Verification of Domain Optimization Theory

根据1994年区域优化理论对二维问题的验证结果，即最小化平均柔度、最大化线弹性振动特征值、最小化粘性流场耗散能和最小化势流场速度平方误差范数，我们得到：1.我们开发了一个系统来分析三维最优域的平均柔度最小化问题和振动特征值最大化问题的线弹性连续体利用通用有限元程序。利用该系统分析三维问题，得到了平均柔度最小化问题和振动本征值最大化问题的单调收敛结果.此外，我们开发了另一种系统来识别二维域，其中势或平方速度的分布，即，利用通用有限元程序，在指定子域中的理想流体的流场中的压力与规定的分布一致。用该系统对给定温度的二维传热体在给定的子域内进行了分析，得到了满意的结果。此外，我们获得了NACA 0012的机翼截面从不同的部分，通过改变机翼截面，以尽量减少误差范数的NACA 0012的机翼截面的表面附近的压力分布的有限元程序之前分析。该系统适用于使用三维元素的三维问题。

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.