An improved size, matching, and scaling synthesis method for the design of meso-scale truss structures

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Chang, Patrick
Rosen, David W.
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The recent improvement of additive manufacturing has allowed designers to achieve a level of complexity and customizability that is difficult or impossible to accomplish using traditional manufacturing processes. As a result, much research has been conducted on developing new methods to utilize the larger design space brought by additive manufacturing. One such research area is in the design of mesoscale lattice structures. Mesoscale lattice structures are a type of cellular structure with support element sizes on the order of magnitude of centimeters. These types of structures are engineered for high performance and have applications in industries where both low weight and high strength are desired. However, due to the small size of their struts, these structures can easily have hundreds to thousands of individual struts. As a result, design poses a unique challenge. Current methods approach design of mesoscale lattice structures as a topological optimization problem, treating each strut diameter in the structure as a design variable. For structures with a fewer number struts, these optimization methods can converge, but will generally be very time-consuming. For structures with a large number of struts, the optimization problem becomes too large for current algorithms to solve. In previous research, a new, highly efficient design method for mesoscale lattice structures was presented that eliminates the need for global size or topological optimization. This method, termed the Size, Matching and Scaling method, used a unique combination of a solid-body finite element analysis and a library of pre-defined lattice configurations, termed the "unit-cell library," to generate lattice topologies. The results from this method were highly promising: design time was significantly reduced when compared to optimization methods. Furthermore, lattices designed using the SMS method had performance results that were either comparable or better than their optimized counterparts. However, the method developed was highly conceptual, lacking a true systematic methodology for generating topologies and suffering from some gaps in implementation. In this research, we present a modified Size Matching and Scaling (SMS) design method. Firstly, we introduce and outline the modified methodology. This methodology particularly includes an optimization step for determining strut diameters that replaces the manual search used in the original method. Secondly, we expand and explore the unit-cell library in an attempt to improve the performance of lattices generated using the SMS method. In particular, we optimize several unit-cell configurations and compare their performance in the context of the SMS method. Finally, we test the updated SMS methodology and unit-cell library using various design examples. Results from the various example problems indicate that optimization is not only a viable systematic method for determining diameter values, but is actually preferred to the manual, iterative process used in the original method. Furthermore, various optimization algorithms and approaches yield different results. Between the two optimization algorithms utilized in this method: constrained optimization and least-squares minimization, constrained minimization converges faster, but least-squares minimization yields slightly improved performance results. In addition to these algorithms, a one-variable approach using an untested, simplifying assumption, dubbed the "28% approach," was tested. Results indicate that this assumption was incorrect and cannot be utilized. Finally, results from the expanded unit-cell library indicate that the best unit-cell configuration is still the same original unit-cell configuration utilized in the first SMS method. The addition of more unit-cell does not improve the performance of structures generated using the SMS method. In fact, both performance and design time worsen when additional configurations are utilized.
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