Displacement dependent pressure load for finite deflection of doubly-curved thick shells and plates

• Exact derivation of virtual work by displacement dependent pressure for finite displacements of shells.
• Derivation for shells of any variable curvature and plates.
• Application to post-buckling and static loads.
• Comparison of numerical results for exact and approximate solutions.

The formulation of the displacement dependent pressure load for shells of generic shape and plates is derived in the present study in curvilinear coordinates without any approximation and any hypothesis on material properties. Derivation is initially carried out for pressure load on the middle shell surface, and then for load on the external and internal surfaces by making use of a third-order shear and thickness deformation shell theory, which is a significant improvement for thick shells. The explicit formulation in curvilinear coordinates allows immediate implementation in numerical codes. An approximate formulation is also derived and compared to (i) the exact formulation and to (ii) the displacement independent pressure load which is still widely used in the literature. Applications to circular cylindrical shells and rectangular plates are presented. Comparison of results show that only the exact formulation for displacement dependent pressure load can be used for large deformations of shells and plates, while the displacement independent pressure load can be used only in case of small displacements of the middle surface (or middle plane).