T-element analysis of plates on unilateral elastic Winkler-type foundation

• Autorzy: Jirousek J. , Zieliński A. P. , Wróblewski A.
• Konferencja: International Workshop on the Trefftz Method (2 ; 1999 ; Lisbon, Portugal)
• Języki publikacji: EN

Abstrakty

EN

This paper presents a hybrid-Trefftz finite element algorithm designated as fictitious load approach. Its originality resides in the formulation and practical application of concepts which make it possible to account for the unilateral contact conditions of a plate without modification of the finite element mesh. To reach this aim, the approach allows the movable interface between the contact and non-contact parts of the plate to travers any finite element subdomain. The adjustments are confined to fictitious load dependent terms, while the element stiffness matrices remain unchanged during the whole iterative process. Several numerical examples are analysed to assess the effectivity of the T-element algorithm and to compare it with some of the existing solutions of the same problem. Keywords: finite elements, Trefftz method, contact problem

Słowa kluczowe

EN

Trefftz method

PL

metoda Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2001
• Tom: Vol. 8, No. 2-3
• Strony: 343--358
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr.

Twórcy

autor

Jirousek J.

• LSC-DGC, Swiss Federal Institute of Technology, CH-1015 Lousanne, Switzerland

autor

Zieliński A. P.

• Institute of Mechanics and Machine Design, Cracow University of Technology, al. Jana Paw0la II 37, 30-864 Krak´ow, Poland

autor

Wróblewski A.

• Institute of Mechanics and Machine Design, Cracow University of Technology, al. Jana Paw0la II 37, 30-864 Krak´ow, Poland

Bibliografia

• [1] G. Bezine. A new boundary element method for bending of plates on elastic foundations. Int. J. Solids Struct., 24(6):556–565, 1988.
• [2] J.A. Costa and C.A. Brebia. The boundary element method applied to plates on elastic foundations. Engng. Anal., 2(4):174–183, 1985.
• [3] I. Herrera. Boundary Methods – an Algebraic Theory. Pitman Advanced Publishing Program, Boston-London-Melbourne, 1984.
• [4] X. Jiarun and X. Shouze. Application of LCEM of the plate bending problems with contact conditions. In Proceedings of the Fifth East Asia–Pacific Conference on Structural Engineering and Construction, pages 139–144, Queensland, Australia, 1995.
• [5] J. Jirousek. Basis for development of large finite elements locally satisfying all field equations. Comput. Methods Appl. Mech. Engrg., 14:65–92, 1978.
• [6] J. Jirousek. Structural analysis program SAFE – Special features and advanced finite element models. Adv. in Engng Software, 7:68–76, 1985.
• [7] J. Jirousek. T–elements: An approach uniting the advantages of finite element and boundary element methods. In Proc. XI Polish Conference on Comput. Methods in Mech., pages 21–40, Kielce–Cedzyna, Poland, 1993.
• [8] J. Jirousek and N. Leon. A powerful finite element for plate bending. Comput. Methods Appl. Mech. Engrg., 12:77–96, 1977.
• [9] J. Jirousek and M. Stojek. Numerical assessment of a new T–element approach. Comput. Struct., 57(3):367–378, 1995.
• [10] J. Jirousek, A. Venkatesh, A.P. Zieli´nski, and H. Rabemanantsoa. Comperative study of p-extensions based on conventional assumed displacement and hybrid–Trefftz models. Comput. Struct., 46:261–278, 1993.
• [11] J. Jirousek and A. Wróblewski. T–elements: State of the art and future trends. Arch. Comput. Meth. Engng, 8(4), 1996.
• [12] J. Jirousek and A.P. Zieliński. Study of two complementary hybrid–Trefftz p–element formulations. In C. Hirsch, O.C. Zienkiewicz, and E. O˜nate, editors, Numerical Methods in Engineering ’92, Proc. First European Conf. on Numer. Methods in Engng, pages 583–590, Brussels, 1992. Elsevier.
• [13] J. Jirousek and A.P. Zieliński. Survey of Trefftz–type element formulations. Comput. Struct., 63:225– 242, 1997.
• [14] J.T. Katsikadelis at al. Plates on elastic foundation by B.I.E. methods. J. Engng. Mech., 110(7):1086– 1105, 1984.
• [15] R. Lewandowski and R. Świtka. Unilateral plate contact with the elastic–plastic Winkler–type foundation. Computer & Structures, 39(6):641–651, 1991
• [16] J. Puttonen and P. Varpasuo. Boundary element analysis of a plate on elastic foundations. Int. J. Numer. Methods Engng, 23:287–303, 1984.
• [17] S. Timoshenko and S. Woinowsky–Krieger. Theory of Plates and Shells. McGraw–Hill Book Company, Inc., New York-Toronto-London, 1959
• [18] B. Xiaoming and Y. Zhongda. Bending problems of rectangular thin plate with free edges laid on tensionless Winkler foundation. Appl. Math. Mech., 10(5):435–442, 1989.