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.