Abstract
We consider a nonshallow arch, clamped at its ends and submitted to a reference loading f. The aim of this work is to find the shape of the midcurve of the arch in order to maximize the critical buckling load of the arch.
Buckling loads appear as eigenvalues. Our purpose here is.
1. to give a mathematical proof of existence of critical buckling load.
2. to prove that this critical buckling load is differentiable (in a sense which will be defined later) with respect to the shape of the midline of the arch, and to give an analytical formula for the derivative.
The differentiation property (although it is not always Fréchet-differentiable, due to multiple eigenvalue situation) is strong enough to lead to optimality necessary conditions, and then to run optimization procedures using the derivative of the buckling load.
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References
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© 1988 Springer-Verlag
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Chenais, D., Rousselet, B. (1988). Shape optimization of a nonshallow arch towards critical buckling load. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042233
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DOI: https://doi.org/10.1007/BFb0042233
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