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本文提出并证明了两个定理,对于结构优化问题来说,其最优解必定出现在可行域边界上,而不可能出现在可行域内部。因此在求解结构优化问题时,不必到可行域内部去搜索最优解,只要在可行域边界上搜索,于是把搜索范围从一个n维空间减小到约束曲面上。基于这两个定理,本文提出了一个新的结构优化解法,把原来的约束极值问题转化为无约束极值问题,因而可用比较简单的无约束优化方法求解。计算实例表明,这个方法具有概念明确、方法简便、计算效率高等优点。
This thesis proposes and proves two theorems. For the structural optimization problem, the optimal solution must appear on the boundary of the feasible region, but it cannot appear inside the feasible region. Therefore, when solving the structural optimization problem, it is not necessary to search for the optimal solution inside the feasible region. As long as the search is performed on the boundary of the feasible region, the search range is reduced from an n-dimensional space to a constrained surface. Based on these two theorems, this paper proposes a new structural optimization solution, transforms the original constrained extremum problem into an unconstrained extremal problem, and can be solved by a relatively simple unconstrained optimization method. Calculation examples show that this method has the advantages of clear concept, simple method and high computational efficiency.