Post-Buckling Behavior of Nonlinear Elastic Beams and Three-Dimensional Frames Using the Theory of a Cosserat Point

Abstract

The theory of a Cosserat point for rods has been developed to formulate the numerical solution of problems for nonlinear elastic rod and beams. This theory is fully nonlinear and can be used to model dynamic problems with large deformations and rotations. One objective of this paper is to show that this theory can be used to accurately predict the lateral buckling load and the three-dimensional post-buckling response of a cantilever beam with rectangular cross-section. The theory of a Cosserat point for homogeneous deformations is also used to formulate the theory of a flexible Cosserat joint which connects a finite set of beams at arbitrary orientations in three-space. Using this Cosserat joint and the Cosserat points for beam elements it is possible to formulate the numerical solution of problems of three-dimensional frames which are constructed by connecting beams by joints. A simple two-dimensional frame is considered, and both in-plane and out-of-plane large deformations are analyzed to test the Cosserat theory.

Umbrella spherical integration: a stable meshless method for non‐linear solids

“…Instabilities of this type are well-known to occur in non-linear materials at finite deformation (see, e.g. Nadler and Rubin [43]). It is important to point out that this instability is a real physical phenomenon and not a numerical instability associated with the methodology.…”

On pseudo-rigid bodies

“…The foregoing remarks do not apply to the use of pseudo-rigid bodies as effective substitutes for conventional uniform-strain finite elements (Nadler & Rubin 2004).…”