A Novel Approach to Requirement Driven Lattice Design and Optimization

Open Access
- Author:
- Fisher, Joseph
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 19, 2024
- Committee Members:
- Robert Kunz, Professor in Charge/Director of Graduate Studies
Michael Yukish, Outside Field Member
Nicholas Meisel, Major Field Member
Timothy Simpson, Chair & Dissertation Advisor
Simon Miller, Outside Unit Member
Mary Frecker, Major Field Member - Keywords:
- Lattice Structures
Triply Periodic Minimal Surface
TPMS
Design Theory
Design Framework
Optimization
MBB Beam
Homogenization
Finite Element Analysis
Mechanical Testing
Design of Experiments
Lattice Property Models - Abstract:
- In the field of additive manufacturing, highly ordered cellular structures with repeating patternsin space, known as lattice structures or simply “lattices,” can significantly improve the performance per unit mass of engineered components compared to traditionally machined designs. The characteristics of these lattices depend on many design decisions due to their geometric complexity and the opportunity for spatial variability, leading to challenges in deciding how to best use them, where they are best suited, and which is appropriate for a given problem and process. Many methods have been proposed to optimally distribute material within a lattice structure à la topology optimization; however, these methods typically exist in a bubble, independent of broader engineering design criteria and processes. The research in this dissertation develops a framework, based on systems engineering, to guide the design of lattice structures using the component requirements as inputs and outputting a verified and validated design based on those requirements. The framework decomposes component requirements down to the lattice structure and provides a method to verify and validate design choices with testing and integration so as to meet those requirements similar to the System Vee Model. The framework is explored with multiple examples supported by empirical results and numerical simulations to provide a holistic approach to lattice integrated design. The choice of a lattice topology is critical in maximizing the value of the lattice structure and its unique properties for the intended application, and selecting the best topology requires an understanding of the relative performance of different topologies. To support this, we compile a catalog of lattice structures from the literature that includes all Triply Periodic Minimal Surfaces (TPMS) for which a low-order Fourier series fit is known (ensuring they can be modeled and manufactured). This repository helps to clarify several discrepancies and inconsistencies in the literature and to generate useful engineering data to support the proposed framework with simulated lattice property data. Our generated content includes high-resolution images, elastic property data, CAD models, and implicit function definitions that are useful for the visualization, selection, and implementation of these lattice structures. A novel aspect of this research includes exercising an optimal experiment design to generate mechanical property maps that can be used to define the geometry of your lattice directly from the desired performance. These maps are introduced into the proposed framework as a design assist tool to increase usability and demonstrate its extension. The design space offered by lattices is vast, and new lattices can be generated relatively easily to support engineering decision making. We develop several novel lattice variants based on existing topologies through geometric curvature analysis and multi-objective optimization. Our results show that new lattice definitions are readily incorporated into the proposed framework and that new formulations of lattices can be proposed to increase performance relative to contemporary lattices. Finally, the proposed framework is explored through several case studies. These case studies explore problems of varying complexity from 2D to 3D and compare our approach against topology optimization. We show that the framework can be readily applied to engineering problems by careful decomposition of component requirements onto the lattice, lattice design choices and manufacturing considerations, then integrated via field-driven (engineering property maps) to produce solutions. Comparison problems of the proposed approach to topology optimization show that engineering intuition and guiding principles can be used to define suitable design spaces with commensurate solution spaces.