CURVATURE EFFECTS IN THE LIMIT FROM NONLI NEAR SPHERICAL-SHELLS TO CIRCULAR PLATES

This Note aims at studying some particularities of the axisymmetric be havior of an elastic spherical cap undergoing non-linear strains. We f irst recall that the corresponding equilibrium problem loses uniquenes s on the one hand without any external load if the shell is thin enoug h, and on the other hand under radial traction at the rim, also for a sufficiently small thickness. Then we analyze the case for which the c ap goes closer and closer to its tangent plane. We establish that the limit problem is actually a circular plate problem and, depending on t he order of the load with respect to the curvature parameter, the limi t problem loses uniqueness under radial compresive forces for the clas sical buckling load of an elastic simply supported circular plate.