Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming

In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness...

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Published in:Applied Mechanics and Materials Vol. 807; pp. 229 - 238
Main Authors: Pfetsch, Marc E., Kuttich, Anja, Gally, Tristan, Gehb, Christopher M., Ulbrich, Stefan, Kolvenbach, Philip
Format: Journal Article
Language:English
Published: Zurich Trans Tech Publications Ltd 01.11.2015
Subjects:
Compliance
Cross-sections
Elasticity
Mathematical analysis
Mathematical models
Matrix methods
Mechanical engineering
Mixed integer
Optimization
Robustness (mathematics)
Semidefinite programming
Stiffness matrix
Truss Topology Design
Semidefinite Programming
Beam Element
Robust Optimization
ISBN:3038356522, 9783038356523
ISSN:1660-9336, 1662-7482, 1662-7482
Online Access:Get full text
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Summary:In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.
Bibliography:Selected, peer reviewed papers from the 2nd International Conference on Uncertainty in Mechanical Engineering (ICUME 2015), November 19 – 20, 2015, Darmstadt, Germany
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ISBN:3038356522
9783038356523
ISSN:1660-9336
1662-7482
1662-7482
DOI:10.4028/www.scientific.net/AMM.807.229