Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

Abstract

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

“…Pagani et al [44] utilized a refined CUF plate model to investigate the effect of various strain-displacement nonlinear approximations on the large deflection and post-buckling of isotropic plates. Readers can be referred to [45,46,47] for important works on nonlinear analyses of 2D isotropic and composite shell structures in the CUF framework.…”

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

“…The Carrera Unified Formulation (CUF) was implemented to perform geometrically nonlinear analyses of isotropic and laminated plates and shells in the last years [30,31,32,33,34,35,36,37] and characterizes the foundations of the proposed method. In the framework of CUF, any degree of refinement of a model can be obtained since the adopted theory's order is treated as an analysis input.…”