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

TL;DR

This paper evaluates various geometrically nonlinear strain measures, such as von Karman strains, in shell analysis using the Carrera Unified Formulation, highlighting the importance of full nonlinear analysis for large displacements and compressive loads.

Contribution

It introduces a refined shell formulation based on CUF to compare different nonlinear strain approximations within a total Lagrangian framework.

Findings

Full nonlinear analysis is necessary for large displacements and compressive loads.

Simplified strain measures may be insufficient for post-buckling and snap-through problems.

The study demonstrates the effectiveness of the proposed formulation through various load cases.

Abstract

The structural analysis of ultra-lightweight flexible shells and membranes may require the adoption of complex nonlinear strain-displacement relations. These may be approximated and simplified in some circumstances, e.g., in the case of moderately large displacements and rotations, in some others may be not. In this paper, the effectiveness of various geometrically nonlinear strain approximations such as the von Karman strains is investigated by making use of refined shell formulations based on the Carrera Unified Formulation (CUF). Furthermore, geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. Test cases include the study of shells subjected to pinched loadings, combined flexure and compression, and post-buckling including snap-through problems. It is demonstrated that full geometrically nonlinear analysis accounting for full Green-Lagrange strains shall be performed whenever displacements are higher than the order of magnitude of the thickness and if compressive loads are applied.