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Cost-oriented Topology Optimization with Manufacturing Constraints

Hung Lin, "Cost-oriented Topology Optimization with Manufacturing Constraints", Technische Universität München, 2021.

Abstract

This thesis proposes a framework of gradient-based topology optimization (TO), which is able to handlenon-continuous objective functions (e.g. total cost) with multiple constraints, via using the finite difference (FD) scheme for the sensitivities. The thesis especially focuses on the sheet metal stamping process in the automotive industry, thus the cost of such process is set as the objective, submitted to given maximum compliance as constraint. The cost estimation for a given sheet metal geometry is based on [6] and [4]. The TO scheme chosen is Solid Isotropic Material with Penalization (SIMP), based on [7], [1] and [3].Topology optimization is a very important tool for engineers and designers in their early stages of design-ing a new product. It finds the optimal material distribution for an objective under a constraint-set in agiven design domain. Traditional TO methods often only focus on minimizing the compliance or mass, which are the structure-related properties. However, these structural properties are not the only focus inthe industry. Often we encounter a circumstance that a relatively good design is already available and afurther reduction of its cost is desired. Nonetheless, only few TO work researched on direct minimizing the cost of design through the gradient-based process. Furthermore, these cost-related TO work either utilizes very simple cost functions or only cost-related geometry parameters, thus they are still not suitablefor industrial use. The sheet metal forming process is especially important in the automotive industry. Not only the skins but also the structure of uni-body designed vehicles are manufactured through such a process. The cost of each stamped sheet metal part consists of its material cost, its energy cost and a share of the set-up cost, and the die cost of the batch. Among these costs, the material cost and the die cost are the two essentials. When a part geometry is given, the process to estimate its cost is to compute its unfolded material geometry and the corresponding die geometry. With these two geometries, we then are able to determine the material and the die cost. However, these costs are not continuous. For instance, the die cost is not only relevant to its size and complexity but also the number of holes on the part geometry. It would be very useful if we are able to have a relatively accurate cost estimation built into TO at the early phase of design. The cost estimation technique is undoubtedly going to be improved in the future. Thus the goal of the proposed framework is to be as general as possible that the user can plug any further cost model in. This includes advance commercial cost estimation software like aPriori, models obtained via machine learning processes, or simply an improved version of analytical cost estimation. A finite difference scheme is chosen for sensitivity computation in order to consider the cost estimation model as a black box, realizing the ability for the model to be updated without further modification in the TO framework. While utilizing the finite difference scheme for the sensitivity, the efficiency and computation time becomes very essential. A random-grid-size element clustering scheme together with a state-based element clustering scheme is proposed to boost the efficiency with only little affection on the performance of the proposedframework. Element clustering even is essential in some cases. With the TO framework proposed in this thesis, we are able to obtain designs with lower cost (how much lower will be added) comparing to the results from the traditional compliance-oriented TO, while having the same compliance. The optimization process is able to be ’cost-oriented’ instead of ’structure-oriented’. The proposed TO framework is alsoable to finish its job in a feasible computation time. Finally, experiment results, comparison, and discussionof cost-oriented TO in 2D, 3D, and 2.5D design domains will be presented.



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