[hal-00579623] Shape analysis in membrane vibration

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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