Topology optimization based on spline-based meshfree method using topological derivatives

• Published in: Journal of mechanical science and technology Vol. 31; no. 5; pp. 2423 - 2431
• Main Authors: Hur, Junyoung, Kang, Pilseong, Youn, Sung-Kie
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Mechanical Engineers 01.05.2017; Springer Nature B.V; 대한기계학회
• Subjects: Basis functions; Control; Derivatives; Design analysis; Dynamical Systems; Engineering; Industrial and Production Engineering; Mathematical analysis; Mechanical Engineering; Meshless methods; Sensitivity analysis; Topology optimization; Vibration; 기계공학; Isogeometric analysis; Topology optimization; Non-uniform rational B-spline; Spline-based meshfree method; Topological derivative
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-017-0440-6

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. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.