Shape optimization of the initial blank in the sheet metal forming process using equivalent static loads

Abstract

SUMMARYIn 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.

A Preliminary Study on the Optimum Parameters in Sheet Metal Forming

“…where, 15 b are BHF, DBRF and DBL and these design variables are used in RSM. k s is the standard deviation and the standard deviation is used to reduce wrinkling.…”

“…The equivalent static loads method for non linear static response structural optimization (ESLSO), which is a structural optimization method, is adopted for this formulated optimization. [13][14][15] Equivalent static loads (ESLs) are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. In ESLSO, nonlinear dynamic loads are transformed to ESLs and the ESLs are used as the loading conditions in linear static response optimization.…”

“…However, various design variables cannot be selected because only the design variables for linear static response optimization can be used in optimization using ESLSO. [13][14][15][16][17][18][19] The new ESLs are proposed to solve the metal forming optimization and the nonlinear strains and displacements from nonlinear analysis are considered by these ESLs. Nonlinear dynamic analysis of the sheet metal forming process is performed using the commercial software LS-DYNA.…”

Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method

“…27 Kim and Park performed nonlinear dynamic response optimization, 28 and the research was expanded for the metal forming process. 29–31 However, ESLM has not been applied to the optimization of structures with viscoelastic materials.…”

“…ESLM has been used for the metal forming problems that have a path dependency similar to viscoelastic material and uses a few time steps. 29–32 The optimization formulations are defined for some automotive dampers. Three objective functions are proposed using the sum of damping ratios, the sum of weighted damping ratios, and the sum of squared displacements.…”