Popular benchmarks of nonlinear shell analysis solved by 1D and 2D CUF-based finite elements

Abstract

This research work deals with the analysis of elastic shell structures in the large displacement and rotation field adopting one-dimensional (1D) and two-dimensional (2D) unified models. Namely, higher order beam and shell theories accounting for geometrical nonlinearities are formulated by employing a unified framework based on the Carrera unified formulation (CUF) and a total Lagrangian approach. Thus, a finite element (FE) approximation is used along with a Newton-Raphson method and an arc-length path-following approach to perform nonlinear analyses. Low- to higher order beam and shell theories are used to evaluate the nonlinear equilibrium path, and results are compared between the two models, with reference solutions coming from literature or 2D and three-dimensional (3D) models from NASTRAN. Convergence analyses show how CUF 1D models are able to describe the geometrical nonlinear behavior of analyzed structure with a lower number of degrees of freedom (DoFs) than 2D and 3D models.

Keywords:

• Beam and shell theories
• Carrera unified formulation
• convergence analyses
• geometrical nonlinearities