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Keywords:
Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method
Reissner-Mindlin plate model; mixed-interpolated elements; weight minimization; penalty method
Summary:
The problem to find an optimal thickness of the plate in a set of bounded Lipschitz continuous functions is considered. Mean values of the intensity of shear stresses must not exceed a given value. Using a penalty method and finite element spaces with interpolation to overcome the “locking” effect, an approximate optimization problem is proposed. We prove its solvability and present some convergence analysis.
References:
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[2] Hlaváček, I.: Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method. Appl. Math. 39 (1994), 375–394. MR 1288150
[3] Brezzi, F. – Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, Berlin, 1991. MR 1115205
[4] Brezzi, F. – Fortin, M. – Stenberg, R.: Error analysis of mixed-interpolated elements for Reissner-Mindlin plates. Math. Models and Meth. in Appl. Sci. 1 (1991), 125–151. DOI 10.1142/S0218202591000083 | MR 1115287
[5] Ciarlet, P.G.: Basic error estimates for elliptic problems. Handbook of Numer. Analysis, ed. by P. G. Ciarlet and J. L. Lions. vol. II, North-Holland, Amsterdam, 1991, pp. 17–352. MR 1115237
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