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On the asymptotic behaviour of sensitive shells with small thickness. (English. Abridged French version) Zbl 0886.73031
Summary: Sensitivity is a type of instability that appears in the limit behavior of certain shells as the thickness \(\varepsilon\) tends to zero. We consider the behavior for small \(\varepsilon >0\) in two cases. In the first case (elliptic shell clamped on a part of the boundary and free on the remainder), a Fourier expansion shows that the components of order \(k\) grow exponentially with \(k\) up to a saturation value \(\sim \log \varepsilon^{-1}\). In the second example (elliptic shell submitted to \(u_3=0\) on the boundary, \(u_3\) is normal component of the displacement), a boundary layer appears with thickness and amplitude of orders \(\varepsilon^{1/2}\) and \(\varepsilon^{-1/2}\), respectively.

MSC:
74K15 Membranes
35Q72 Other PDE from mechanics (MSC2000)
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