Efficient sizing of structures under stress constraints

Zhi Hong, Mostafa M. Abdalla

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Optimisation algorithms used to automatically size structural members commonly involve stress constraints to avoid material failure. Therefore the cost of optimisation grows rapidly as the number of structural members is increased due to the corresponding increase in the number of constraints. In this work, an efficient method for large scale stress constrained structural sizing optimisation problems is proposed. A convex, separable, and scalable approximation for stress constraints which splits the approximation into a local fully stressed term and a global load distribution term is introduced. Predictor-corrector interior point method, an excellent option for large scale optimization problem, is chosen to solve the approximate subproblems. The core idea in this work is to achieve computational efficiency in the optimization procedure by avoiding the construction and the solution of the Schur complement system generated by the interior point method. Avoiding the Schur complement, and explicit sensitivity analysis, eliminates the high cost of solving stress constrained problems within the interior point optimisation. This is achieved using the preconditioned conjugate gradient method, and a new preconditioner is proposed specifically for stress constrained problems. The proposed method is applied to a number of beam sizing problems. Numerical results show that optimal complexity is achieved by the algorithm, the computational cost being linearly proportional to the number of sizing variables.

Original languageEnglish
Title of host publicationECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering
PublisherNational Technical University of Athens
Number of pages25
ISBN (Electronic)9786188284401
Publication statusPublished - 2016
Event7th European Congress on Computational Methods in Applied Sciences and Engineering - Crete, Greece
Duration: 5 Jun 201610 Jun 2016
Conference number: 7


Conference7th European Congress on Computational Methods in Applied Sciences and Engineering
Abbreviated titleECCOMAS Congress 2016
Internet address


  • Preconditioned conjugate gradient method
  • Sensitivity analysis
  • Sizing optimization
  • Stress constraints

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