CAJ | 학술논문

为了提高导重法求解拓扑优化问题的计算效果，提出一种改进的导重法，并引入了灰度过滤技术抑制优化过程中灰度单元的产生。首先基于RAMP(the rational approximation of material properties)模型结合导重法求解最小柔度拓扑优化问题的迭代表达式，利用二分法对表达式中的拉格朗日乘子求法进行了改进；为减少优化后结构图像中的灰度单元数量，在迭代表达式中引入灰度过滤函数；最后将上述理论拓展到多工况拓扑优化问题中，采用归一化组合处理方法建立目标函数。对多工况拓扑优化问题的2个典型算例进行计算的结果表明，应用文中理论求解拓扑优化问题具有收敛稳定、求解快速、图像清晰的特点。
위료제고도중법구해탁복우화문제적계산효과，제출일충개진적도중법，병인입료회도과려기술억제우화과정중회도단원적산생。수선기우RAMP(the rational approximation of material properties)모형결합도중법구해최소유도탁복우화문제적질대표체식，이용이분법대표체식중적랍격랑일승자구법진행료개진；위감소우화후결구도상중적회도단원수량，재질대표체식중인입회도과려함수；최후장상술이론탁전도다공황탁복우화문제중，채용귀일화조합처리방법건립목표함수。대다공황탁복우화문제적2개전형산례진행계산적결과표명，응용문중이론구해탁복우화문제구유수렴은정、구해쾌속、도상청석적특점。
An improved guide-weight method is presented to improve the computational efficiency of the guide-weight method on solving topology optimization problems, and the gray-filter method is introduced to restrain the gray-scale element which is generated in the optimization process. Since the optimization model was established based on RAMP(rational approximation of material properties, RAMP) scheme, and the guide-weight method was used as an algorithm combining for proposing the iteration formulas of the least compliance in multi objective topology optimization problems. First, the Lagrange multipliers solution me-thod of the formulas were improved by the bi-sectioning algorithm. Then, with the purpose to suppress the generating of gray-scale element, the gray-scale filtering function was introduced into iterative formulas. Moreover, the proposed theory were extended to multi objective optimization problem, and ill-conditioning were avoided by normalizing single objective. Finally, two examples of multi objective optimizations prob-lems were calculated respectively. The results calculated by examples demonstrate that using the proposed theory above can solve topology optimization problems with steady convergence, fast calculate speed and image sharpening.