Shape Optimization of the Initial Blank in the Sheet Metal Forming Process Using Equivalent Static Loads

Abstract

In the sheet metal forming process, forming the final desired shape is difficult to obtain due to wrinkling, tearing, failure of material, etc. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. Many researchers have conducted studies to predetermine the initial blank shape. The structural optimization technique is one of them. Non-linear response structural optimization is required because non-linearities are involved in the analysis of the metal forming process. When the conventional method is utilized, the cost is extremely high due to repeated non-linear analysis for function and sensitivity calculation. In this paper, the equivalent static loads (ESLs) method is used to determine the blank shape which leads to the final desired shape and reduced wrinkling. The ESLs method is a structural optimization method where non-linear dynamic loads are transformed into ESLs, and these ESLs are utilized as external loads in linear response optimization. The design is updated in linear response optimization. Non-linear analysis is performed with the updated design and the process proceeds in a cyclic manner. An optimization formulation is defined for the examples, the formulated problems are solved to verify the proposed method and the results are discussed. Non-linear analysis is performed using the commercial software LS-DYNA, NASTRAN is used for calculating the ESLs and linear response optimization, and an interface program for LS-DYNA and NASTRAN is developed.