静定化假设对结构优化设计解的影响

Effect of hypothesis of static determinate on solutions of structural optimum designs

研究了结构优化设计通常采用的静定化假设对最优解的影响.建立了桁架结构优化的数学模型,分别得到了解析的约束条件和基于静定化假设的约束条件的近似显式表达.以两个超静定桁架为例,分别用相对微分法求解析最优解和近似最优解,比较两者后得到结论:除了仅有应力强度约束的问题,静定化假设对最优解没有影响;在仅有应力强度约束的情况下,静定化假设导致满应力准则设计,从而影响最优解;凡存在全局约束、其他局部约束或稳定约束为最严约束,则静定化假设不影响最优解.

Hypothesis of static-determinate-structure has been widely used in approximation of behavior constraints for structural optimization. The mathematical model of optimization for truss structures is presented with multiple constraints. Expressions of analytical constraints and explicitly approximate constraints based on the hypothesis of static-determinate-structure are obtained, respectively. Optimum designs are determined by using the method of relative difference quotient algorithm with analytical and approximate constraints individually for two truss examples. Comparison of the two solutions shows that the hypothesis generates no influence on optimum solutions, except for the ones subjected to stress constraints only. No influence is found when there exist global constraints, other local constraint or the local stability constraint is the most dominant constraint as well.