Computational synthesis of structures and mechanisms using topology optimization with variable boundary conditions

Topology optimization is a computational design method capable of automatically generating optimal structures after only being given a set of design requirements, a space to distribute material within, and the boundary conditions of the problem. However, there are many problems where the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads and supports are often difficult to find manually. This substantially limits topology optimization’s effectiveness for many structural and mechanism design problems. The work of this dissertation removes this limitation by developing methods which automatically determine optimal boundary condition configurations simultaneously with optimal material layouts. To parameterize the shapes, locations, and orientations of loads and supports, a modified finite element model is constructed where elastic support springs and applied forces are placed everywhere in the domain. A feature-mapping method is then used to control the distributions of support stiffness and load magnitude, as well as the shapes and locations of movable non-design regions. By this parameterization, the boundary conditions are made smooth and continuous functions of the design variables. The design sensitivities are computed using the adjoint sensitivity analysis method and the optimization problems are solved using the method of moving asymptotes. The technique is first implemented in a two-dimensional topology optimization algorithm with linear elastic physics. Several simple cases of static structures and compliant mechanisms are synthesized, showing improvements in design performance of up to 150%. A prototype compliant mechanism is additively manufactured to demonstrate the practical applicability of the method. The method is then extended to three dimensions to solve a structural optimization problem of a component within an assembly, where the load transfer point between parts is a design parameter. Using a variable applied load, manufacturing constraint methods, and high-performance computing, a wheel-and-axle structure is successfully synthesized from only a high-level description of its intended function. Finally, using nonlinear elastic physics, methods for a variable input displacement are developed. A variety of compliant mechanisms are synthesized with large output displacements, snap-through responses, and prescribed output paths, producing designs with significantly improved performance in every case tested. Compared to optimal designs generated using best-guess boundary conditions used in previous studies, the mechanisms presented see performance increases ranging from 23%-430%. Overall, the work of the dissertation expands the capabilities of the topology optimization method and shows that significantly improved designs can be discovered in both structural and compliant mechanism design problems when the boundary conditions are automatically optimized parameters.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Alacoque, Lee R.

Contributors dc:contributor

• James, Kai A
• Geubelle, Philippe H
• Goza, Andres
• Zhang, Xiaojia

• Topology Optimization
• Structural Optimization
• Structures
• Compliant Mechanisms
• Finite Element Method
• Variable Loads
• Variable Supports
• Design Of Loads
• Design Of Supports
• Boundary Condition Optimization
• Design Of Boundary Conditions
• Morphing Wing Design
• Nonlinear
• Large Displacement
• Hyperelastic
• Bistable
• Snap-through
• Path Generating
• Displacement Control
• Machine Design
• Elasticity
• Geometry Projection
• Feature Mapping

Statement dc:rights

• Copyright 2023 Lee R. Alacoque

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121936

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121936