遗传算法在单层球壳质量、刚度模糊优化中的应用

在单层球壳的优化设计过程中,必然会遇到大量的不确定性信息和因素,对这些不确定性因素应该使用模糊理论加以分析和处理。同时往往要考虑多个目标如质量最小和整体刚度最大等,而各个目标之间存在矛盾,要使各个目标都达到最优很困难。采用模糊数学的原理建立单层球壳多目标模糊优化模型,通过模糊判决法,将多目标的模糊优化问题转化为单目标的非模糊优化问题,最后利用小生境遗传算法(ANGA算法)对非模糊化的优化模型进行求解。对70 m跨单层球壳进行质量、刚度模糊优化,结果令人满意,验证了该方法的合理性和可行性,说明基于ANGA算法的模糊优化方法可以有效解决优化变量繁多的大中型网格结构多目标模糊优化问题。

Application of genetic algorithm in the mass and stiffness fuzzy optimization of single layer dome

In the process of designing single-layer latticed domes, a lot of uncertain information and factors are inevitable, and should be solved by fuzzy theory. In addition, several optimal objectives, such as structural dead weight and stiffness, are difficult to reach the optimum at the same time. In this paper, a multi-objective fuzzy optimum model of single-layer latticed dome is built, on the basis of fuzzy mathematics. Using the fuzzy judgment method, the multi-objective fuzzy optimization problem is transformed into that of single-objective non-fuzzy optimization. Then, the non-fuzzy optimum model is analyzed, based on ANGA method. An optimum research on dead weight and stiffness of 70m single-layer latticed dome is carried out. The results show that the fuzzy judgment method proposed in the paper is rational and feasible, and the ANGA can be used to solve multi-objective fuzzy optimization of large and medium grid structures with several optimum variables effectively.