 71 Dai, Liu, Nguyen (bib13) 2007; 43 Belytschko, Bachrach (bib35) 1986; 54 FEM), Comput. Mech. (revised). Reddy (bib27) 2004 Zienkiewicz, Taylor (bib26) 2000 Flanagan, Belytschko (bib34) 1981; 17 Timoshenko, Goodier (bib30) 1970 Zhou, Nie (bib39) 2001; 51 Liu, Dai, Nguyen (bib43) 2007; 39 Cook (bib4) 1991; 31 Arnold (bib16) 1990; 82 Fredriksson, Ottosen (bib32) 2004; 61 Liu, Zhang, Dai, Wang, Zhong, Li, Han (bib10) 2005; 2 Piltner, Taylor (bib5) 2000; 75 Chen, Wu, Yoon, You (bib8) 2000; 50 Bathe (bib22) 1996 Mijuca, Berković (bib19) 1998 Liu, Quek (bib25) 2003 G.R. Liu, T.T. Nguyen, X.H. Nguyen, K.Y. Lam, A node-based smoothed finite element method for upper bound solution to solid problems (N-SFEM), Comput. Struct. (Revised). Rong, Lu (bib18) 2003; 192 Yoo, Moran, Chen (bib9) 2004; 60 T.T. Nguyen, G.R. Liu, K.Y. Lam, A FEM using scaled gradient of strains with scaling factor alpha (alpha-FEM), in: Proceeding of the International Conference on Computational Methods 2007 (ICCM07), 2007, p. 194. Pian, Wu (bib28) 2006 Kosloff, Frazier (bib36) 1978; 2 Xie, Zhou (bib40) 2004; 59 Liu, Li, Dai, Luan, Xue (bib11) 2006; 3 G.R. Liu, G.Y. Zhang, Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM), Int. J. Numer. Method Engrg. in press (Published online 8 Oct, 2007). Almeida Pereira (bib41) 2008; 24 Dohrmann, Heinstein, Jung, Key, Witkowski (bib7) 2000; 47 Bergan, Felippa (bib3) 1985; 50 G.R Liu, T.T. Nguyen, K.Y. Lam, A novel FEM by scaling the gradient of strains with scaling factor Allman (bib2) 1988; 26 Rong, Lu (bib17) 2001; 191 Taylor, Beresford, Wilson (bib33) 1976; 10 Dohrmann, Key, Heinstein, Jung (bib6) 1998; 42 Timoshenko (10.1016/j.cma.2008.03.011_bib30) 1970 Liu (10.1016/j.cma.2008.03.011_bib10) 2005; 2 Reddy (10.1016/j.cma.2008.03.011_bib27) 2004 10.1016/j.cma.2008.03.011_bib20 10.1016/j.cma.2008.03.011_bib42 Allman (10.1016/j.cma.2008.03.011_bib2) 1988; 26 Liu (10.1016/j.cma.2008.03.011_bib12) 2007; 71 10.1016/j.cma.2008.03.011_bib21 Kosloff (10.1016/j.cma.2008.03.011_bib36) 1978; 2 Cook (10.1016/j.cma.2008.03.011_bib31) 1974; 100 Allman (10.1016/j.cma.2008.03.011_bib1) 1984; 19 Zienkiewicz (10.1016/j.cma.2008.03.011_bib26) 2000 Liu (10.1016/j.cma.2008.03.011_bib11) 2006; 3 Yoo (10.1016/j.cma.2008.03.011_bib9) 2004; 60 Johnson (10.1016/j.cma.2008.03.011_bib23) 1987 Dohrmann (10.1016/j.cma.2008.03.011_bib6) 1998; 42 Simo (10.1016/j.cma.2008.03.011_bib29) 1986; 53 Pian (10.1016/j.cma.2008.03.011_bib37) 1984; 20 Rong (10.1016/j.cma.2008.03.011_bib18) 2003; 192 Dai (10.1016/j.cma.2008.03.011_bib13) 2007; 43 Rong (10.1016/j.cma.2008.03.011_bib17) 2001; 191 Pian (10.1016/j.cma.2008.03.011_bib28) 2006 Liu (10.1016/j.cma.2008.03.011_bib25) 2003 Cook (10.1016/j.cma.2008.03.011_bib4) 1991; 31 Taylor (10.1016/j.cma.2008.03.011_bib33) 1976; 10 10.1016/j.cma.2008.03.011_bib14 10.1016/j.cma.2008.03.011_bib15 Arnold (10.1016/j.cma.2008.03.011_bib16) 1990; 82 Bathe (10.1016/j.cma.2008.03.011_bib22) 1996 Bergan (10.1016/j.cma.2008.03.011_bib3) 1985; 50 Dohrmann (10.1016/j.cma.2008.03.011_bib7) 2000; 47 Almeida Pereira (10.1016/j.cma.2008.03.011_bib41) 2008; 24 Fredriksson (10.1016/j.cma.2008.03.011_bib32) 2004; 61 Flanagan (10.1016/j.cma.2008.03.011_bib34) 1981; 17 Piltner (10.1016/j.cma.2008.03.011_bib5) 2000; 75 Hughes (10.1016/j.cma.2008.03.011_bib24) 1987 Xie (10.1016/j.cma.2008.03.011_bib40) 2004; 59 Chen (10.1016/j.cma.2008.03.011_bib8) 2000; 50 Zhou (10.1016/j.cma.2008.03.011_bib39) 2001; 51 Xie (10.1016/j.cma.2008.03.011_bib38) 2005; 21 Liu (10.1016/j.cma.2008.03.011_bib43) 2007; 39 Belytschko (10.1016/j.cma.2008.03.011_bib35) 1986; 54 Mijuca (10.1016/j.cma.2008.03.011_bib19) 1998 |
| References_xml | – reference: G.R. Liu, G.Y. Zhang, Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM), Int. J. Numer. Method Engrg. in press (Published online 8 Oct, 2007). – reference: G.R. Liu, T.T. Nguyen, X.H. Nguyen, K.Y. Lam, A node-based smoothed finite element method for upper bound solution to solid problems (N-SFEM), Comput. Struct. (Revised). – year: 2004 ident: bib27 article-title: An Introduction to Nonlinear Finite Element Analysis – volume: 82 start-page: 281 year: 1990 end-page: 300 ident: bib16 article-title: Mixed finite element methods for elliptic problems publication-title: Comput. Method Appl. Mech. Engrg. – reference: G.R Liu, T.T. Nguyen, K.Y. Lam, A novel FEM by scaling the gradient of strains with scaling factor – volume: 2 start-page: 57 year: 1978 end-page: 72 ident: bib36 article-title: Treatment of hourglass patterns in low order finite element codes publication-title: Int. J. Numer. Anal. Method Geomech. – reference: ( – volume: 54 start-page: 279 year: 1986 end-page: 301 ident: bib35 article-title: Efficient implementation of quadrilaterals with high coarse-mesh accuracy publication-title: Comput. Method Appl. Mech. Engrg. – volume: 42 start-page: 1181 year: 1998 end-page: 1197 ident: bib6 article-title: A least squares approach for uniform strain triangular and tetrahedral finite elements publication-title: Int. J. Numer. Method Engrg. – volume: 100 start-page: 1851 year: 1974 end-page: 1863 ident: bib31 article-title: Improved two-dimensional finite element publication-title: J. Struct. Div., ASCE – year: 1970 ident: bib30 article-title: Theory of Elasticity – volume: 71 start-page: 902 year: 2007 end-page: 930 ident: bib12 article-title: Theoretical aspects of the smoothed finite element method (SFEM) publication-title: Int. J. Numer. Method Engrg. – volume: 26 start-page: 2645 year: 1988 end-page: 2655 ident: bib2 article-title: Evaluation of the constant strain triangle with drilling rotations publication-title: Int. J. Numer. Method Engrg. – volume: 10 start-page: 1211 year: 1976 end-page: 1219 ident: bib33 article-title: A non-conforming element for stress analysis publication-title: Int. J. Numer. Method Engrg. – volume: 61 start-page: 1809 year: 2004 end-page: 1834 ident: bib32 article-title: Fast and accurate four-node quadrilateral publication-title: Int. J. Numer. Method Engrg. – volume: 43 start-page: 847 year: 2007 end-page: 860 ident: bib13 article-title: An publication-title: Finite Elem. Anal. Des. – year: 1987 ident: bib24 article-title: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis – volume: 17 start-page: 679 year: 1981 end-page: 706 ident: bib34 article-title: A uniform strain hexahedron and quadrilateral with orthogonal hourglass control publication-title: Int. J. Numer. Method Engrg. – volume: 19 start-page: 1 year: 1984 end-page: 8 ident: bib1 article-title: A compatible triangular element including vertex rotations for plane elasticity analysis publication-title: Comput. Struct. – volume: 50 start-page: 25 year: 1985 end-page: 69 ident: bib3 article-title: A triangular membrane element with rotational degrees of freedom publication-title: Comput. Method Appl. Mech. Engrg. – reference: FEM), Comput. Mech. (revised). – year: 1987 ident: bib23 article-title: Numerical Solution of Partial Differential Equations by the Finite Element Method – volume: 51 start-page: 181 year: 2001 end-page: 202 ident: bib39 article-title: A combined hybrid approach to finite element schemes of high performance publication-title: Int. J. Numer. Method Engrg. – reference: F. Cugnon, Automatisation des calculs elements finis dans le cadre de la methode-p, Universite de Lie, Ph.D. Thesis, 2000. – volume: 53 start-page: 51 year: 1986 end-page: 54 ident: bib29 article-title: On the variational foundations of assumed strain methods publication-title: J. Appl. Mech. – volume: 47 start-page: 1549 year: 2000 end-page: 1568 ident: bib7 article-title: Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes publication-title: Int. J. Numer. Method Engrg. – volume: 24 start-page: 157 year: 2008 end-page: 165 ident: bib41 article-title: Hybrid equilibrium hexahedral elements and super-elements publication-title: Commun. Numer. Method Engrg. – year: 2000 ident: bib26 article-title: The Finite Element Method – year: 2006 ident: bib28 article-title: Hybrid and Incompatible Finite Element Methods – year: 1996 ident: bib22 article-title: Finite Element Procedures – volume: 59 start-page: 293 year: 2004 end-page: 313 ident: bib40 article-title: Optimization of stress modes by energy compatibility for four-node hybrid quadrilaterals publication-title: Int. J. Numer. Method Engrg. – year: 1998 ident: bib19 article-title: On the efficiency of the primal-mixed finite element scheme publication-title: Advances in Computational Structured Mechanics – year: 2003 ident: bib25 article-title: The Finite Element Method: A Practical Course – volume: 192 start-page: 4981 year: 2003 end-page: 5000 ident: bib18 article-title: Generalized mixed variational principles and solutions for ill-conditioned problems in computational mechanics: Part II. Shear locking publication-title: Comput. Method Appl. Mech. Engrg. – volume: 2 start-page: 645 year: 2005 end-page: 665 ident: bib10 article-title: A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems publication-title: Int. J. Comput. Method – volume: 60 start-page: 861 year: 2004 end-page: 890 ident: bib9 article-title: Stabilized conforming nodal integration in the natural-element method publication-title: Int. J. Numer. Method Engrg. – volume: 31 start-page: 825 year: 1991 end-page: 835 ident: bib4 article-title: Modified formulations for nine-dof plane triangles that include vertex rotations publication-title: Int. J. Numer. Method Engrg. – reference: T.T. Nguyen, G.R. Liu, K.Y. Lam, A FEM using scaled gradient of strains with scaling factor alpha (alpha-FEM), in: Proceeding of the International Conference on Computational Methods 2007 (ICCM07), 2007, p. 194. – volume: 191 start-page: 407 year: 2001 end-page: 422 ident: bib17 article-title: Generalized mixed variational principles and solutions for ill-conditioned problems in computational mechanics: Part I. Volumetric locking publication-title: Comput. Method Appl. Mech. Engrg. – volume: 75 start-page: 361 year: 2000 end-page: 368 ident: bib5 article-title: Triangular finite elements with rotational degrees of freedom and enhanced strain modes publication-title: Comput. Struct. – volume: 21 start-page: 1 year: 2005 end-page: 12 ident: bib38 article-title: An accurate hybrid macro-element with linear displacements publication-title: Commun. Numer. Method Engrg. – volume: 50 start-page: 435 year: 2000 end-page: 466 ident: bib8 article-title: A stabilized conforming nodal integration for Galerkin meshfree method publication-title: Int. J. Numer. Method Engrg. – volume: 39 start-page: 859 year: 2007 end-page: 877 ident: bib43 article-title: A smoothed finite element method for mechanics problems publication-title: Comput. Mech. – volume: 3 start-page: 401 year: 2006 end-page: 428 ident: bib11 article-title: A Linearly conforming radial point interpolation method for solid mechanics problems publication-title: Int. J. Comput. Method – volume: 20 start-page: 1685 year: 1984 end-page: 1695 ident: bib37 article-title: Rational approach for assumed stress finite elements publication-title: Int. J. Numer. Method Engrg. – volume: 31 start-page: 825 year: 1991 ident: 10.1016/j.cma.2008.03.011_bib4 article-title: Modified formulations for nine-dof plane triangles that include vertex rotations publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1620310502 – year: 2006 ident: 10.1016/j.cma.2008.03.011_bib28 – volume: 21 start-page: 1 year: 2005 ident: 10.1016/j.cma.2008.03.011_bib38 article-title: An accurate hybrid macro-element with linear displacements publication-title: Commun. Numer. Method Engrg. doi: 10.1002/cnm.721 – volume: 50 start-page: 435 year: 2000 ident: 10.1016/j.cma.2008.03.011_bib8 article-title: A stabilized conforming nodal integration for Galerkin meshfree method publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A – year: 1970 ident: 10.1016/j.cma.2008.03.011_bib30 – ident: 10.1016/j.cma.2008.03.011_bib42 – ident: 10.1016/j.cma.2008.03.011_bib21 – year: 1998 ident: 10.1016/j.cma.2008.03.011_bib19 article-title: On the efficiency of the primal-mixed finite element scheme – volume: 54 start-page: 279 year: 1986 ident: 10.1016/j.cma.2008.03.011_bib35 article-title: Efficient implementation of quadrilaterals with high coarse-mesh accuracy publication-title: Comput. Method Appl. Mech. Engrg. doi: 10.1016/0045-7825(86)90107-6 – year: 1987 ident: 10.1016/j.cma.2008.03.011_bib24 – volume: 60 start-page: 861 year: 2004 ident: 10.1016/j.cma.2008.03.011_bib9 article-title: Stabilized conforming nodal integration in the natural-element method publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.972 – volume: 2 start-page: 645 issue: 4 year: 2005 ident: 10.1016/j.cma.2008.03.011_bib10 article-title: A linearly conforming point interpolation method (LC-PIM) for 2D solid mechanics problems publication-title: Int. J. Comput. Method doi: 10.1142/S0219876205000661 – volume: 26 start-page: 2645 issue: 12 year: 1988 ident: 10.1016/j.cma.2008.03.011_bib2 article-title: Evaluation of the constant strain triangle with drilling rotations publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1620261205 – volume: 100 start-page: 1851 issue: ST6 year: 1974 ident: 10.1016/j.cma.2008.03.011_bib31 article-title: Improved two-dimensional finite element publication-title: J. Struct. Div., ASCE doi: 10.1061/JSDEAG.0003877 – volume: 17 start-page: 679 year: 1981 ident: 10.1016/j.cma.2008.03.011_bib34 article-title: A uniform strain hexahedron and quadrilateral with orthogonal hourglass control publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1620170504 – volume: 39 start-page: 859 year: 2007 ident: 10.1016/j.cma.2008.03.011_bib43 article-title: A smoothed finite element method for mechanics problems publication-title: Comput. Mech. doi: 10.1007/s00466-006-0075-4 – volume: 24 start-page: 157 issue: 2 year: 2008 ident: 10.1016/j.cma.2008.03.011_bib41 article-title: Hybrid equilibrium hexahedral elements and super-elements publication-title: Commun. Numer. Method Engrg. doi: 10.1002/cnm.967 – volume: 71 start-page: 902 year: 2007 ident: 10.1016/j.cma.2008.03.011_bib12 article-title: Theoretical aspects of the smoothed finite element method (SFEM) publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1968 – volume: 191 start-page: 407 year: 2001 ident: 10.1016/j.cma.2008.03.011_bib17 article-title: Generalized mixed variational principles and solutions for ill-conditioned problems in computational mechanics: Part I. Volumetric locking publication-title: Comput. Method Appl. Mech. Engrg. doi: 10.1016/S0045-7825(01)00281-X – volume: 192 start-page: 4981 year: 2003 ident: 10.1016/j.cma.2008.03.011_bib18 article-title: Generalized mixed variational principles and solutions for ill-conditioned problems in computational mechanics: Part II. Shear locking publication-title: Comput. Method Appl. Mech. Engrg. doi: 10.1016/S0045-7825(03)00460-2 – year: 1987 ident: 10.1016/j.cma.2008.03.011_bib23 – ident: 10.1016/j.cma.2008.03.011_bib14 – year: 1996 ident: 10.1016/j.cma.2008.03.011_bib22 – volume: 53 start-page: 51 year: 1986 ident: 10.1016/j.cma.2008.03.011_bib29 article-title: On the variational foundations of assumed strain methods publication-title: J. Appl. Mech. doi: 10.1115/1.3171737 – volume: 43 start-page: 847 year: 2007 ident: 10.1016/j.cma.2008.03.011_bib13 article-title: An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2007.05.009 – year: 2003 ident: 10.1016/j.cma.2008.03.011_bib25 – volume: 10 start-page: 1211 year: 1976 ident: 10.1016/j.cma.2008.03.011_bib33 article-title: A non-conforming element for stress analysis publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1620100602 – ident: 10.1016/j.cma.2008.03.011_bib20 – year: 2004 ident: 10.1016/j.cma.2008.03.011_bib27 – volume: 42 start-page: 1181 year: 1998 ident: 10.1016/j.cma.2008.03.011_bib6 article-title: A least squares approach for uniform strain triangular and tetrahedral finite elements publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/(SICI)1097-0207(19980815)42:7<1181::AID-NME402>3.0.CO;2-P – volume: 3 start-page: 401 issue: 4 year: 2006 ident: 10.1016/j.cma.2008.03.011_bib11 article-title: A Linearly conforming radial point interpolation method for solid mechanics problems publication-title: Int. J. Comput. Method doi: 10.1142/S0219876206001132 – volume: 20 start-page: 1685 year: 1984 ident: 10.1016/j.cma.2008.03.011_bib37 article-title: Rational approach for assumed stress finite elements publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1620200911 – volume: 51 start-page: 181 year: 2001 ident: 10.1016/j.cma.2008.03.011_bib39 article-title: A combined hybrid approach to finite element schemes of high performance publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.151 – volume: 59 start-page: 293 year: 2004 ident: 10.1016/j.cma.2008.03.011_bib40 article-title: Optimization of stress modes by energy compatibility for four-node hybrid quadrilaterals publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.877 – volume: 47 start-page: 1549 year: 2000 ident: 10.1016/j.cma.2008.03.011_bib7 article-title: Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/(SICI)1097-0207(20000330)47:9<1549::AID-NME842>3.0.CO;2-K – volume: 50 start-page: 25 year: 1985 ident: 10.1016/j.cma.2008.03.011_bib3 article-title: A triangular membrane element with rotational degrees of freedom publication-title: Comput. Method Appl. Mech. Engrg. doi: 10.1016/0045-7825(85)90113-6 – volume: 19 start-page: 1 issue: 2 year: 1984 ident: 10.1016/j.cma.2008.03.011_bib1 article-title: A compatible triangular element including vertex rotations for plane elasticity analysis publication-title: Comput. Struct. doi: 10.1016/0045-7949(84)90197-4 – volume: 61 start-page: 1809 year: 2004 ident: 10.1016/j.cma.2008.03.011_bib32 article-title: Fast and accurate four-node quadrilateral publication-title: Int. J. Numer. Method Engrg. doi: 10.1002/nme.1133 – volume: 82 start-page: 281 year: 1990 ident: 10.1016/j.cma.2008.03.011_bib16 article-title: Mixed finite element methods for elliptic problems publication-title: Comput. Method Appl. Mech. Engrg. doi: 10.1016/0045-7825(90)90168-L – volume: 75 start-page: 361 year: 2000 ident: 10.1016/j.cma.2008.03.011_bib5 article-title: Triangular finite elements with rotational degrees of freedom and enhanced strain modes publication-title: Comput. Struct. doi: 10.1016/S0045-7949(99)00095-4 – year: 2000 ident: 10.1016/j.cma.2008.03.011_bib26 – volume: 2 start-page: 57 year: 1978 ident: 10.1016/j.cma.2008.03.011_bib36 article-title: Treatment of hourglass patterns in low order finite element codes publication-title: Int. J. Numer. Anal. Method Geomech. doi: 10.1002/nag.1610020105 – ident: 10.1016/j.cma.2008.03.011_bib15 doi: 10.1002/nme.2384 |
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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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