Methodologies of rapidly assessing maximum possible forming heights are needed for three-dimensional $3D$ sheet metal forming processes at the preliminary design stage. In our previous work, we proposed to use an axisymmetric finite element model with an enlarged tooling and blank size to calculate the corner failure height in a $3D$ part forming. The amount of enlargement is called center offset, which provides a powerful means using $2D$ models for the prediction of $3D$ forming behaviors. In this work, an analytical beam model to calculate the center offset is developed. Starting from the study of a square cup forming, a simple analytical model is proposed and later generalized to problems with corners of an arbitrary geometry. The $2D$ axisymmetric models incorporated with calculated center offsets were compared to $3D$ finite element simulations for various cases. Good assessments of failure height were obtained.

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