Summary
A procedure for numerical, high precision finite element calculation of stresses in Kirchhoff plates is proposed. Constant curvature triangles in mixed form are used. They represent a minimum of complementary energy for concentrated loads at the vertices. Moment isolines have been used for steering of a remeshing design code based on uniform distribution of a priori error estimates. The successive meshes are smoothed by an r-method and finally locally enriched guided by local a posteriori error estimates.
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References
Morgenstern, D: Herleitung der Plattentheorie aus der dreidimensionalen Elasticitätsteori, Arc. Rat. Mech. Anal. 4 (1959) 145–152.
Timoshenko, S.: Theory of Plates and Shells, Mc Graw Hill, New York 19 40.
Babuska, I. and Scaloppa, T.: Benchmark Computation and Performance Evaluation for a Rhombic Plate Bending Problem, Int. J. Numerical Meth. in Eng. 28 (1989) 155–179.
Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech. 12 (1945) 69–76.
Mindlin, R.D.: Influence of rotatory intertia and shear in fluxural motions of isotropic elastic plates. J. Appl. Mech. 18 (1951) 31–38.
Zienkiewicz, O.C.; Taylor, R.L.; Papadopolous, P.: Onate, E.: Plate bending elements with discrete constraints: new triangular elements. Int. J. Num. Meth. Eng. 1989.
Arnold, D.N.; Falk, R.S.: A uniformly accurate finite element method for Mindlin-Reissner plate. Num. Math. 1989.
Zienkiewicz, O.C.; Zhu, J.Z.: The Essential Ingredients of Engineering FEM Analysis. Benchmark 19 89, p. 9.
Herrmann, L.R.: Finite-element bending analysis for plates. J. Eng. Mech. Div. ASCE, V. 93, EM5 (1967) 13–26.
Hellan, K.: Analysis of elastic plates in flexure by a simplified finite element method. Acta Polytechnica Scandinavica, CI46, Trondheim 1967.
Visser, W.: A Refined Mixed-Type Plate Bending Element. AIAA Journal, 7, (1969) 1801–1804.
Johnson, C.: On the convergence of some mixed element methods in plate bending problems, Num. Meth. 21, 1973.
Eriksson, K. and Johnsson, C.: An adaptive finite element method for linear elliptic problems. Math. of Comp. 50 (1988) 361–383.
Rank, E; and Zienkiewicz, O.C.; A simple error estimator in the finite element method. Coram. Appl. Num. Meth. 5, 1988.
Jin, H.; Wiberg, N-E.: Two-dimensional mesh generation, adaptive remeshing and refinement, under publication.
Zienkiewicz, O.C. and Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Num. Eng. 24 (1987) 337–357
Löhner, R.; Morgan, K.; Zienkiewicz, O.C.: Adaptive grid refinement in finite element computations, in Accuracy Estimates, Wiley (1986) 281–297.
Akesson, B..: Rationalization of Lévy’s Plate Solution. Trans. Chalmers Univ. of Technology 252, Göteborg 1961.
Koiter, W.T. and Alblas, J.B.: On the Bending of Cantilever, Rectangular Plates, Proc. k. Ned. Ak. Wet. (B) 1954.
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Kjellman, M., Samuelsson, A. (1990). A High-Precision Adaptive Procedure for Solving Kirchhoff Plates. In: Kuhn, G., Mang, H. (eds) Discretization Methods in Structural Mechanics. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49373-7_12
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DOI: https://doi.org/10.1007/978-3-642-49373-7_12
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