Abstract
Moderate and finite rotation theories [7] [4] [6] are available including the finite element analysis, especially the treatment of shear locking problems. The five parameter shell model used in this paper is based on geometrically non-linear Reissner-Mindlin kinematics where the finite element formulation may be derived using the Biot— or 2. Piola— Kirchhoff stress resultants, alternatively. The description of finite rotations of the shell normal is expressed in terms of a scew-symmetric tensor.
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References
Babuška I. & Miller A.: A feedback finite element method with a posteriori error estimates: Part I. The finite element mothod and some properties of the a posteriori estimator, Comp. Meth. Appl. Mech. Engng. 61 (1987).
Babuška I. & Rheinhodt W.C.: Error estimates for adaptive finite element computations, SIAM Journal on Numerical Analysis 15 (1978) 736–754.
Johnson, C. and Hansbo, P.: Adaptive finite element methods in computational mechanics, Comp. Meth. Appl. Mech. Engng. 101 (1992) 143–181.
Gruttmann F., Stein E. & Wriggers P.: Theory and Numerics of Thin Elastic Shells with Finite Rotations, Ingenieur Archiv 59 (1989) 54–67.
Rheinboldt W.C.: Error estimates for nonlinear finite element computations. Computers and Structures Vol. 20 (1985) pp. 91–98.
Simo J.C., Fox D.D. & Rifai M.S.: On a Stress Resultant Geometrically Exact Shell Model, Part III: Computational Aspects of the Nonlinear Theory, Comp. Meth. Appl. Mech. Engng. 79 (1990) 21–70.
Stein E., Rust W. & Ohnimus S.: h-and d-adaptive FE element methods for two dimensional structural problems including post-buckling of shells, In: Proceedings of the Second Workshop on Reliability in Computational Mechanics (Krakov, 1991), Comp. Meth. Appl. Mech. Engng. 101 (1992) 315–354.
Stein E. & Ohnimus S.: Concept and realisation of integrated adaptive finite element methods in solid-and structural-mechanics in: Proceedings of the First European Conference on Numerical Methods in Engeneering (7-11 Sept. 1992, Brussels, Belgium), Int. J. Num. Meth. Eng. (1992) 163-170.
Stein, E. & Carstensen, C. & Scifert, B. & Ohnimus, S.: Adaptive finite element analysis of geometrically non-linear plates and shells, especially Buckling, Int. J. Num. Meth. Eng., in press.
Verfürth R.: A posteriori error estimates for non-linear problems. Finite element discretizations of elliptic equations (preprint 1993).
Zienkiewicz O.C. & Zhu J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Num. Meth. Eng. 24 (1987) 337–357.
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© 1994 Springer Fachmedien Wiesbaden
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Stein, E., Seifert, B., Ohnimus, S. (1994). Selfadaptive FE—approach of shell buckling and postcritical solution branches including dimensional recovery in disturbed subdomains. In: Jentsch, L., Tröltzsch, F. (eds) Problems and Methods in Mathematical Physics. TEUBNER-TEXTE zur Mathematik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-85161-1_18
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DOI: https://doi.org/10.1007/978-3-322-85161-1_18
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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