Design Optimization using Advanced New Three Points Approximation Method

• Main Authors: Jing-Lung Jan, 詹景隆
• Other Authors: Chien-Jong Shih
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/06078708855199807913

碩士 === 淡江大學 === 機械與機電工程學系碩士班 === 97 === Some optimization and finite element software are well-developed during last two decades that provide very efficient tools for engineering design and analysis. Although individual software is useful in its specialized function, however, it is not convenient of cooperating two soft wares into one phase for engineering application. This paper presents some examples of uniting two specialized software to perform engineering design optimization. Particularly, in a structural optimization problem takes considerable computation of finite element analysis and somehow increase the nonlinearity of problem characteristic. A general recognized strategy of dealing with this difficulty is to adopt the approximation method of transforming some mathematical functions. In design optimization model, the objective function or some constrained functions require to transform to approximate functions. One-point or two-point approximations are relatively simpler methods in this category. Because the desk-computer has a great computation speed, the recent development of those approximation techniques had explored three-point approximation technique. The most recent development is called the new three point approximation (nTPA). This thesis work applies the approximation to 2nd order term in Taylor series where only the diagonal items are included, as called advanced new three point approximation (AnTPA). The feature of AnTPA includes the computation of whole index parameters using for intervening variable. So that there comes up 3n+2 coefficients required to solve. The solution is complicated as compared with nTPA of 2n+2 coefficients. This thesis describes the complete mathematical modeling and the error analysis of proposed AnTPA with several numerical problems. The AnTPA is then applied to engineering design optimization. By considering the characteristic of AnTPA, an efficient optimization process is consequently developed and presented. The presented numerical processing shows the promotion of the solution efficiency for some structural optimization problems. The proposed AnTPA can be applied to large-scale structural optimization problems to verify the solution effectiveness.