Application of a Well-Behaved Function Function for Structural Optimization

• Main Authors: Huang,Jyh-Cherng, 黃志誠
• Other Authors: Lin,Tsung-Wu
• Format: Others
• Language: zh-TW
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/05660249327563195081

碩士 === 國立臺灣大學 === 土木工程研究所 === 81 === Hyperbolic penalty functions have many advantages : they are defined for all real values of design variables , continuous in themselves and in any order of derivative , not flat at the feasible side near the constraint boundary and approximate the exact penalty function . From the investigation of the former , they are pretty suited for the zero , first , and second ordered methods. This paper applies the hyperbolic penalty functions in the structural optimization , assembles the penalty function method , finite element method , and structural sensitivity analysis to develop a computer program . In the optimization method , we apply the Newton's method but don't calculate the second derivatives of the constraints only use the approximate Hessian matrix from the first derivatives . In the structural senstivity analysis , we apply the state space method . The constraints deletion and design variables linking are also considered in the program . Finally , four trusses with eleven design cases are tested in the program . From the history of the iterations we get the conclusions : The effect of convergence is fast in the cases without displacement constraints but is poor in the cases with displacement constraints due to the neglecting of the second derivative . The optimal solution may be obtained by just one unconstraint optimization , and the global convergence also performs very well .