The optimization algorithm presented in this thesis employs principal stress trajectories generate an optimal topology by focusing on the manipulation of strut layout with fixed thicknesses between all elements in the resulting frame. Layout and thickness are, however, coupled with regard to their effects on structural performance. It is anticipated that a topology optimization algorithm that determines optima for both strut layout and independent element thicknesses will lead to improved mass performance while still meeting the maximum stress requirements of the design. It is also possible that thinner struts would encourage the most optimally performing layouts to employ larger numbers of trajectories compared to the cases presented in this thesis. The addition of strut thickness as a design variable would also require modification of the application of constraints on overlap of materials in the design.
Simulated annealing was the optimization algorithm used for all of the analyses presented in this thesis. While simulated annealing is a versatile algorithm, other heuristic techniques were not explored. Some other heuristic techniques that could be employed include Genetic Algorithms and Particle Swarm Optimization. Any of these algorithms could potentially result in more rapid convergence to the optimal solution.
Maximum stiffness was used as the optimization goal for determining frame layouts in this thesis because of the definition of Michell structures as the stiffest possible structures for the amount of material that they employ. It could be beneficial to implement the use of numeric stress trajectory mapping for building optimal frames that use different objectives to determine
layout, such as minimizing mass, maximizing stiffness per unit mass, maximizing damping properties of the frame, or removing stress concentrations from the design.
Additional study could be conducted on how the strut layout is affected by the mesh density of the initial ANSYS finite element analysis used to extract the principal stress field that determines the stress trajectory paths. Relatively dense finite element models were utilized in this thesis, but the mesh was not graded near boundary conditions or corners. It is possible that a finer mesh near the boundary could account for unusual stress behavior occurring around boundary conditions.
Improvements to the finite element analysis model employed in Matlab could be introduced to this topology optimization model. The beam elements employed do not account for localized stresses that occur at the boundary conditions, points of loading, and strut intersections. Modelling the new design using two dimensional solid elements may help to account for this shortcoming, though it would require a significantly more complex decision making process to automate the procedure of creating nodes and elements.
As explained in Chapter 5, there is potential for this algorithm to be applied to more complex geometries. Any features that cause stress concentrations such as corners or holes in the structure could have a significant impact on the effectiveness of numerical determination of the principal stress trajectories.
The optimal layouts generated using principal stress trajectories show some geometric differences compared to existing optimal structure designs, particularly in regard to strut placement near boundaries and where struts are connected to boundaries. It would be beneficial
to compare the performance of designs generated numerically using principal stress trajectories to designs resulting from analytical methods or optimization procedures.
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