Isogeometric analysis of topologically complex shell structures

Abstract

In the conventional isogeometric analysis, a topologically complex shell structure is required to be modeled using multiple NURBS patches. In the CAD industry, however, the topologically complex shell structure is conveniently and efficiently created via trimming techniques rather than constructing multiple untrimmed NURBS patches. With this feature, the isogeometric analysis which enables to handle the topologically complex shell structure with a single NURBS patch is presented in this paper. In the present method, the information of the topologically complex shell structure composed of the untrimmed surface and trimming curves is directly utilized into isogeometric shell analysis. For numerical integration, a special integration scheme is adopted considering the inside or the outside of the trimmed boundaries which are described by the trimming curves. For the shell formulation, the degenerated shell element based on the Reissner-Mindlin theory is employed. The exact surface normal vectors and their analytic derivatives are adopted into the formulation. The shell formulation is validated with linear elastic benchmark problems. Then linear elastic problems of topologically complex shell structures are dealt with using the proposed procedures, and the effectiveness is illustrated.