| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 105 === The purpose of this thesis is to improve conservative approximation methods for structural optimization. A new two-point approximation method based on method of moving asymptotes approximation (MMA) is developed, which is called two-point adaptive method of moving asymptotes approximation (TAMMA). It modifies intervening variables of MMA to generate oblique asymptotes and utilizes function values and sensitivities at two successive design points to adjust the slopes of the oblique asymptotes automatically. In other words, it can consider the monotonicity of structural behavior to construct approximate functions to ensure the approximation quality. Also, a new modification strategy which adopts piecewise approximate functions is proposed to avoid the singularity and inappropriate approximation that existing conservative approximation schemes would encounter. With the use of TAMMA, several kinds of structural behavior can be represented as explicit functions of design variables. Therefore, the optimum design can be found with sequential approximate optimizations solved by mathematical optimization techniques. Moreover, a program integrating ANSYS, AutoCAD and Microsoft Visual C++ is developed for automated structural optimization. TAMMA and the modification strategy are tested in several structural optimization problems. The results indicate that TAMMA can converge to accurate optimum designs quickly, and the modification strategy can deal with singularities and inappropriate approximations effectively. Those prove that the proposed methods are practical in structural optimization.
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