Characterization of Additive Manufacturing Constraints for Bio-Inspired, Graph-Based Topology Optimization

Date of Award


Degree Name

M.S. in Mechanical and Aerospace Engineering


Department of Mechanical and Aerospace Engineering


Markus P. Rumpfkeil


With more efficient computational capabilities, the use of topology optimization (TO) is becoming more common for many different types of structural design problems. Rapid prototyping and testing is often used to further validate optimized designs, but depending on a design's complexity, the structural behavior of physical models can vary significantly compared to that of their computational counterparts. For graph-based topologies such differences are caused, in part, by a need to realize finite-thickness structures from the infinitely thin geometries described by graph theory. Other differences are caused by limitations on manufacturing processes such as the need to fabricate large models from smaller components. While additive manufacturing (AM) can be more conducive for fabrication of complex topologies, its limitations are generally less understood than those for traditional subtractive manufacturing processes. Understanding and incorporating limitations on AM into a TO process in the form of added constraints would allow the algorithm to produce not only optimal designs, but also those that are feasible for AM. In this work, two specific AM constraints are characterized for Lindenmayer system (L-system) graph-based topologies of a multi-material, diamond-shaped, morphing airfoil in supersonic flow. One constraint is related to the feasible generation of thick structural members from the infinitely thin beams of graph-based topologies. To characterize the effects of geometric overlap, structural behavior of finite element models made of lower-fidelity beam elements is compared to that of finite element models made of higher-fidelity volume elements. Results indicate that at intersections where 10% or more of a member's length is overlapped, there will be significant variations in stress and effective torsional stiffness when thin members are converted to thick members. The second AM constraint characterized in this work is related to partitioning of large models that exceed a 3D printer's build size. Finite element analyses and laboratory experiments indicate that differences in localized displacements and distribution of maximum principal strain will occur when partitioning a physical model derived from the multi-material graph-based topologies. Partitioning perpendicular through structural members is recommended since it proved to be the most consistent method employed in the studies in terms of affecting structural behavior of the geometry.


Aerospace Engineering, Mechanical Engineering, Engineering, Additive Manufacturing, Additive Manufacturing Constraints, Graph-Based Topology, Graph-Based Topologies, Topology Optimization, Optimization, Design for Additive Manufacturing, DfAM, Optimization Constraints, Multi-Component Topology Optimization, Assembly Synthesis, Finite Element Analysis, FEA, Digital Image Correlation, DIC, L-system

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Copyright 2021, author.