饮料罐尺寸的最优解证明及其优化设计

The Proof of the Optimal Solution of the Size of a Pop-can and Its Optimal Design

为了发掘节省原料的潜力,对销量很大的饮料易拉罐进行优化设计.建立起具有通用性的优化模型;运用压缩变量技术,解决了模型复杂不易求解的困难;给出了便于实施计算的一整套显式求解公式.通过方向导数分析和流动极值分析,证明了解的最优性,指出了目标函数的退化特征及其临界状态;结合数学理论分析、具体数值计算和实际工艺条件,形成了层层递进式的优化设计途径.

For exploiting the potentialities of the material-saving, we gave a optimal design for the pop-can, established a optimal model which can be used commonly. By use of the technique of varlables-contracting, we gave a set of explicit formula which can be used for calculation easily, and using the direction derivative analysis method and the current extremum analysis method, we proved the optimal of the solution , point out the degenerate character of the objective function and its critical state. And finally, combine with the theoretical analysis, numerical evaluation and the actual technological condition, we obtained the recursive optimal design process.