Non-gradient based 3-D preform shape optimization using the response surface method(RSM)is presented in this work.Currently,the 2-D design sensitivity analysis for preform shape optimization is widely used,however,in cases where the parts are neither axisymmetric nor plane strain,2-D assumptions do not hold well.The number of design variables required to define the 3-D preform shape is high,making most approximation methods impractical for shape optimization.The goal is to make design optimization practical and efficient by developing reduced-order-modeling techniques for 3-D preform shape optimization.Preform shape is treated as a combination of basis shapes.Forging simulations are conducted at predefined design of experiment points(DOE).RSM models for underfill and strain variance are developed,which are functions of the preform shape.The preform shape is defined by a linear combination of various billet shapes,called basis vectors,with the coefficients or the weights for each basis vector used as design variables.The optimization problem is formulated to minimize strain variance while placing constraints on underfill.Flash is restricted to between 3 to 6 % as per industry requirements,using scale factors.Test problems are used to demonstrate the effectiveness of the approach.Preform,response surface method,shape optimization,basis shapes.
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