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Pms1: Partial Differential Equations with multiple scales Location: G309 Session Chair: Matthias Röger Session Chair: Ben Schweizer | |
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Derivation of Mindlin-Timoshenko model from nonlinear elasticity. 1: Humboldt-Universität zu Berlin, Germany; 2: Weierstraß-Institut für Angewandte Analysis und Stochastik, Germany; 3: V.N. Karazin Kharkiv National University, Ukraine We discuss how the Reissner-Mindlin plate model [3,4] can be derived from nonlinear three-dimensional finite elasticity in terms of Γ-convergence. The presence of transverse shear effects in the model requires to scale different components of the three-dimensional elastic strain differently, unlike the approach used in classical papers for Kirchhoff–Love elasticity [1,2]. References. [1] G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Comm. Pure Appl. Math., 55(11) (2002), pp. 1461--1506. https://doi.org/10.1002/cpa.10048 [2] G. Friesecke, R.D. James, S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence, Arch. Rational Mech. Anal., 180 (2006), pp. 183--236. https://doi.org/10.1007/s00205-005-0400-7 [3] R. D. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, J. Appl. Mech., 18 (1951), pp. 31--38. https://doi.org/10.1115/1.4010217 | |
