Stability analysis for geometric nonlinear functionally graded sandwich shallow shell using a new developed displacement field

Although the stability of the sandwich structures under in-plane excitation has been reported, few of them focus on the functionally graded materials (FGM) sandwich doubly curved shallow shells. Moreover, for the study of static bifurcation, stability and dynamic stability analysis, it is common to ignore the effect of thickness tension or compression. The purpose of this paper is to explore the bifurcation and stability of the FGM sandwich doubly curved shallow shell which is subjected to the in-plane excitation in thermal environment. By introducing the secant function to the transverse displacement, a new displacement field based on the Reddy's third order shear deformation theory is derived. It is assumed that the material properties of sandwich doubly curved shallow shell are temperature dependent. The distribution of component materials in FGM layer obeys the rule of power law in the radial direction. Considering the geometric nonlinear, using an energy approach and the Galerkin's method, a two-degree-of-freedom non-autonomous nonlinear dynamic equation with parametric excitation is derived. The threshold of the bifurcation and the stability of the structure are investigated. The instability regions are plotted by dynamic load factor against excitation frequency in α₁-Ω plane.