ON THE ASYMPTOTIC-BEHAVIOR OF SENSITIVE SHELLS WITH SMALL THICKNESS

Sensitivity is a type of instability that appears in the limit behavio r of certain shells as the thickness epsilon tends to zero. We conside r the behavior for small epsilon > 0 in two cases. In the first case ( elliptic shell clamped by a part of the boundary and free from the rem ainder), a Fourier expansion shows that the components of order k grow exponentially with k up to a saturation value similar to log epsilon( -1). In the second example (elliptic shell submitted to u(3) = 0 on th e boundary, u(3) = normal component of the displacement), a boundary l ayer appears with thickness and amplitude of orders epsilon(1/2) and e psilon(-1/2), respectively.