一个结构优化的能量方法

本文提出了一种用于结构最优材料分布的能量方法.该方法将结构在一定约束条件下的承载能力转化成结构吸收应变能的能力.文章给出了拉格朗日函数, 通过包括对区域的变分确定材料分布.文中以悬臂梁为例说明了这一方法,并就此情况给出了解析解.若将位移约束以外力势能项代替,那么得到的结果相同.为了说明对较复杂情况的处理.本文建议用离散化方法进行数值解,仍以悬臂梁为例加以说明,结果表明,数值解收敛于前面的解析解.

ENERGY WETHOD OF STRUCTURAL OPTIMIZATION

This paper propounds an energy method of structural optimization. Under certain constriant conditions, it assumes that the maximum absorbability of structure strain energy is equivalent to its maximum load-bearing capacity. According to this assumption, a Lagrange function in terms of energy is provided, and then, maximize it using variational principle. So, the optimal structures are determined. Taking a cantilever beam as an exampel, the paper describes this method and gives out an analytic solution which is proven by other method. Based upon the same theory and the same example, a numerical method is also mentioned. Theresults show that the two solutions are identical, that is, the numerical solution converges to the analytical solution.