Finding two-dimensional optimum topology with various constraints using sizing optimization technique

• Main Authors: Yan- Siang You, 顏祥祐
• Other Authors: Ting-Yu Chen
• Format: Others
• Language: zh-TW
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/56226627501859679111

碩士 === 國立中興大學 === 機械工程學系所 === 103 === Abstract Solving minimum-compliance topology optimization problems must calculate the sensitivity of compliance with respect to the design variable by using element strain energy. The constraint is the amount of material used in the design space. If other constraints are needed, their sensitivities must be computed. This is not an easy job. To avoid this difficulty, this thesis tries to use sizing optimization module in MSC / NASTRAN to solve 2-D topology optimization problems with all kinds of constraints. In doing so, no complicated sensitivity computation is needed. The objective function in this thesis to be minimized is the sum of compliance and the penalty function value. Two penalty functions and two methods to increase penalty parameter are introduced. The penalty function is used to penalize these elements whose thickness is not maximum or minimum value. During optimization search process, the penalty parameter is increased gradually to force the thickness of each element toward its maximum or minimum value in order to generate the topology of the structure. The penalty parameter would affect the topology obtained. Based on the examples, no matter how many constraints exist, better topologies will appear as long as the values of compliance and penalty term maintain a reasonable difference. Four 2-D test problems are used to test the idea of this thesis. The results show that the idea of this thesis feasible.