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Structural Optimization under Stability and Vibration Constraints pp 69–144Cite as

Part II

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 308))

Abstract

After a very short description of Pontryagin’s maximum principle and sensitivity analysis as applied to eigenvalue problems, a unified approach to column optimization has been presented. Particular attention has been paid to multimodal solutions obtained for compressed columns in an elastic medium and elastically clamped columns for buckling in two planes. Next, a general statement of the optimization of arches has been formulated. The necessity of multimodal optimization was pointed out, especially if in-plane and out-of-plane buckling was taken into account. The sensitivity analysis has been applied to a new optimization problem of annular plates compressed by uniformly distributed non-conservative forces. Both the precritical membrane state and the small transverse vibration has been taken into account. Finally, the parametrical optimization of a visco-elastic column compressed by a follower force with respect to its dynamic stability, as well as the optimization of a plane bar system in conditions of internal resonance has been considered.

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  1. Technical University of Cracow, Cracow, Poland

    A. Gajewski

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  1. A. Gajewski
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  1. Technical University of Cracow, Poland

    M. Zyczkowski

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Gajewski, A. (1989). Part II. In: Zyczkowski, M. (eds) Structural Optimization under Stability and Vibration Constraints. International Centre for Mechanical Sciences, vol 308. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2969-2_2

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  • DOI: https://doi.org/10.1007/978-3-7091-2969-2_2

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