There are three kinds of structure optimization, they are: size optimization, shape optimization and topology optimization. Three optimization methods correspond to the three stages of the product design process, namely the detailed design, basic design and conceptual design, as shown in Figure 1.

Size optimization keeps the structural shape and topology structure invariant, to optimize the various parameters of structure, such as thickness, section size of beam, materials’ properties; shape optimization maintains the topology structure, to change the boundary of structure and shape, seek the most suitable structure boundary situation and shape; topology optimization is to find the optimal path of materials’ distribution in a continuous domain which meet the displacement and stress conditions in structure, make a certain performance optimal. Thus, compared to size and shape optimization, topology optimization with more freedom degree and greater design space, its greatest feature is under uncertain structural shape, according to the known boundary condition and a given load to determine the reasonable structure, both for the conceptual design of new products and improvement design for existing products, it is the most promising aspect of structural optimization [5] .

For continuous structure topology optimization, there are some mature methods like: uniform method, evolutionary structural optimization method, variable density method .etc. Uniform method introduced cell structure of micro structure (unit cell) in the elements of the structure, each unit cell has three forms, namely non-material voids (size = 1), isotropic-material entity medium (size = 0) and orthotropic-material opening-hole medium (0 < size < 1). Wherein the distribution of each form will be able to describe the form of topology and the shape of structure; evolutionary structural optimization method believe that stress in any parts of the structure should under the same level in an ideal structure [6] . That means the local material with a low stress state is not fully utilized, so you can delete the material artificially. So gradually remove material which in a low stress state, and then delete the update rate, so optimized structure becomes more uniform.

Variable density method is used to conduct optimization in this paper. The basic idea is to introduce a hypothetical material which density is variable and range from 0 to 1. After changing the continuous structure to finite element model, then making per units’ density as the design variables, to convert topology optimization

problem into the optimal distribution of material, while in order to suppress the intermediate density of the material (material between void and entities), the introduction of a interpolation penalty factor used to describe the relationship between Young’s modulus and density of the material which shown as the following formula:

where: p―interpolation penalty factor (p > 1); E₀―Young’s modulus of densified material unit; E―Young’s modulus after interpolation. So that the original model with intermediate density will be eliminated or replaced by densified material and will achieve optimal results which close to the entity [7] .

Therefore, during topology optimization, variable is relative density of units, then structural topology optimization problem is converted into the optimal distribution of the material.

Based on HyperWorks platform topology optimization holder, first, according to the engine mounting position, we establish the three-dimensional geometric model of engine bracket, and then pretreated in HyperMesh, define design area, objective function and constraints under the optimization panel, finally operate topology optimization which design process is as Figure 2.

To simplify FE model in software then a high quality mesh can be got. Ignore some of the features which have very small impact on analysis such as holes and fillets. The material is aluminum, the related parameters are shown in Table 1.

Mesh the model with four-node tetrahedral element which the size is 3 mm. The total number of element is 90,847 and using the bar element to simplify screw connection. The final FE model is as Figure 3.

We complete pre-treatment in HyperMesh and transfer the user profile to RADIOSS solver. The most dangerous condition of bracket is resonance with the engine when start the car. The car is under the horizontal force 12,000 N, vertical force 10,000 N. 6 degrees of freedom constraint is applied to the area between engine and engine bracket. We calculate the distribution of stress finally.

From the displacement contour, as shown in Figure 4, maximum displacement 0.4 mm occurs in the upper right ligament; from the stress contour, maximum stress 331 Mpa occurs in the upper right connection. Both of them exceed the design requirements, so the bracket needs to optimize.