Optimization of geometrical parameters of covers and hoops of metal packaging boxes

摘要

Finding the best compromise between economic, mechanic and technologic imperatives is still being one of the most important goal for the engineer. Working methods to achieve this goal of excellence have advanced considerably in recent years. Nowadays, optimization programs are included in many commercial codes of finite elements (ANSYS, LS-DYNA, Msc-Marc,... ), so that optimization can be made from the design phase. Therefore, it may be a part of an integrated design process. In this work we try to find the ideal geometric parameters of covers and hoops of metal packaging boxes. A similar approaches were introduced in the past, we can presents the following example: To minimize the weight of can ends of beverage cans, K.Yamazaki et al. (2006). (Yamazaki. [1]). applied the method of response surface approximation to develop the can ends. The geometric parameters of the sheet metal are considered as design variables to optimize. The strategy is to combine between the design of experiments using orthogonal arrays and a series of simulations with the finite elements code Msc Marc to approximate the expression of stresses and displacements at the center of can end according to design variables. Finally a numerical optimization program, in this case, DOT from Vanderplaats, is used to minimize the weight, under three constraints. In our study, we have shape optimization of metal boxes under internal pressure, with the condition to avoid opening the cover, the objective function to optimize is difficult to interpret analytically, we opted for an approximation method based on design of experiments coupled with the finite elements code ABAQUS. The optimization method applied is hybrid in a way because it use both the response surfaces methodology and nonlinear constrained optimization algorithm (SQP). It is divided into two steps: A first step will allow us to express the objective function which is the contact pressure between the lid and hoop by a quadratic polynomial formula with the Box-Behnken method. A second step is to maximize under constraints, the contact pressure at the last increment before final opening of the cover, this maximization is solved by the SQP algorithm.