|M.Sc Student||Brand Meir|
|Subject||A Simplified Constrained Theory of a Cosserat Point for|
the Numerical Solution of Dynamic Problems of
Nonlinear Elastic Rods
|Department||Department of Mechanical Engineering||Supervisor||Professor Emeritus Miles Rubin|
In this thesis a constrained hyperelastic element for rods with rigid cross-sections is developed based on a more general theory of Cosserat point for rods. The constrained Cosserat point element can be used to solve dynamic, nonlinear problems of large deformations and rotations. The kinetic boundary conditions for the more general Cosserat rod element with deformable cross-sections are formulated in terms of forces and director couples which are applied to the cross-sections of the element. On the other hand, the boundary conditions for the constrained Cosserat element for rods with rigid cross-sections are somewhat less abstract, since they are characterized by forces and physical mechanical moments applied to the cross-sections of the element. In this thesis, the kinematic and kinetic quantities characterizing the constrained element, and the associated balance laws of motion are described in detail. Also, explicit constitutive equations for an elastic element with additional viscous damping are presented. The constants characterizing the response of the element are determined by comparison of exact solutions of the linear theory of elasticity with solutions of the constrained Cosserat element. Finally, three nonlinear examples are solved with the constrained element: static deformation of a cantilever beam; two-dimensional dynamic Spin-up of rotating beam; and three-dimensional steady state deformation of a rotor blade subjected to constant angular velocity and gravity.