education

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 wish to invite students and young researchers to the summer school "From Nonlinear Physics to Biology and Medicine" that will be held in Cargèse, Corsica from the 9th to the 21st of July, 2012. 

this book is about designing 2d and 3d modeles.

for any question or guide add comment , i will answer all questions.

Dear All,

I am modeling 3D beams with arbitrary cross sections and for that purpose I need to calculate the warping function numerically. The warping function ψ(y,z) is defined as a solution of the following Laplace equation with Neumann boundary conditions:

∂2ψ/∂y2 + ∂2ψ/∂z2 = 0 in Ω,

∂ψ/∂n = z*ny - y*nz on Γ,

where Ω is the cross sectional area, and Γ is its contour. This system can be solved by different numerical methods, for example, finite element method, boundary element method, finite differences...

Numerically I obtain that

hello,

     I have encountered a problem to calculate the stress at interfacial Guass point of each hexahedron element. Since the effective stress is needed to decide whether a cohesive element should be inserted when using the extrinsic cohesive element model, the stress at interfacial Guass point of each element is chosen to calculate effective stress. In the calculation process, the stress at Guass point of each hexaderon element can be obtained.Is there anyone who knows how to calculate the interfacial stress accurately? I would appreciate your comments.