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Two New Quadrilateral Elements Based on Strain States | ||
Civil Engineering Infrastructures Journal | ||
مقاله 10، دوره 48، شماره 1، شهریور 2015، صفحه 133-156 اصل مقاله (1.03 M) | ||
نوع مقاله: Research Papers | ||
شناسه دیجیتال (DOI): 10.7508/ceij.2015.01.010 | ||
نویسندگان | ||
Mohammad Rezaiee-Pajand* 1؛ Majid Yaghoobi2 | ||
1Professor, Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran | ||
2Ph.D. Candidate, Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran | ||
چکیده | ||
In this paper, two new quadrilateral elements are formulated to solve plane problems. Low sensitivity to geometric distortion, no parasitic shear error, rotational invariance, and satisfying the Felippa pure bending test are characteristics of these suggested elements. One proposed element is formulated by establishing equilibrium equations for the second-order strain field. The other suggested element is obtained by establishing equilibrium equations only for the linear part of the strain field. The number of the strain states decreases when the conditions among strain states are satisfied. Several numerical tests are used to demonstrate the performance of the proposed elements. Famous elements, which were suggested by other researchers, are used as a means of comparison. It is shown that these novel elements pass the strong patch tests, even for extremely poor meshes, and one of them has an excellent accuracy and fast convergence in other complicated problems. | ||
کلیدواژهها | ||
Equilibrium Conditions؛ Optimization Criteria؛ Plane Problems؛ Quadrilateral Elements؛ Strain States | ||
مراجع | ||
Allman, D.J. (1984). "A compatible triangular element including vertex rotations for plane elasticity analysis", Computers and Structures, 19(1-2), 1-8. Andelfinger, U. and Ramm, E. (1993). "EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements", International Journal for Numerical Methods in Engineering, 36(8), 1311-1337. Bergan, P.G. and Felippa, C.A. (1985). "A triangular membrane element with rotational degrees of freedom", Computer Methods in Applied Mechanics and Engineering, 50(1), 25-69. Cen, S. Chen, X.M. and Fu, X.R. (2007). "Quadrilateral membrane element family formulated by the quadrilateral area coordinate method", Computer Methods in Applied Mechanics and Engineering, 196(41-44), 4337-4353. Cen, S. Chen, X.M. Li, C.F. and Fu, X.R. (2009). "Quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method (QACM-II)", International Journal for Numerical Methods in Engineering, 77(8), 1172-1200. Chen, X.M. Cen, S. Long, Y.Q. and Yao, Z.H. (2004). "Membrane elements insensitive to distortion using the quadrilateral area coordinate method", Computers and Structures, 82(1), 35-54. Choi, N. Choo, Y.S. and Lee, B.C. (2006). "A hybrid Trefftz plane elasticity element with drilling degrees of freedom", Computer Methods in Applied Mechanics and Engineering, 195(33-36), 4095-4105. Choo, Y.S. Choi, N. and Lee, B.C. (2006). "Quadrilateral and triangular plane elements with rotational degrees of freedom based on the hybrid Trefftz method", Finite Elements in Analysis and Design, 42(11), 1002-1008. Cook, R.D. Malkus, D.S. and Plesha, M.E. (1989). Concepts and Applications of Finite Element Analysis, 3rd Edition, Wiley, New York. Cook, R.D. (1974). "Improved two-dimensional finite element", Journal of the Structural Division, ASCE, 100(ST6), 1851-1863. Cook, R.D. (1986). "On the Allman triangle and a related quadrilateral element", Computers and Structures, 22(6), 1065-1067. Dow, J.O. (1999). A unified approach to the Finite Element method and error analysis procedures, Academic Press. Felippa, C.A. and Militello, C. (1990). "The variational formulation of high performance finite elements: parametrized variational principles", Computers and Structures, 36(1), 1-11. Felippa, C.A. (2000). "Recent advances in finite element templates (Chapter 4)", In: Topping, B.H.V. (Ed.), Computational Mechanics for the Twenty-First Century, pp. 71-98, Saxe-Coburn Publications, Edinburgh. Felippa, C.A. (2003). "A study of optimal membrane triangles with drilling freedoms", Computer Methods in Applied Mechanics and Engineering, 192(16-18), 2125-2168. Felippa, C.A. (2004). "A template tutorial", In: Mathisen, K.M., Kvamsdal, T., Okstad, K.M. (Eds.), Computational Mechanics: Theory and Practice, CIMNE, Barcelona, 29-68. Felippa, C.A. (2006). "Supernatural QUAD4: a template formulation", invited contribution to J.H. Argyris Memorial Issue, Computer Methods in Applied Mechanics and Engineering, 195(41-43), 5316-5342. Fu, X.R. Cen, S. Li, C.F. and Chen, X.M. (2010). "Analytical trial function method for development of new 8-node plane element based on the variational principle containing Airy stress function", Engineering Computations, 27(4), 442-463. Ibrahimgovic, A. Taylor, R.L. and Wilson, E.L. (1990). "A robust quadrilateral membrane finite element with rotational degrees of freedom", International Journal for Numerical Methods in Engineering, 30(3), 445-457. Jirousek, J. and Venkatesh, A. (1992). "Hybrid Trefftz plane elasticity elements with p method capabilities", International Journal for Numerical Methods in Engineering, 35(7), 1443-1472. Long, Y.Q. and Xu, Y. (1994). "Generalized conforming quadrilateral membrane element with vertex rigid rotational freedom", Computers and Structures, 52(4), 749-755. Long, Z.F. Cen, S. Wang, L. Fu, X.R. and Long, Y.Q. (2010). "The third form of the quadrilateral area coordinate method (QACM-III): theory, application, and scheme of composite coordinate interpolation", Finite Elements in Analysis and Design, 46(10), 805-818. MacNeal, R.H. and Harder, R.L. (1985). "A proposed standard set of problems to test finite element accuracy", Finite Elements in Analysis and Design, 1(1), 3-20. MacNeal, R.H. and Harder, R.L. (1988). "A refined four-node membrane element with rotation degrees of freedom", Computers and Structures, 28(1), 75-84. MacNeal, R.H. (1971). The nastran theoretical manual, NASA-SP-221(01). Nygard, M.K. (1986). The free formulation for nonlinear finite elements with applications to shells, Ph.D. Dissertation, Division of Structural Mechanics, NTH, Trondheim, Norway. Paknahad, M. Noorzaei, J. Jaafar, M.S. and Thanoon, W.A. (2007). "Analysis of shear wall structure using optimal membrane triangle element", Finite Elements in Analysis and Design, 43(11-12), 861-869. Pian, T.H.H. and Sumihara, K. (1984). "Rational approach for assumed stress finite elements", International Journal for Numerical Methods in Engineering, 20(9), 1685-1695. Piltner, R. and Taylor, R.L. (1995). "A quadrilateral mixed finite element with two enhanced strain modes", International Journal for Numerical Methods in Engineering, 38(11), 1783-1808. Piltner, R. and Taylor, R.L. (1997). "A systematic constructions of B-bar functions for linear and nonlinear mixed-enhanced finite elements for plane elasticity problems", International Journal for Numerical Methods in Engineering, 44(5), 615-639. Prathap, G. and Senthilkumar, V. (2008). "Making sense of the quadrilateral area coordinate membrane elements", Computer Methods in Applied Mechanics and Engineering, 197(49-50), 4379-4382. Rezaiee-Pajand, M. and Yaghoobi, M. (2012). "Formulating an effective generalized four-sided element", European Journal of Mechanics A/Solids, 36, 141-155. Santos, H.A.F.A. and Moitinho de Almeida, J.P. (2014). "A family of Piola–Kirchhoff hybrid stress finite elements for two-dimensional linear elasticity", Finite Elements in Analysis and Design, 85, 33–49. Taylor, R.L. Beresford, P.J. and Wilson, E.L. (1976). "A non-conforming element for stress analysis", International Journal for Numerical Methods in Engineering, 10(6), 1211-1219. Wilson, E.L. Taylor, R.L. Doherty, W.P. and Ghabussi, T. (1973). "Incompatible displacement models", In: Fenven, S.T., et al. (Eds.), Numerical and Computer Methods in Structural Mechanics, pp. 43-57, Academic Press, New York. Wisniewski, K. and Turska, E. (2006). "Enhanced Allman quadrilateral for finite drilling Rotations", Computer Methods in Applied Mechanics and Engineering, 195(44-47), 6086-6109. Wisniewski, K. and Turska, E. (2008). "Improved four-node Hellingere Reissner elements based on skew coordinates", International Journal for Numerical Methods in Engineering, 76(6), 798-836. Wisniewski, K. and Turska, E. (2009). "Improved 4-node Hu-Washizu elements based on skew coordinates", Computers and Structures, 87(7-8), 407-424. Wu, C.C. Huang, M.G. and Pian, T.H.H. (1987). "Consistency condition and convergence criteria of incompatible elements: general formulation of incompatible functions and its application", Computers and Structures, 27(5), 639-644. Yeo, S.T. and Lee, B.C. (1997). "New stress assumption for hybrid stress elements and refined four-node plane and eight-node brick elements", International Journal for Numerical Methods in Engineering, 40(16), 2933-2952. | ||
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