Inverse Method in Sheet Metal Forming for Auto-body Design

Abstract

This paper is concerned with inverse analysis in sheet metal forming for auto-body design that includes the feasibility of forming of sheet metal parts and the crashworthiness assessment of formed parts as auto-body structures. The inverse analysis is an efficient and convenient method to evaluate the plastic strain distribution in formed sheet metal parts without preparation of tooling prior to process design as well as the crashworthiness of formed parts considering the fabrication history. The method also provides information on the optimum process parameters for sheet metal forming and remedy for forming of complicated and infeasible sheet metal parts. The inverse method incorporates with the plastic deformation theory, minimization of plastic work with constraints, and a pertinent initial guess in order to obtain the plastic strain distribution and the initial blank shape from a desired final shape. The method needs to deal with the corresponding sliding constraint surfaces for minimization iteration and the convergence among intermediate shapes for multi-stage forming processes. Although the present method requires many numerical schemes mentioned above, it needs only short computing time for the sake of its inherence. The numerical example demonstrates the versatility and efficiency of the present method. One of them is a multi-stage deep-drawing process of a rectangular cup with the large aspect ratio, which is hardly realized without the aid of the present method. Another is the prediction of the plastic strain distribution in formed sheet metal members of which an auto-body structure consists. With the strain distribution predicted, the crashworthiness assessment of auto-body structures can be carried out accurately at the initial stage of auto-body design.