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Shape analysis in membrane vibration

Abstract : In order to characterize the domain Ω minimizing the normal stress on the boundary of a membrane, we are concerned with the shape derivative of the functional J(Ω) = ∫I∫∂Ω(∂y/∂n)2g dx dt, where I is the time interval, y is the solution to the wave equation and g a weight coefficient. We first recall some results on the transformation of domains and investigate the shape derivative of the state. Then we compute the derivative of J with respect to the domain. Eventually, we give a necessary condition of optimality which relies heavily on the oriented distance function and its properties around the neighbourhood of the boundary.
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Submitted on : Thursday, March 24, 2011 - 2:27:02 PM
Last modification on : Wednesday, November 17, 2021 - 12:30:59 PM

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John Cagnol, Jean-Paul Zolésio. Shape analysis in membrane vibration. Mathematical Methods in the Applied Sciences, Wiley, 2000, 23 (11), pp.985-1010. ⟨10.1002/1099-1476(20000725)23:11<985::AID-MMA147>3.0.CO;2-L⟩. ⟨hal-00579623⟩



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