# zbMATH — the first resource for mathematics

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)
Full Text: