engleski

A Naghdi type shell model for irregular shells

A shell model is a two-dimensional model of a three-dimensional elastic body which is thin in one direction. There are several linear and nonlinear shell models in the mathematical literature that are rigorously justified starting from the 3d elasticity. Examples in the mathematical literature are membrane shell models, the flexural shell model in linear and nonlinear context and the Koiter shell model in the case of linearized elasticity. Application of a particular model depends on the particular geometry of the shell’s middle surface and the boundary condition which allow or disallow inextensional displacements. Furthermore, since the models are usually written in local coordinates high smoothness of geometry is required for the formulation. Therefore, a model applicable for general geometries and boundary conditions is called for. In this talk a linear and nonlinear Naghdi type shell model will be presented and related to the classical models. These new models are given in terms of a displacement vector and the (infinitesimal) rotation of the cross-section of the shell, both being in H1 . The models unite different possible behaviors of shells, they are applicable for all geometries and all boundary conditions, no complicated differential geometry is necessary for the analysis of new models and the models are also well formulated for geometries of the middle surface of the shell with corners. The models will be related to classical models and their asymptotic properties (using weak and Gamma convergence) with respect to the small thickness will be presented.

elastiicty ; shells ; Naghdi type ; irregular

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