Application of isogeometric analysis in structural shape optimization

In this paper, the isogeometric analysis method is utilized in the three-dimensional shape optimization of structures, instead of finite elements. The main obstacles in shape optimization problems are inherent in the currently practiced numerical analysis methods and their distinction from the geometry definition model. The newly developed isogeometrical analysis has the potential to be employed for this goal. The main advantage of this technique, besides being computationally less costly, and its ease and precision in defining boundaries, is that it does not require several remeshings in the process of optimization. In this research work, the domain of interest is defined by using Non-Uniform Rational B-Splines (NURBS). Also, a numerical analysis tool is developed, which uses the NURBS basis functions for approximation. The control points defining the design boundary surface are considered as the design variables of the shape optimization problem. To demonstrate the performance of the method, some examples of two and three dimensional problems are presented.