(A) study on the improvement of isogeometric shape and topology optimization

Abstract

Spline-based meshfree method (SBMFM) is originated from the isogeometric analysis (IGA) which integrates design and analysis through Non-Uniform Rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated using the curve fitting algorithm. The relationship between topological derivative and update of trimming curve is verified numerically. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several benchmarking compliance minimization problems. It is shown that optimization results show good agreements with previous works while explicit and smooth boundary representation of SBMFM and appropriate topological changes are maintained. Furthermore, the extendable design space problem is easily treated by adaptive extension of NURBS background mesh. Finally, proposed work is applied to the design dependent problem with great advantage in treating loaded boundaries.