Nonlinear dynamic response of functionally graded shallow shells under harmonic excitation in thermal environment using finite element method

The nonlinear dynamic response of functionally graded material (FGM) shallow shells subjected to thermal and harmonic loads is studied using finite element method. The material properties vary continuously in the thickness direction based on a simple power law distribution. The equations of motion are obtained using modal reduction method based on the third order shear deformation theory. The shooting method is used to obtain appropriate initial conditions for having only steady state response. The effects of thickness ratio and radii of curvature on the dynamic response of FGM shallow shells are studied. Buckled equilibrium positions (BEPs) are obtained for thermally loaded FGM shallow shells with immovable middle or physical neutral surfaces. It is shown that there exist one stable and two unstable BEPs. Then the behavior of an FGM shallow shell subjected to harmonic excitation in thermal environment is investigated. It is seen that the thermally loaded FGM shallow shell has different responses for the same frequency and amplitude of excitation depending on its initial conditions.