Geometric projection-based design optimization for manufacturable structures subjected to transient dynamic loads

Gabriel J. Holder

doi:10.17918/00000399

One of the quintessential tasks of an engineer is to increase the efficiency of a system to get better performance for the same or decreased cost. In structural design optimization, an orderly approach is taken to find a final design that yields the most satisfactory response to a given situation. Most problems in this domain are solved under static conditions, but real-world applications often require the consideration of time-dependent forces and inertial properties of the structure. Structural responses to transient dynamic loads have been considered in designing for impacts, crashworthiness (energy dissipation), and elastic wave propogation management. In most of these methods, a free-form density-based approach is used. Although some manufacturing constraints can be applied, it is tough to enforce highlevel geometric constraints on the final structure such as restrictions on the shape and size of members. Additionally, extra heuristics must be used to mitigate the issue of mesh dependency, where optimized designs for different mesh sizes are not consistent. Projection methods provide an alternative to the free-form density-based approach and are capable of forcing the final design to be composed of geometric primitives such as bars or plates. This also enables the designer a greater ability to enforce constraints on the characteristics of each component of the structure and can lead to greater mesh independence. To achieve better dynamic performance from designs well-suited for fabrication, this work implements the geometric projection topology optimization framework to optimize structures subjected to transient dynamic loads. Designs are composed of sets of rectangular bars with semi-circular end-caps and each bar is parameterized by its endpoints, thickness, and a size parameter which facilitates the removal or inclusion of bars. For each step of the design process, the bars are projected onto a fixed-mesh and the stiffness and mass properties of the structure are calculated. The response of the structure due to the transient dynamic loading is found and a sensitivity analysis is performed to find the direction in which the optimizer should step. Since the design space of projection methods are a smaller subset of the free-form density approach, caution is taken to move carefully through the optimization to avoid local minima by employing move limits and a continuation approach for penalization. Numerical examples are solved to illustrate the performance of this implementation and explore some of its characteristics. The method is found to show promise in tailoring designs to different load rate and produces simpler structures than the free-form density method, while not showing much decrease in performance. A trade-off between manufacturability and performance is found when restricting the ability of bars' radii to vary continuously compared to fixing all the radii at the beginning. Finally, optimizations completed with the geometric projection method for dynamic response are shown to have mesh independent properties that may allow the use of coarser meshes, potentially reducing computational cost.

Geometric projection-based design optimization for manufacturable structures subjected to transient dynamic loads

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Geometric projection-based design optimization for manufacturable structures subjected to transient dynamic loads

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