Buckling and Parametric Instability Behavior of Functionally Graded Shells

Abstract

The concept of functionally graded (FG) materials was first introduced in 1984 by a group of material scientists in Japan, as ultrahigh temperature resistant materials for aircraft, space vehicles and other engineering applications. FG materials are a class of composites that have a continuous variation of material properties from one surface to another and thus eliminate interface problems found in laminated composites. The gradation in properties of the material reduces thermal stresses, residual stresses and stress concentration factors. The gradual variation results in a very efficient material tailored to suit the needs of the structure and, therefore, designated as a FG material. FG materials are typically manufactured from isotropic components such as metals and ceramics since they are used as thermal barrier structures in environments with severe thermal gradients. FG materials have the advantage of heat and corrosion resistance typical of ceramics and mechanical strength and toughness typical of metals.

Buckling and parametric instability behavior of functionally graded shells subjected to in-plane static and pulsating loads are carried out in the present paper. The properties of functionally graded materials are considered to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The shell forms considered here are cylindrical (CYL), spherical (SPH) and hypar (HYP). Temperature change through the thickness is not uniform, and is governed by one-dimensional Fourier equation of heat conduction. Finite element formulation based on a higher order shear deformation theory is used to carry out the analyses. The formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. The parametric instability problem is solved using the Bolotin’s approach. The accuracy of the formulation is validated by comparing the results with those available in the existing literature. Effects of material composition and geometrical parameter