An efficient and robust Reissner–Mindlin shell formulation for isogeometric analysis

Abstract

The novel idea of isogeometric analysis is to use the basis functions of the geometry description of the design model also for the analysis. Thus, the geometry is represented exactly on element level. A closer integration of design and analysis is fostered by the usage of one common geometry model for design and analysis. A prevalent choice for the geometry description in isogeometric shell analysis are Non-Uniform Rational B-spline (NURBS) surfaces, which are commonly used in industrial design software to model thin structures. In order to directly compute structures defined by NURBS surfaces, an efficient isogeometric shell formulation is required. In this contribution an isogeometric Reissner-Mindlin shell formulation derived from the continuum theory is presented. The shell body is described by a shell reference surface, which is defined by NURBS surfaces, and a director vector. The director vector in the current configuration is computed by an orthogonal rotation using Rodrigues' tensor in every integration point. The axial vector of the rotation is interpolated. A multiplicative update formulation for the rotations accounts for finite rotations. A benchmark example shows the superior accuracy of the presented shell formulation for nonlinear computations.

Patch coupling with the isogeometric dual mortar approach

“…(4). Numerical results, which are given in detail in [5], show that the approximate dual basis functions are the most promising candidate for the use in the isogeometric mortar method. The accuracy of the global stress distribution obtained with the approximate duals agrees very well with computations with the inverse Gram matrix and with reference computations using the Lagrange Multiplier method.…”