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Surface distortions are frequently introduced into the Class “A” surfaces during various sheet metal forming operations such as drawing, trimming and flanging. The origins of those surface distortions have not been well understood. The scope of this research is to investigate the distortion that occurs in draw operation and to find effective and practical corrective methods. Five geometric parameters are first identified to represent a typical depression feature in automobile outer panels. Experimental dies are then designed to reflect various combinations of these five geometric parameters with the assistance of numerical simulations to ensure that the dies can make parts free of major defects like splits and wrinkles. Surface distortions are observed in our stamping experiments and various techniques are used to measure and record the distortions for further mathematical analysis.

This report describes the use of meshfree methods for response and design sensitivity calculations within structural reliability analysis when geometric shape is a random variable. Brief descriptions of meshfree methods and advanced probabilistic methods are provided. An existing interface between the probabilistic analysis and traditional finite element method is modified to allow the use of meshfree methods for response and design sensitivity calculations within the probabilistic analysis routine. Two examples that treat design shape as a random variable are presented to assess the accuracy and use of meshfree methods for reliability analysis.

The slope discontinuity in C° contact formulation is known as the cause of iteration convergence difficulty in sliding contact. In this paper, a smooth contact surface representation is introduced to remove the slope discontinuity in a C° contact formulation. The non-uniqueness in the solution of closest point projection near the junction of C° surfaces is eliminated by this new approach. The smooth surface representation is incorporated into meshfree formulation to yield a consistent tangent operator for frictional contact problems. The proposed method is successfully applied to a sheet metal deep drawing problem involving large sliding contact and a sheet metal stamping problem.

Roller offsetting is an incremental forming technique used to generate offset stiffening or mating features in sheet metal parts. Compared to die forming, roller offsetting utilizes generic tooling to create versatile designs at a relatively lower forming speed, making it well-suited for low volume productions in automotive and other industries. However, more significant distortion can be generated from roller offset forming process resulting from springback after forming. In this work, we use particle swarm optimization to identify the tool path and resulting feature geometry that minimizes distortion. In our approach, time-dependent finite element simulations are adopted to predict the distortion of each candidate tool path using a quarter symmetry model of the part. A multi-objective fitness function is used to both minimize the distortion measure while constraining the minimal radius of curvature in the tool path.