Evaluation of Various Geometrical Nonlinearities in the Response of Beams and Shells

Abstract

This paper investigates the consistency and compatibility of various assumptions and strain measurements in a large displacements/geometric nonlinear analysis of beams and thin-walled structures. For this purpose, a refined beam model with enhanced three-dimensional accuracy is employed in a total Lagrangian scenario. This model is developed in the domain of the Carrera unified formulation, which allows expression of the nonlinear governing equations in terms of fundamental nuclei. These nuclei are independent of the theory approximation order; thus, low- to high-order theories of structures can be implemented with ease. Various numerical problems are addressed, and solutions are provided by using a classical finite element method and a Newton–Raphson linearization scheme. Given the intrinsic scalable nature of Carrera unified formulation, investigating the effects of the various nonlinear strain components is straightforward. It is demonstrated that the full Green–Lagrange strain tensor produces good approximation in case of large rotations, postbuckling, and nonlinear couplings. In contrast, approximations may be reasonable as moderate displacements and simpler problems (for example, slender beams under flexure) are considered.