Effect of Reissner’s Parameter on Strain Energies of Spherical Sandwich Shells

Abstract

With the objective of identifying dominant deformation modes for clamped spherical sandwich shells of different geometries and materials, and especially that of Reissner’s parameter for a shell , the infinitesimal quasi-static deformations are analyzed by using a third-order shear and normal deformable shell theory and the finite element method. For spherical shells subjected to normal tractions on a major surface, the effects are delineated on strain energies (SEs) of the in-plane, out-of-plane, stretching, and bending deformations of the following ratios: span/thickness (); radius of curvature/span (); core to face-sheet thickness (); and face sheet’s elastic modulus along the fiber axis to that of the core (), where . It is found that, for fixed values of other parameters, the proportions of SEs of bending to that of the total deformations, as well as of the transverse normal to that of the transverse shear deformations, increase with an increase in or a decrease in the RPS. For , the SE due to bending deformations of the face sheets equals 29%; and, those due to transverse normal and shear deformations of the core are, respectively, 20 and 5% of the total SE. Thus, one should incorporate transverse normal deformations of the core in the shell theory for such problems. For fixed values of other parameters, the core’s in-plane deformations become more significant than its transverse shear deformations, with an increase in or a decrease in the RPS. The SE of the core’s in-plane deformations equals 30% of the total SE for , suggesting a need to account for in-plane deformations of the core for such shells. The present results provide useful insights into deformation modes for spherical sandwich shells of different Reissner’s parameters.