Abstract Nowadays, the casting structure of stamping dies is designed according to die design standards. These standards are usually not based on a structural optimization algorithm and often rely on high safety factors which cause the weight of die components to be more than required. This in turn calls for higher prices of dies and production energy required per part. Therefore, alternative methods to reduce the weight of these components are required. In this paper, a software package is presented which can design an improved structure of stamping dies with a substantial reduction in weight. This package im- plements Abaqus software and uses the bi-directional evolu- tionary structural optimization (BESO) method to create a new lighter structure which resembles the shape of the sheet metal part and applied forces in the operation. It obtains the desired optimum design by removing from and adding mate- rial to the die component structure. This method involves adding material to that part of the component where the struc- ture is overstressed and simultaneously removing material where the structure is understressed. This procedure is carried out again and again until the objective function is minimized. Finally, the proposed structure can also be reconstructed by the designer to accommodate for a simpler casting method. The operation of the software is demonstrated by an example where the dies for a sheet metal part are studied. The die components are initially designed, analyzed, and compared with the standard die (the die which is in general use today). The final results show a reduction of 31 % of volume while the maximum displacement and stress of the die do not change

1 Introduction

Stamping dies are used in automotive industry to produce large sheet metal parts. The main components of these dies, including die, punch, and blank holder, are large in size and weight. In most cases, forming forces applied to these compo- nents are not great enough to cause a noticeable displacement and stress. So in order to overcome these forces, a totally solid part is not required, and uniformly distributed ribs are gener- ally designed for supporting the die face. The structure of these dies is designed in accordance with the rules used by the experts and the existing standards. However, in some cases, the pressure distribution of the die face is ignored by the designer [1]. This design thus leads to the increase of the size and weight of these dies, which results in excessive costs as well as difficulties in transportation and installation and operation [2]. On the other hand, die design with fewer struc- tural ribs can save energy consumption in transportation and operation and the cost of material of die but may have the problem of die failure. Therefore, the light-weight design of the large-scaled stamping die with structural optimization methods is certainly important.

In the last three decades, structural optimization methods were applied to generate an appropriate structural configura- tion by redistributing the material in the design space with the boundary conditions and prescribed loads. In the final design, a light-weight structure is obtained with the required structural strength and stiffness [3–5]. The distribution of the material is generally described with some different methods. Up to now, considerable research and several structural optimization methods such as homogenization methods [6, 7], level set methods (LSM) [8, 9], evolutionary structural optimization (ESO) methods [10, 11], bi-directional evolutionary structural optimization (BESO) methods [12–14], solid isotropic mate- rial with penalization (SIMP) methods [15–18], genetic algo- rithms (GAs) [19, 20], particle swarm optimization (PSO) algorithm [21, 22], cuckoo search algorithm [23, 24], artificial bee colony (ABC) algorithm [25], and harmony search (HS) algorithm [26, 27] have been proposed. Among these methods, the ESO and SIMP methods are more popular and used widely in both engineering optimization and academic research [28].