The effect of elastic foundations on the nonlinear buckling behavior of axially compressed heterogeneous orthotropic truncated conical shells

•Nonlinear buckling of heterogeneous orthotropic conical shells in elastic media.•Basic equations of heterogeneous orthotropic shell in elastic media are derived.•von-Karman nonlinearity, superposition and Galerkin methods are used.•The expression for upper and lower critical loads are found.

The buckling problem of a heterogeneous orthotropic truncated conical shell subjected to an axial load and surrounded by elastic media is analyzed based on the finite deformation theory. Using von-Karman nonlinearity, the governing equations of elastic buckling of heterogeneous orthotropic truncated conical shells surrounded by elastic media are derived. The governing equations are solved using superposition and Galerkin methods and obtained expressions for upper and lower critical axial loads. The influences of elastic foundations, heterogeneity, orthotropy and geometric characteristics on the upper and lower critical loads of conical shells with and without elastic foundations are studied in detail.