Speaker
Description
A hierarchy of classical plate models such as nonlinear bending theory, von Karman theory and linearized von Karman theory was derived from three-dimensional nonlinear elasticity by Gamma-convergence (see [2], [3]). The justification of the linear Timoshenko beam model and the Reissner-Mindlin plate model via Gamma-limit of the linear-elasticity model for a three-dimensional body was obtained in [1], [4]. We are looking for a way to justify the Timoshenko model by Gamma-convergence starting from a nonlinear model for a three-dimensional elastic body.
REFERENCES
[1] Falach L., Paroni R. , Podio-Guidugli P. , A justification of the Timoshenko beam model through Γ-convergence,Analysis and Applications 15:02, 261-277 (2017).
[2] Friesecke, G., James, R.D., Müller, S., A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence, Arch. Rational Mech. Anal., 180, 183-236 (2006).
[3] Friesecke, G., James, R.D., Müller, S., Rigorous derivation of nonlinear plate theory and geometric rigidity, C.R. Acad. Sci.Paris. Sér I, 334, 173-178 (2002).
[4] Paroni R., Podio-Guidugli P., Tomassetti G., The Reissner–Mindlin plate theory via Γ-convergence, C. R. Math. Acad. Sci. Paris, 343, 437–440 (2006).
