梁的弹性最优设计*
Optimal Elastic Design of Beams
-
摘要: 本文根据最小余能原理建立了弹性梁最优强度设计问题的数学形式,它为一个具有等式和不等式约束的泛函极值问题。进而应用拉格朗日乘子法得到了极值的必要条件,并由此导出最优解所必须满足的一组关系式,这组关系式可以用来检验等强度设计或任一可行弹性设计的最优性。当等强度设计不是最优设计时文中还建议了一个迭代寻优的数值解法。Abstract: According to the principle of minimum complementary energy a mathematical statement of optimal strength design problem for elastic beams is formulated in this research, which is an extremum problem of functionals with equality and inequality constraints. Further the application of the Lagrangian multiplier method yields the necessary conditions for extrema. A set of relations that must be satisfied for the optimal solution follows afterwards. This set of relations can be used to verify the optimality of a uniform strength design or any feasible elastic design. An iterative numerical method to find the optimal solution when the uniform strength design is not optimal is also presented in this paper.
-
[1] 唐燮黎、叶开沅,静不定梁的等强度设计,应用数学和力学,6, 12 (1985), 1053-1060. [2] 叶开沅、唐燮黎,具有非零最小弯曲刚度梁在多载荷情况作用下的等强度设计,应用数学和力学(待发表). [3] 钱伟长,《变分法及有限元》(上册),科学出版社(1980). [4] Rozvany, G.I.N.,Optimal Design of Flexural Systems(1976).
计量
- 文章访问数: 1808
- HTML全文浏览量: 79
- PDF下载量: 544
- 被引次数: 0