Since Additive Manufacturing (AM) techniques allow the manufacture of complex-shaped structures the combination of lightweight construction, topology optimization, and AM is of significant interest. Besides the established continuum topology optimization methods, less attention is paid to algorithm-driven optimization based on linear optimization, which can also be used for topology optimization of truss-like structures.
To overcome this shortcoming, we combined linear optimization, Computer-Aided Design (CAD), numerical shape optimization, and numerical simulation into an algorithm-driven product design process for additively manufactured truss-like structures. With our Ansys SpaceClaim add-in construcTOR, which is capable of obtaining ready-for-machine-interpretation CAD data of truss-like structures out of raw mathematical optimization data, the high performance of (heuristic-based) optimization algorithms implemented in linear programming software is now available to the CAD community.
Author(s): Christian Reintjes
Publisher: Springer Vieweg
Year: 2022
Language: English
Pages: 229
City: Wiesbaden
Acknowledgments
Zusammenfassung
Abstract
Contents
Symbols
Acronyms
List of Figures
List of Tables
1 Introduction
1.1 Motivation
1.2 Structure of the Thesis
1.3 Own Contribution to Knowledge
2 Physical and Technical Background
2.1 Structural Mechanics
2.1.1 Three-Dimensional Continuum Mechanics
2.1.2 One-Dimensional Linear Theory of Structural Members
2.1.3 Truss Structures
2.2 Additive Manufacturing
2.2.1 Basics
2.2.2 Technologies
2.2.3 Support Structures
2.3 Mathematical Programming
2.3.1 Graph Theory and Flow in Networks
2.3.2 Mixed-Integer Linear Programming
2.3.3 The Optimality Gap
3 Optimization of Truss Structures
3.1 The Problem Statement
3.1.1 Theoretical Basics
3.1.2 The Ground Structure Approach
3.1.3 Truss Topology Optimization
3.2 RelatedWork
3.2.1 Literature Review
3.2.2 The Global Optimization Perspective
3.2.3 The Engineering Perspective
4 Bridging Algorithm-Driven Truss Optimization and Additive Manufacturing
4.1 Algorithm-Driven Design Methodology for Additive Manufacturing
4.1.1 A Technical Operations Research Approach
4.1.2 An Algorithm-Driven Product Design Process
4.2 Basic Problem Statements and Kinematic Indeterminacy
4.2.1 Basic Problem Statements
4.2.2 Kinematic Compatibility
4.3 Preparations Towards a Truss Design Problem
4.3.1 Structural Member
4.3.2 Force Equilibrium
4.3.3 Moment Equilibrium
4.4 Design Space
4.4.1 Additive Manufacturing Constraints
4.4.2 Assembly Space
4.4.3 Ground Structure
4.5 Support Structure Optimization
5 Mixed-Integer Linear Programming for Truss Optimization
5.1 Preliminaries
5.2 The MILP TTOl;p for Powder-Based Additive Manufacturing
5.3 The MILP TTOl;s for Support-Free Truss-Like Structures
5.4 The MILP TTOl;m for Manufacturable Cross-Sectional Areas
5.5 The QMIP TTOl;q for Robust Truss Topology Optimization
6 CAD-Based Mathematical Optimization
6.1 Motivation
6.2 Implementation Details
6.3 Performance Study
6.4 User Interface
7 Computational Study
7.1 Optimization for Powder-Based Additive Manufacturing Systems: MILP TTOl;p
7.2 Optimization of Support-Free Truss-Like Structures: MILP TTOl;s
7.3 Segmented Blank Holder: MILP TTOl;m
7.4 Robust Truss Optimization: QMIP TTOl;q
8 Conclusion and Outlook
8.1 Conclusion
8.2 Outlook
Bibliography
