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The structural analysis of ultra-lightweight flexible shells and membranesmay require the adoption of complex nonlinear strain-displacement relations.These may be approximated and simplified in some circumstances, e.g., in thecase of moderately large displacements and rotations, in some others may benot. In this paper, the effectiveness of various geometrically nonlinear strainapproximations such as the von Karman strains is investigated by making use ofrefined shell formulations based on the Carrera Unified Formulation (CUF).Furthermore, geometrical nonlinear equations are written in a total Lagrangianframework and solved with an opportune Newton-Raphson method. Test casesinclude the study of shells subjected to pinched loadings, combined flexure andcompression, and post-buckling including snap-through problems. It isdemonstrated that full geometrically nonlinear analysis accounting for fullGreen-Lagrange strains shall be performed whenever displacements are higherthan the order of magnitude of the thickness and if compressive loads areapplied.

Effect of different geometrically nonlinear strain measures on the  static nonlinear response of isotropic and composite shells with constant  curvature