Minimum weight topology optimization subject to displacement or frequency constraints

• Main Authors: Shao-Jui Hsu, 許劭睿
• Other Authors: 陳定宇
• Format: Others
• Language: zh-TW
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/50590576612602386088

碩士 === 國立中興大學 === 機械工程學系所 === 98 === Since 1988 BendsØe and Kikuchi [1] published the homogenization method to solve structural topology optimization problems, more and more researchers have used this method to generate initial shapes of structures. In this thesis, the objective function is defined as minimum weight subject to two types of constraints: one is the displacement and the other one is the natural frequency. The normalized density of each finite element is adopted as the design variable. Some formulas representing the relationship between Young’s modulus and the normalized density are used in the optimization process. The results are compared. A MATLAB program is written to use SQP optimizer to solve the optimization problems. While MSC/NASTRAN and MSC/PATRAN are used to do the pre- and post- processing. Because of the existence of uncertain elements, higher order elements or penalty function is employed to improve this drawback to make the structure clearer and recognizable. Compared with using minimum weight and minimum compliance as objective function, the biggest advantage of using minimum weight as the objective function is that there is no need to assign an amount of mass in the design space. By choosing an appropriate α in the formula relating Young’s modulus and design variables, the weight saving is found in the cantilever plate case.