M.Sc Thesis
M.Sc Student Nadler Ben Post-Buckling Behavior of Nonlinear Elastic Beams and Truss- Like Structures (with Beam Element) Using the Theory of a Cosserat Point Department of Mechanical Engineering Professor Emeritus Miles Rubin

Abstract

The theory of Cosserat point is a continuum model of a small finite body like a finite-element. The Cosserat theory introduces director vectors that characterize the deformations of a small finite region of space. Specifically, the Cosserat theory for a beam element is characterized by six directors and the Cosserat joint is characterized by four directors. This theory can be used as a fully nonlinear continuum theory of a finite-element for the numerical solution of beam problems (Rubin, 2000, 2001) and three-dimensional truss-like structures constructed by beams with flexible joints.

This research is divided into two parts. The first part analyzes the predictions of the Cosserat theory for lateral buckling of a cantilever beam. The Cosserat theory for a beam element includes axial extension, cross-sectional extension, transverse shear deformation, cross-sectional shear deformation, and it models the effects of pre-buckled deformations.  Specifically, the buckling load, post-buckling behavior and the effects of additional loads are examined in detail.  The results are compared with linear and nonlinear analyses that appear in the literature.

In the second part, a three-dimensional truss-like structures is constructed by connecting beams (modeled by a Cosserat point for a beam element) with flexible joints. This research also develops theory for modeling these joints as flexible Cosserat points.  Specific equations are presented for connecting any finite number of beams at arbitrary orientations in three-dimensions with joints that exhibit elastic response with additional viscous damping. A three-dimensional simple planar structure constructed with two beams and a joint is presented and analyzed. The structure's behavior to loads applied at different locations on the joint, the in-plane collapse of the structure, and the influence of the joint's rigidity are analyzed.