Achyuthan Jootoo

PhD Candidate

TO for Structural Design

Topology Optimization (TO) has been used for mechanical and aeronautical component design. However, since TO treats the optimization problem as a material redistribution problem and generates optimal monolithic structures, its use in structural design is limited. This study evaluates the performance of structures obtained from TO and compares it with structures developed using optimization heuristics. The impact of different parameters (initial conditions, volume ratio and mesh resolution) on the obtained structure was analyzed (this analysis is not presented here). This study forms the first part of my design methodology which generates structures using TO, converts them into node and element representations and then finally optimizes them using an optimization heuristic.

Methodology

In order to perform TO, Sigmund's 99 line code for topology optimization was modified as per the needs of the problem. A parameter that defined the initial conditions was also added to this program. Several initial conditions were generated by using Cellular Automata. Once a structure was optimized using TO, it was manually imported into Risa and analyzed for stress and displacements. In some cases, the structure was modified, by adding additional members, to convert the TO output into a valid truss. The performance of this truss was then compared with the performance of optimal structures obtained in the literature.

Results

The figure below shows (a) the 18 bar truss, (b) the optimal structure obtained for the 18 bar truss by Rahami et al. 2008, (c) optimal TO structure and (d) the modified TO structure imported into Risa. Since the TO structure was not a stable truss, additional members were added. From the figure, it can be clearly seen that the topologies obtained by TO is significantly different from the optimal topologies obtained previously.

The modified topology obtained from TO was compared with the topologies obtained by Kaveh and Kalatjari 2004 and Rahami et al. 2008. The table below shows this comparison.

MetricsKaveh and KalatjariRahami et. al.TO Result
(Frame)
TO Result
(Truss)*
Weight (kgs)2062.92055.12098.72101.4
Deflection (mm)463.3511.81283.7229.4
Max. Stress (ksi)137.41137.90123.14135.21
Avg. Stress (ksi)75.0179.5759.4362.88
Truss obtained after modification and addition of members

The table above shows that the structures optimized in the literature are lighter than the TO designed structures by about 2% for the frame structure and 6.7% for the truss structure. However, while the TO structure is heavier, it has slightly lower maximum stress, lesser average stress and significantly lower deflections. The deflection of the TO truss structure is less than half the deflection of the structures optimized by Kaveh and Kalatjari 2004 and Rahami et al. 2008. Further, since the average stress and deflection are lower for the TO result, it is possible to further reduce the weight of the structure by employing a subsequent optimization step.