Abstract
Keywords - Multidisciplinary Optimization, Automotive Door, Stiffness, Natural Frequency, Side Impact
Abstract - The automotive door has a large finite element model in analysis and many design requirements such as stiffness, natural frequency, side intrusion, etc. Thus, various related governing equations should be solved for systematic analysis and design. Because each governing equation has different characteristics, it is almost impossible to solve them simultaneously. Instead, they are separately handled and the analysis results are incorporated into the design separately. Currently, the design is usually conducted by trials and errors with engineering intuition in design practice. Optimization can be employed to overcome the difficulties. Especially, multi-disciplinary optimization (MDO) can be exploited well to include various analysis disciplines.
First, single optimizations are carried out by considering one discipline for the automobile door design. Various optimization formulations are defined and the formulated problems are solved to determine the topology, shape and size of the door. The design is expanded to MDO to consider multiple disciplines. From an extensive survey of existing MDO methods, it is found that they are too complicated mathematically. Therefore, they are appropriate for areas where design equations are explicitly well defined. Also, they are focused on solving coupling characteristics between disciplines. In an automobile door design, design equations do not generally exist and there are not strong couplings. Instead, design variables are shared through disciplines with weak couplings.
In this research, a few MDO methods are proposed to solve the problems that share design variables in disciplines. The idea is from the Gauss-Seidel type method for multi-discipline analysis. First, the optimization of the entire system is divided into multiple domains according to the required analysis methods. Second, design variables are assigned to one domain according to the contribution or sensitivity. An optimization formulation is defined for each domain. Third, optimization is performed at each domain where only the assigned variables are regarded as design variables and others are constant. If all the design variables are updated, then the single optimizations are iteratively conducted until the design is not changed.
The developed method is verified by a standard mathematical problem and the design of Golinskis speed reducer. And then the developed methods are applied to the design of the automobile door. The design considers the stiffness, the natural frequency and the side intrusion of the door. Most of the optimization processes use mathematical optimization. When mathematical optimization is too complicated, an approximation method such as response surface method (RSM) is utilized. The developed methods show stable convergence and the weight of the door is reduced by fifteen percent. Since commercial systems are adopted for analysis and design by coding the interfacing parts, the developed methods can be easily employed in design practice.