Application of hybrid-Trefftz finite element method to frictional contact problems

  • Qing-Hua Qin Australian National University
  • Ke-Yong Wang Tianjin University

Abstract

A contact algorithm, based on the hybrid-Trefftz (HT) finite element method (FEM), is developed for the solution of contact problems with Coulomb friction. Contact conditions are directly imposed with the aid of a direct constraint approach. On the other hand, static condensation technique is used to reduce the contact system to a smaller one which involves nodes within the potential contact surfaces only so that it may save computing time significantly. The final contact interface equation is constructed by considering contact conditions as additional equations. An incremental-iterative algorithm is introduced to determine proper load increments and find correct contact conditions. The applicability and accuracy of the proposed approach are demonstrated through three numerical problems.

Keywords

References

[1] W.J. Chen, X.W. Li. Equivalence between iterative method and nonlinear complementary method for two dimensional contact problems with friction. Engrg. Mech., 18: 33-38, 200l.
[2] J.A.T. Freitas, Hybrid-Trefftz displacement and stress elements for elastodynamic analysis in the frequency domain. CAMES, 4: 345-368, 1997.
[3] J. Jirousek, L. Guex. The hybrid-Trefftz finite element model and its application to plate bending. Int. J. Num. Meth. Engrg., 23: 651-693, 1986.
[4] J. Jirousek, N. Leon. A powerful finite element for plate bending. Compo Meth. Appl. Mech. Engrg., 12: 77-96, 1977.
[5] J. Jirousek, Q.H. Qin. Application of Hybrid-Trefftz element approach to transient heat conduction analysis. Comp. Struct., 58: 195-201, 1996.
[6] J. Jirousek, A. Venkatesh. Hybrid Trefftz plane elasticity elements with p-method capabilities. Int. J. Num. Meth. Engrg., 35: 1443- 1472, 1992.
[7] J. Jirousek, A. Venkatesh, A.P. Zieliński, H. Rabemantantsoa. Comparative study of p extensions based on conventional assumed displacement and hybrid-Trefftz FE models. Comp. Struct., 46: 261-278, 1993.
[8] J. Jirousek, A. Wróblewski. T-elements: State of the art and future trends. Arch. Comp. Meth. Engrg., 3: 323-434, 1996.
[9] J. Jirousek, A. Wróblewski, B. Szybiński. A new 12 DOF quadrilateral element for analysis of thick and thin plates. Int. J. Num. Meth. Engrg., 38: 2619-2638, 1995.
[10] S.Y. Ma. The solution of two-dimensional frictionless elastic contact problems using boundary element method. J. Hebei Instit. Technol., 2: 11-21, 1984.
[11] D. Martin, M.H. Aliabadi. Boundary element analysis of two-dimensional elastoplastic contact problems. Engrg. Anal. Boundary Elem., 21: 349-360, 1998.
[12] K. Peters, E. Stein, W. Wagner. A new boundary-type finite element for 2-D- and 3-D-elastic structures. Int. J. Num. Meth. Engrg., 37: 1009-102, 19945
[13] Q.H. Qin. Hybrid Trefftz finite element approach for plate bending on an elastic foundation. Appl. Math. Modelling, 18: 334-339, 1994.
[14] Q.H. Qin. Post buckling analysis of thin plates by a hybrid Trefftz finite element method. Compo Meth. Appl. Mech. Engrg., 128: 123-136, 1995.
[15] Q.H. Qin. Nonlinear analysis of thick plates by HT FE approach. Compo Struct., 61: 271-281, 1996.
[16] Q.H. Qin. Transient plate bending analysis by hybrid Trefftz element approach. Commun. Num. Meth. Engrg., 12: 609-616, 1996.
[17] Q.H. Qin. Postbuckling analysis of thin plates on an elastic foundation by HT FE approach. Appl. Math. Modelling, 21: 547-556, 1997.
[18] Q.H. Qin. Advances in hybrid-Trefftz finite element method. Adv. Mech., 28: 71-82, 1998.
[19] Q.H. Qin. The Trefftz Finite and Boundary Element Method. WIT Press, Southampton, 2000.
[20] Q.H. Qin. Dual variational formulation for Trefftz finite element method of elastic materials. Mech. Res. Commun., 31: 321-330, 2004.
[21] Q.H. Qin. Trefftz finite element method and its applications. Appl. Mech. Rev., 58: 316-337, 2005.
[22] Q.H. Qin. Formulation of hybrid Trefftz finite element method for elastoplasticity. Appl. Math. Modelling, 29: 235-252, 2005.
[23] Q.H. Qin, S. Diao. Nonlinear analysis of thick plates on an elastic foundation by HT FE with p-extension capabilities. Int. J. Solids Struct., 33: 4583-4604, 1996.
[24] Q.H. Qin, X.Q. He. Variational principles, FE and MPT for analysis of non-linear impact-contact problems. Comp. Meth. Appl. Mech. Engry., 122: 205-222, 1995.
[25] E. Trefftz. Ein Gegenstuck zum Ritz'schen Verfahren. In: Proc. the 2nd International Congress on Applied Mechanics, Zurich, Switzerland, 1926; pp. 131-137.
[26] K.Y. Wang, Q.H. Qin, Y.L. Kang, J.S. Wang, C.Y. Qu. A direct constrain-Trefftz FEM for analysing elastic contract problems. Int. J. Num. Meth. Engrg., 63: 1694-1718, 2005.
[27] E. Wilson. The static condensation algorithm. Int. J. Num. Meth. Engrg., 8: 199-203, 1974.
[28] J.X. Xu, S.Y. Long. A new load scaling technique for frictional contact problems-Accurate load increment technique used to bring target-pair into contact without causing either under- or over- loading. J. Hunan Univ., 25: 23-26, 1998.
[29] Y.H. Zhang, M.C. Xi, C.S. Cheng. Computational Methods and their Algorithms. Science Press, Beijing, 2000.
[30] A.P. Zieliński. Trefftz method: elastic and elastoplastic problems. Camp. Meth. Appl. Meeh. Engrg., 69: 185- 204, 1988.
[31] A.P. Zieliński, O.C. Zienkiewicz. Generalized finite element analysis with T-complete solution functions. Int. J. Num. Meth. Engrg., 21: 509-528, 1985.
Published
Jul 20, 2022
How to Cite
QIN, Qing-Hua; WANG, Ke-Yong. Application of hybrid-Trefftz finite element method to frictional contact problems. Computer Assisted Methods in Engineering and Science, [S.l.], v. 15, n. 3-4, p. 319-336, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/739>. Date accessed: 22 nov. 2024.
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Vol 15 No 3-4 (2008)
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Articles