易拉罐形状和尺寸的最优设计的数学模型

The Mathematical Model of the Optimal Design of the Shape and Size of Cans

易拉罐作为产品包装,要尽量符合消费者的审美观念、做到使用方便、造价最低。将易拉罐的罐身设制成弧度,同时引入了"黄金分割点"这个完美的比例关系,设计出一个符合大众审美观念的易拉罐形状。在此基础上进行最优化设计,即使产品所耗材料最少。在这些必要的假设前提下,建立了最优化模型,利用MATLAB软件对模型进行了求解,得出了易拉罐的尺寸比例。这个设计方案考虑了主要因素的作用,使得易拉罐的设计能够适用市场,满足消费者的需求和厂商的经济利益,具有很好的推广性。

As a product packaging, cans should try to meet the consumers＇ aesthetic sense, and be easy to use and with the lowest cost.The shape of the cans were designed to radian, and at the same time, the perfect proportion of ＂golden section＂ was introduced to design a can shape that was in line with the general aesthetic concept. Based on this, the optimal design is made, that is the product consumes the least material. Based on these necessary assumptions, an optimization model was established and the model was solved using MATLAB software. The size ratio of the cans was obtained. This design plan takes into account the role of major factors, making the design of cans suitable for the market, meeting the needs of consumers and the economic interests of manufacturers, and has a very good promotion.