Exact global optimization of frame structures for additive manufacturing

We consider the problem of designing lightweight load-bearing frame structures with additive manufacturability constraints. Specifically, we focus on mathematical programming approaches to finding exact globally optimal solutions, given a pre-specified discrete ground structure and continuous design...

Full description

Saved in:
Bibliographic Details
Published in:Structural and multidisciplinary optimization Vol. 65; no. 3
Main Authors: Toragay, Oguz, Silva, Daniel F., Vinel, Alexander, Shamsaei, Nima
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer Nature B.V
Subjects:
Computational Mathematics and Numerical Analysis
Continuity (mathematics)
Engineering
Engineering Design
Frame structures
Global optimization
Integer programming
Linear programming
Load bearing elements
Manufacturability
Mathematical programming
Mixed integer
Nonlinear programming
Research Paper
Stiffness matrix
Theoretical and Applied Mechanics
Mixed integer non-linear programming
Frame structures
Additive manufacturing
Mixed integer linear programming
Mixed integer quadratically constrained programming
Discrete topology optimization
ISSN:1615-147X, 1615-1488
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We consider the problem of designing lightweight load-bearing frame structures with additive manufacturability constraints. Specifically, we focus on mathematical programming approaches to finding exact globally optimal solutions, given a pre-specified discrete ground structure and continuous design element dimensions. We take advantage of stiffness matrix decomposition techniques and expand on some of the existing modeling approaches, including exact mixed-integer nonlinear programming and its mixed-integer linear programming restrictions. We propose a (non-convex) quadratic formulation using semi-continuous variables, motivated by recent progress in state-of-the-art quadratic solvers, and demonstrate how some additive-specific restrictions can be incorporated into mathematical optimization. While we show with numerical experiments that the proposed methods significantly reduce the required solution time for finding global optima compared to other formulations, we also observe that even with these new techniques and advanced computational resources, discrete modeling of frame structures remains a tremendously challenging problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-022-03178-0