an:01053796
Zbl 0886.73031
Pitkaranta, Juhani; Sanchez-Palencia, Evariste
On the asymptotic behaviour of sensitive shells with small thickness
EN
C. R. Acad Sci., Paris, S??r. II, Fasc. b, M??c. Phys. Chim. Astron. 325, No. 3, 127-134 (1997).
00042997
1997
j
74K15 35Q72
elliptic shell; singular perturbation; Fourier expansion; boundary layer
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.