Buckling analysis of shallow shells having linear-variable thickness

One way to increase the overall stiffness of a shell structure is to design shells with variable thickness. The effect of thickness change on the stability of flexible shallow panels has been little studied due to the complexity of solving such non-linear problems. Geometrically nonlinear deformation, buckling and postbuckling behavior of thin elastic shells of linearly variable thickness subjected to uniform normal pressure is investigated. The behavior of shallow axisymmetric spherical panels is compared for three laws of thickness distribution along the meridian of the shell. A more rational distribution of the material in the volume of the shell from the point of view of the stability of the structure is revealed. The same mass of material will be used more rationally if the shell is thickened in its central part. The method is based on geometrically nonlinear equations of the three-dimensional thermoelasticity without the use of simplifying hypotheses of the shell theory, and the use of the moment finite-element scheme and the 3D universal finite element. The universal finite element makes it possible to model sections of the shell with both step-variable and smooth-variable thickness, as well as shells with other geometric features. The problem of nonlinear deformation, buckling, and postbuckling behavior of inhomogeneous shells is solved by a combined algorithm that employs the parameter continuation method, a modified Newton–Kantorovich method, and a procedure for automatic correction of algorithm parameters. The results of calculations performed using the moment finite-element scheme are compared with the solutions obtained using the LIRA and SCAD software packages.