Dynamic Buckling of Functionally Graded Spherical Caps

Abstract

The dynamic behavior of functionally graded spherical caps under suddenly applied loads is studied by using a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory, and it includes the in-plane and rotary inertia effects. Geometric nonlin- earity is introduced in the formulation using von Karman's strain-displacement relations. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. The governing equations obtained are solved employing the Newmark's integration technique coupled with a modified Newton-Raphson iteration scheme. The load corresponding to a sudden jump in the maximum average displace- ment in the time history of the shell structure is taken as the dynamic buckling pressure. The present model is validated against the available isotropic cases. A detailed numerical study is carried out to bring out the effects of shell geometries, power-law index of functional graded material, boundary conditions, and finite pressure pulse with different duration on the axisymmetric dynamic buckling load of shallow spherical shells.