基于遗传算法的圆环板的优化设计

Optimal Design of Circular and Annular Plate Based on Genetic Algorithm

利用阶梯折算法,由传递矩阵导出变厚度圆环板平衡问题的初参数解的显式表达式,将圆环板的优化设计转化为极小化目标函数的非线性规划问题.用一种离散变量结构优化设计的单向搜索法与标准遗传算法结合的混合遗传算法求解该优化问题,发挥了单向搜索法局部搜索能力强、高效省时和遗传算法全局性好的优点.对典型问题的计算表明,该方法能解决受强度、刚度和几何等约束的离散变量结构优化设计问题,并具有编制程序方便、收敛快和精度高的优越性.

With the stepped-reduction method, the solution of a circular and annular plate with arbitrary axisymmetrical boundary conditions and arbitrary vertical pressure can be obtained. The optimal design involves to minimize its volume under constraints of the stress and deflection, under the condition of the volume being constant. The optimization reduces to a nonlinear program. A hybrid genetic algorithm（HGA） composed of the standard genetic（SGA） and unidirectional searching algorithm（USA） is proposed, with the advantages of time saving and powerful local searching capability of USA method, as well as the global searching capability of genetic algorithm. Several examples are provided to illustrate the method.