A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA

This study aims to present a three-dimensional (3D) numerical solution for investigating the free vibration and buckling responses of annular plate, conical and cylindrical shell made of functionally graded (FG) porous rock materials. Isogeometric analysis (IGA) is utilized in order to develop the 3D numerical solution. Furthermore, the computational package is developed using C# Programming, which is an object-oriented programming language. The distribution of porosity along the thickness direction obeys the cosine function rule, for which the top surface is porosity-free, and the bottom surface is porosity-rich. The weak form for free vibration and buckling analyses are discretized and approximated through 3D NURBS based IGA. The accuracy of the present solutions is verified by the results obtained from published data. The convergence of 3D FGP solutions is checked, and it is found that a quartic NURBS element can yield high-accuracy results with the lowest computational cost. Afterward, the numerical results showed the impact of porosity of the FGP annular plate, FGP conical, and cylindrical shell on free vibration and buckling problems.