Adaptive solution of truss layout optimization problems with global stability constraints

Alemseged Weldeyesus, Jacek Gondzio, Linwei He, Matthew Gilbert, Paul Shepherd, Andy Tyas

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Truss layout optimization problems with global stability constraints are nonlinear and nonconvex and hence very challenging to solve, particularly when problems become large. In this paper, a relaxation of the nonlinear problem is modelled as a (linear) semidefinite programming problem for which we describe an efficient primal-dual interior point method capable of solving problems of a scale that would be prohibitively expensive to solve using standard methods. The proposed method exploits the sparse structure and low-rank property of the stiffness matrices involved, greatly reducing the computational effort required to process the associated linear systems. Moreover, an adaptive ‘member adding’ technique is employed which involves solving a sequence of much smaller problems, with the process ultimately converging on the solution for the original problem. Finally, a warm-start strategy is used when successive problems display sufficient similarity, leading to fewer interior point iterations being required. We perform several numerical experiments to show the efficiency of the method and discuss the status of the solutions obtained.

Original languageEnglish
Pages (from-to)2093-2111
JournalStructural and Multidisciplinary Optimization
Volume60
Issue number5
Early online date15 Jun 2019
DOIs
Publication statusPublished - 30 Nov 2019

Keywords

  • Global stability
  • Interior point methods
  • Semidefinite programming
  • Truss structures

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization

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