3D Chinese lantern-type stability loss of a cylinder composed of functionally graded materials under axial compression

Abstract A fixed-supported circular cylinder, both solid and hollow, made from functionally graded material (FGM), is analyzed for stability loss in a Chinese lantern-type under uniformly distributed axial external pressure applied at both ends. The mathematical model for this issue is based on the exact three-dimensional geometrically nonlinear equations of elasticity theory. The solution of this geometrically nonlinear problem is reduced by applying the linearization method to the solution of a series of boundary value problems, each of which contains the quantities of the previous problems. This study aims to determine the critical external force that causes the loss of stability of the cylinder. To determine the critical parameters, we apply the initial “infinitesimal imperfection criterion,” which asserts that the critical force is the one that causes the amplitudes of the cylinder’s initial imperfection curves to increase indefinitely. The initial imperfection form has been chosen as sinusoidal. The solution to this problem is reduced to a series of boundary value problems, each dependent on the previous ones. However, it is sufficient to address only the first two boundary value problems (the zeroth and first approximations) to derive the critical parameters (Akbarov in Stability loss and buckling delamination: three-dimensional linearized approach for elastic and viscoelastic composites, Springer, New York, 2013). The solution for the first approximation is obtained numerically using the finite element method (FEM), while the zeroth approximation is determined analytically. The numerical results and their discussion are presented for the case where the cylinder is made of FGM. It is assumed that only the elastic modulus of the material properties of the cylinder varies continuously as a function of the vertical coordinate according to a power law distribution, and the Poisson’s ratio is assumed to be constant. Both gradual stiffening and gradual softening cases are considered for the FGM that progressively varies in the designated direction. This study investigates and analyzes the influence of various geometrical and material’s parameters on this distinct type of structural instability problem of a fixed-supported circular FGM cylinder using the algorithms and programs coded by the authors. The study offers a new approach by analyzing functionally graded materials and their effect on the stability loss of Chinese lantern forms. The results improve the understanding of structural behavior under axial compression and provide information to increase the reliability of the structure through the appropriate lifespan.