Nonlinear free vibration analysis of functionally graded plates and shell panels using quasi-3D higher order shear deformation theory

This paper presents the nonlinear free vibration behavior and response of functionally graded plates and shell panels under various boundary conditions. The displacement formulation followed uses a sinusoidal non-polynomial quasi-3D higher order shear deformation theory with six variables and, the parabolic transverse stress distribution functions are used to model stresses in the thickness direction. Present formulation employs the Green-Lagrange nonlinear strains along with Sander's approximation to account for larger flexural response which could be experienced by the structure. An eight noded C-0 continuous isoparametric finite element is used for numerical implementation of nonlinear finite element solver developed in MATLAB. Developed numerical formulation is employed to study and analyze the nonlinear free vibration response of the spherical, cylindrical and hyperboloid shell panels and the obtained results are seen to be consistent and good agreement with the literature thus establishing the effectiveness and accuracy of the present work.

Automated summary

This paper presents the nonlinear free vibration behavior and response of functionally graded plates and shell panels under various boundary conditions. The displacement formulation used a sinusoidal non-polynomial quasi-3D higher order shear deformation theory with six variables, and parabolic transverse stress distribution functions were used to model stresses in the thickness direction. The numerical implementation employed an eight-noded C-0 continuous isoparametric finite element and MATLAB. The results obtained for the nonlinear free vibration response of the spherical, cylindrical, and hyperboloid shell panels showed good agreement with the literature, demonstrating the effectiveness and accuracy of the present work.