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Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint

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Abstract

We propose a novel formulation of a truss design problem involving a constraint on the global stability of the structure due to the linear buckling phenomenon. The optimization problem is modelled as a nonconvex semidefinite programming problem. We propose two techniques for the numerical solution of the problem and apply them to a series of numerical examples.

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References

  • W. Achtziger, A. Ben-Tal, M. Bendsøe, and J. Zowe “Equivalent displacement based formulations for maximum strength truss topology design,” IMPACT of Computing in Science and Engineering vol. 4, pp. 315-345, 1992.

    Google Scholar 

  • K.-J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall: Englewood Cliffs, NJ, 1982.

    Google Scholar 

  • M. P. Bendsøe, Optimization of Structural Topology, Shape and Material, Springer-Verlag: Heidelberg, 1995.

    Google Scholar 

  • R. D. Cook, Concepts and Applications in Finite Element Analysis, J. Wiley & Sons: New York, 1974.

    Google Scholar 

  • Y. C. Fung, Foundation of Solid Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1965.

    Google Scholar 

  • F. Jarre 1998, 'A QQP-Minimization Method for Semidefinite and Smooth Nonconvex Programs'. Technical report, Trierer Forschungsberichte Mathematik/Informatik Nr. 12, Universität Trier.

  • N. K. Karmarkar “A new polynomial-time algorithm for linear programming,” Combinatorica vol. 4, pp. 373-395, 1984.

    Google Scholar 

  • M. Kočvara, M. Zibulevsky, and J. Zowe: 1998, 'Mechanical design problems with unilateral contact'. M2AN Mathematical Modelling and Numerical Analysis 32, 255-282.

    Google Scholar 

  • J. E. Nesterov and A. S. Nemirovskii, Interior Point Polynomial Methods in Convex Programming: Theory and Applications, SIAM: Philadelphia, 1994.

    Google Scholar 

  • M. J. D. Powell: 1997, 'The use of band matrices for second derivative approximations in trust region algorithms'. Technical report, NA1997/12, Cambridge University.

  • U. T. Ringertz,: 1995a, 'An algorithm for optimization of non-linear shell structures'. Internat. J. Numer. Methods Engrg. 38, 299-314.

    Google Scholar 

  • U. T. Ringertz, “Eigenvalues in optimum structural design,” in Large Scale Optimization, A. Conn and F. Santosa, eds., Springer, 1995b.

  • G. A. Shultz, R. B. Schnabel, and R. H. Byrd: 1985, 'A family of trustregion based algorithms for unconstrained optimization with strong global convergence properties'. SIAM J. on Numerical Analysis 22, 47-67.

    Google Scholar 

  • J. M. T. Thompson and G. W. Hunt, A General Theory of Elastic Stability, J. Wiley & Sons: London, 1973.

    Google Scholar 

  • S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw-Hill: New York, 1961.

    Google Scholar 

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Ben-Tal, A., Jarre, F., Kočvara, M. et al. Optimal Design of Trusses Under a Nonconvex Global Buckling Constraint. Optimization and Engineering 1, 189–213 (2000). https://doi.org/10.1023/A:1010091831812

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  • DOI: https://doi.org/10.1023/A:1010091831812

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