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本文介绍了一种既能满足特定频率要求,又能使得重量最轻的结构分析方法。它是通过变更构件的横截面积来改善结构的。具体做法是:应用梯度方程先求得所需要的结构频率,然后,保持此频率不变而使结构重量最轻。为了直接应用有限元素分析法,在推导梯度方程时,采用矩阵表达式。在所编制的计算机程序中,整个分析过程(包括处理大型复杂结构的子结构分析法在内)都是自动进行的。高达1800个自由度的动力优化问题仅仅通过一次运算就解决了(优化结果改变了100个构件的截面积)。四个例子证明了这种方法是收敛的,而且用不到迭代十次就能得到最优结构。
This article describes a structural analysis method that meets specific frequency requirements while minimizing weight. It is by changing the cross-sectional area of components to improve the structure. The concrete method is: Use the gradient equation to find out the required structure frequency first, then, keep this frequency invariable and make the weight of structure lightest. For the direct application of finite element analysis, matrix expressions are used in deriving gradient equations. The entire analysis process, including the substructure analysis of large and complex structures, takes place automatically in the programmed computer program. The power optimization problem of up to 1800 degrees of freedom is solved in just one operation (the optimization result changes the cross-sectional area of 100 members). Four examples prove that this method is convergent, and the optimal structure can be obtained in less than ten iterations.