A NURBS-based finite cell method for structural topology optimization under geometric constraints

Abstract

In this work, we present a NURBS-based finite cell approach for topology optimizations of structures with arbitrary shaped trimmed design domains. The combination of isogeometric analysis and finite cell method allows for a topology optimization of trimmed geometries directly derived from CAD systems which eliminates the time consuming preprocessing work such as mesh generations. We further propose a variationally consistent Nitsche's method for the weak enforcement of essential boundary conditions along trimming curves. Independent from the analysis domain, a high order and continuous NURBS represented density field is introduced which not only provides an intrinsic filter but also allows for the realization of multi-resolution topology optimizations. Additionally, we also propose a simple and straight forward method to enforce geometric constraints of arbitrary shapes during topology optimizations. We demonstrate the efficiency and accuracy of the proposed method with a number of benchmark problems and engineering oriented models.