engleski

A new Naghdi type shell model

A shell model is a two-dimensional model of a three-dimensional elastic body which is thin in one direction. There are several linear shell models in the mathematical literature that are rigorously justified starting from the linearized 3d elasticity. Examples are the membrane shell models, the flexural shell model and the Koiter shell model. Their application depends on the particular geometry of the shell’s middle surface and the boundary condition which allow or disallow inextensional displacements. In this talk a Naghdi type shell model will be presented and related to the classical models. This new model is given in terms of a displacement vector and the vector of infinitesimal rotation of the cross- section of the shell, both being in H1 . It unites different possible behaviors of the shell, it is applicable for all geometries and all boundary conditions, no complicated differential geometry is necessary for the analysis of the model and the model is also well formulated for geometries of the middle surface of the shell with corners. Asymptotically, with respect to the thickness of the shell, it behaves as the classical membrane, generalized membrane and flexural shell model depending on the particular regime and thus is a good approximation of the three-dimensional elasticity. Further, the solutions of the model continuously depend on the geometry.

elasticity ; shell ; Naghdi type

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