We consider a bilinear reduced-strain nite element formulation for a shallow shell model of Reissner-Naghdi type. The formulation is closely related to the facet models used in engineering practice. We estimate the error of this scheme when approximating an inextensional displacement eld. We make the strong assumptions that the domain and the nite element mesh are rectangular and that the bound...

The large-amplitude vibrational behavior of a shallow spherical-cap shell is investigated theoretically using simple arguments. The results of this approximate analysis are expressed in the form of appealingly simple nondimensional quantities. It is shown that the frequency of the fundamental mode of such ashell falls by as much as 50% as the vibration amplitude is increased to approximately th...

Cylindrical shells exhibit a dense frequency spectrum, especially in the lowest frequency range. In addition, due to the circumferential symmetry, frequencies occur in pairs. So, in the vicinity of the lowest natural frequencies, several equal or nearly equal frequencies may occur, leading to multiple internal resonances. The aim of the present work is to investigate the dynamic behavior and st...

We present a detailed asymptotic analysis of the point indentation of an unpressurized, spherical elastic shell. Previous analyses of this classic problem have assumed that for sufficiently large indentation depths, such a shell deforms by 'mirror buckling'-a portion of the shell inverts to become a spherical cap with equal but opposite curvature to the undeformed shell. The energy of deformati...

In the current study, linear, nonlinear and total relative refractive index changes of a single shallow hydrogenic donor atom confined in semiconductor core/shell/shell quantum dot heterostructure are investigated detail by compact density matrix formalism. For this purpose, energy eigenvalues corresponding wave functions calculated diagonalization method effective mass approximation. Then, int...