Keywords: structure analysis, topology optimization, FEM.

In this paper, the method of structural topology optimization based on the finite element (FE) structural model using ANSYS is studied, on the basis of the "ground structure method" and the "homogenization method", by which the topology structure can be determined. The structural topology optimization problem is considered as that of finding the optimal distribution of structural components and materials for a given structure.

ANSYS can be used as a tool to determine the maximum stiffness, the minimum volume (weight) and maximum natural frequency of a structure. The objective function in the optimization model is to minimize the distortion energy of the structure while the constrained conditions are satisfied. To decrease the distortion energy of the structure corresponds to strengthen the stiffness of the structure.

The idea of converting the topology optimization problem to seeking the optimal material distribution in the structure is used. It is assumed that the design area of a structure is consisted of many tiny structural units. Then the whole structure can be dispersed into many tiny FE units. Some of the units contribute more to resisting the loads than the others and the set of those units could be regarded as the path of force passing through out the whole structure. But the contribution of most of the units are between the two extremeness and the path of force passing through is not so clear. Hence an iterative calculation procedure is necessary to make the path more obviously by polarizing the units of the structure gradually until all of the important units can be determined and the path of force passing through out the structure becomes clear. The topology of the optimal structure will be found.

For that purpose, the FE model with uniformity and a fine unit net should be constructed first. Then the stress analysis will be carried out so that the stress result of every FE unit could be obtained. After that the units with lower stress will be determined by comparing with the threshold value. And their stiffness matrix will be multiplied by a small factor. Those units now could be regarded as being "killed" so that the corresponding area of the structure can be removed and will be ineffective for the applied load. And the left units are the topology optimal result for this cycle's calculation. In the optimization, unit stress and strain are used as the constrained conditions.

The method is developed by using APDL (ANSYS Parameter Design Language) as the program language tool in the ANSYS environment. It has been verified that this method is feasible and applicable not only for the continuum structural topology optimal design but also for the case of truss structures.

1

W.S. Dorn, R.E. Gomory and H.J. Greenberg, "Automatic Design of Optimal Structures", J. de Mechnique, Vol.3(1):25-52, 1964.

2

M.P. Bendsoe and N. Kikuchi, "Generating Optimal Topologies in Structural Design Using a Homogenization Method", Computation Method and Applications in Mechanics Engineering, Vol.71:197-224, 1988. doi:10.1016/0045-7825(88)90086-2

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