Liu, D., He, Y., Zhang, B., 2013. Towards a further understanding of dislocation pileups in the presence of stress gradients. Doi: 10.1080/14786435.2013.774096
http://www.tandfonline.com/doi/abs/10.1080/14786435.2013.774096#preview
After having taught graduate structural mechanics for several years, I am finally
able to write down my lecture notes (attached) for teaching the beam theory. In
the notes, we formulated the complete classical beam model
(extension/torsion/bending in two directions), which is also called
Euler-Bernoulli-Saint beam theory, in three ways: Newtonian method, variational
method, and variational asymptotic method, using 3D elasticity theory as the
starting point. Many self-contradictions of the various assumptions used in both
Newtonian method and variational method are clearly pointed out. The
I have a question regarding simple torsion of a circular shaft with a uniform cross section. Given a hollow circular shaft with inner radius R1 and outer radius R2, length L, shear modulus G, fixed-free boundary conditions and applied torque T about the central axis, the equation for the rotation angle at the end of the beam is
phi = T*L/(J*G)
where J = pi/4*(R2^4-R1^4)
I would like to know how to write a stiffness matrix for a bar under torsional load. I would like to write a code in C++ to do this. I would like to know of any material regarding this.
Thanks in advance
With Br
Ashwin
