Computations on thin non‐inhibited hyperbolic elastic shells. Bench‐marks for membrane locking

Singular perturbations generating complexification phenomena for elliptic shells

“…When the shell is not inhibited, bending displacements are not described sufficiently accurately when the relative thickness ε is small [7,8,20] and the bending displacement is underestimated. Such phenomena also occur in the layers.…”

“…A major problem in shell computations is the membrane locking: it is due to a bad approximation of the subspace of pure bending displacements G defined by (8). When the shell is not inhibited, bending displacements are not described sufficiently accurately when the relative thickness ε is small [7,8,20] and the bending displacement is underestimated.…”

“…29) is quite similar to that obtained for the wellinhibited problem (see Figs. 7,8). The membrane energy concentrates at the four corners near the logarithmic point singularities (even if we can not see them in the graph of u 3 because of the more important instability on the free edge).…”

Adaptive and anisotropic mesh strategy for thin shell problems. Case of inhibited parabolic shells

“…When G -{0}, the shell is said to be not inhibited (or not geometrically rigid) and the limit problem is the pure bending one (Choï, 1999;Sanchez-Hubert and Sanchez-Palencia, 1997). Oppositely, when G = {0}, the shell is inhibited or geometrically rigid, and the limit problem is the membrane problem a m ðu; vÞ ¼ bðvÞ:…”

Anisotropic adaptive mesh procedure for computing very thin hyperbolic shells

“…Examples of membrane locking can be seen in [9] for hyperbolic shells or in [17] for parabolic ones.…”