Verification of Domain Optimization Theory

点击翻译按钮获取中文摘要

Following the verification result of the domain optimization theory to two dimensional problems in 1994 of minimizing a mean compliance, maximizing a vibrational eigenvalue of linear elastic continuum, minimizing a dissipation energy of a viscous flow field and minimizing a velocity square error norm of a potential flow field, we obtained the results :1. We developed a system to analyze three dimensional optimum domains for the mean compliance minimization problems and the vibrational eigenvalue maximization problems of linear elastic continua utilizing a general purpose FEM program. Analyzing three dimensional problems using this system, we obtained the monotonous convergent results for the mean compliance minimization problems and the vibrational eigenvalue maximizaton problems.2. In addition, we developed another system to identify two dimensional domain where a distribution of potential or square velocity, i.e., pressure in a flow field of an ideal fluid, in a specified subdomain agrees with a prescribed distribution utilizing a general purpose FEM program. Analyzing two dimensional heat transfer body having a prescribed temperature in a specified subdomain using this system, we obtained successful results. Furthermore, we obtained the wing section of NACA 0012 from a different section by varying the wing section to minimize an error norm of a pressure distribution near surface of the wing section of NACA 0012 previously analyzed by the FEM program. This developed system is applicable to three dimendional problems using three dimensinal elements.