Keywords: structural design, assembly design, design for manufacturing, design for assembly, multi-objective optimization, genetic algorithms, cost estimation.

Complex structural products such as automotive bodies are made of hundreds of components joined together. While a monolithic design is ideal from a structural viewpoint, it is virtually impossible to economically manufacture complex structures as one piece, requiring them to be assemblies of smaller sized components with simpler geometry. Designing a complex structure as an assembly of components can also facilitate the high dimensional integrity of the final assembly by allowing the adjustments of the critical dimensions during joining operations by means of slip planes, mating surfaces of joints that allow a small amount of relative motions.

During conceptual design, therefore, designers need to decide a set of components and their joining methods through the decomposition the whole structure. In industry, a handful of basic decomposition schemes considering geometry, functionality, and manufacturing issues have been adopted. However, these decomposition schemes are usually non-systematic and depend mainly on the designers' experience, which may cause the following problems:

• Insufficient structural stiffness: Given components and joining methods cannot meet the desired stiffness of the final assembly due to the inappropriate allocation of joints that are less stiff than components.
• Insufficient dimensional adjustability: Given components and joining methods cannot economically achieve the desired dimensional integrity in the final assembly due to the inappropriate design of the slip plains that do not allow adjustments of the critical dimensions during joining operations.
• Insufficient manufacturability: Given components and joining methods cannot be economically manufactured due to the inappropriate geometry in components and joints.

Since these problems are typically found during the detailed design and production phases, solving them requires costly and time-consuming iterations. Hence, a systematic method is highly desired for finding a set of components and their joining methods simultaneously considering structural stiffness, dimensional integrity and manufacturability. Despite its importance, the development of such a method has not been addressed in the past research literature.

This paper presents an approach for the above problem based on the assembly synthesis method [1,2,3]. Assembly synthesis is an optimization-based decomposition of product geometry for given design criteria, tailored for structural products consisting of external enclosures and internal supports. A structure is represented as a graph whose nodes are the smallest decomposable substructures specified by the designer (called basic members), and whose edges are the physical connections between two basic members. Each edge in the graph indicates a potential location of a joint, whose type is selected from the predefined joint library. The library contains feasible joint types for each potential location in the structure, and the properties of the joint types with respect to structural stiffness as a reduced stiffness matrix, dimensional adjustability as adjustable directions. By appropriately assigning a joint type to some edges in the graph, a set of components and their joining methods are uniquely specified. The problem of selecting the edges to become joints and assigning joint types to these edges are formulated as a discrete optimization problem whose objectives are to maximize the stiffness and dimensional adjustability of the final assembly, and manufacturability of each component. The stiffness is evaluated using the structural deflection obtained by finite element analyses. The dimensional adjustability is evaluated as the number of the adjustable critical dimensions. The manufacturability is evaluated as a negative of the sum of the manufacturing costs of the components estimated from their size and geometric complexity. In order to allow close examination of the trade-off among these objectives, the optimization problem is solved by a multi-objective genetic algorithm, which can efficiently generate a well-spread Pareto front over multiple objectives. A graph-based crossover scheme is adopted for the improved convergence of the algorithm. A case study with the body-in-while (BIW) of a middle size passenger vehicle is discussed. Representative designs are selected from the resulting Pareto front and trade-offs among stiffness, dimensional adjustability, manufacturability are discussed.

1

Yetis, A. and Saitou, K., "Decomposition-based assembly synthesis based on structural considerations," Journal of Mechanical Design, Vol. 124, pp. 593-601, 2002. doi:10.1115/1.1519276

2

Lyu, N. and Saitou, K., "Decomposition-based assembly synthesis of a 3D Body-In-White for structural stiffness," Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, Washington, D.C., Nov 15-21, 2003, IMECE2003-43130, 2003. doi:10.1115/IMECE2003-43130

3

Lee, B., and Saitou, K., "Assembly synthesis for optimal dimensional adjustability based on a joint library," Proceedings of the International Conference on Engineering Design, Stockholm, Sweden, August 19-21, 2003.

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