Some continuous stress mixed formulations and inf-sup test

• Autorzy: Berkovic M. , Mijuca D. , Grozdanović Ines
• Języki publikacji: EN

Abstrakty

EN

The most frequent motivation for the use of mixed methods is their robustness in the presence of certain limiting and extreme situations. At variance, the main goal of the present paper is to reconsider the use of mixed formulation as a tool for wider application, i.e., to study the stability of the proposed procedure treating problems in elasticity otherwise well suited for the solution by the usual displacement method. Computational procedure for the inf-sup test is outlined, and the results are given.

Słowa kluczowe

EN

mixed finite element method; inf-sup test

PL

metoda mieszanych elementów skończonych

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2001
• Tom: Vol. 8, No. 1
• Strony: 141--153
• Opis fizyczny: Bibliogr. 15 poz., rys., wykr.

Twórcy

autor

Berkovic M.

• Faculty of Mathematics, P. O. Box 550, Studentski Trg 16, 11000 Belgrade, Yugoslavia

autor

Mijuca D.

• Faculty of Mathematics, P. O. Box 550, Studentski Trg 16, 11000 Belgrade, Yugoslavia

autor

Grozdanović Ines

• Faculty of Mining and Geology, Djugina 7, 11 000 Belgrade, Yugoslavia

Bibliografia

• [1] D.N. Arnold. Mixed finite element methods for elliptic problems. Computer Methods in Applied Mechanics and Engineering, 82: 281-300, 1990.
• [2] I. Babuška. On the inf-sup (Babuśka-Brezzi) condition. TICAM Forum # 5, 1996.
• [3] M. Berković, Z. Drašković. Stress continuity in the finite element analysis. In: J. Robinson, ed., Accuracy, Reliability and Training in FEM Technology, pp. 110-118. Robinson and Associates, 1984.
• [4] M. Berković, Z. Drašković. An efficient solution procedure in mixed finite element analysis. NUMETA 85, pp. 625-633. Balkema, Rotterdam, 1985.
• [5] M. Berković, Z. Drašković. On the essential mechanical boundary conditions in two-field finite element approximations. Computer Methods in Applied Mechanics and Engineering, 91: 1339-1355, 1991.
• [6] M. Berković, Z. Drašković. A two-field finite element model related to the Reissner's principle. Theoretical and Applied Mechanics, 20: 17-36, 1994.
• [7] M. Berković, Z. Drašković, D. Mijuca. A direct block spare solution of the mixed finite element equations. Computer Assisted Mechanics and Engineering Sciences, 5: 21-30, 1998.
• [8] M. Berković, D. Mijuca. An efficient continuous stress mixed model based on the Reissner’s principle. World Congress on Computational Mechanics, Buenos Aires, 1998.
• [9] J.H. Bramble, J.E. Pasciak, A.T. Vassilev. Analysis of the inexact Uzawa algorithm for sadle point problems. SIAM Numer. Anal., 34, 1997.
• [10] F. Brezzi, M. Fortin. Mixed and Hybrid Finite Elemenet Methods. Springer-Verlag, New York, 1991.
• [11] F. Brezzi, M. Fortin, D. Marini. Mixed finite elemen methods with continous stresses. Mathematical Models and Methods in Applied Sciences, 3: 275-287, 1993. Springer-Verlag, New York, 1991.
• [12] D. Chapelle, K.J. Bathe. The inf-sup test. Computers and Structures, 47: 537-545, 1993.
• [13] F.A. Mirza, M.D. Olson. The mixed finite element in plane elasticity. International Journal of Numerical Methods in Engineering, 15: 273-289, 1980.
• [14] 0.C. Zienkiewicz, J.Z. Zhu, R.L. Taylor, S. Naka: The patch test for mixed formulations. International Journal of Numerical Methods in Engineering, 23: 1873-1883, 1986.
• [15] 0.C. Zienkiewicz, R.L. Taylor. The Finite Element Method, Vol. I. McGraw-Hill, London, 1989.