Applying Stress Boundary Conditions in Commercial Finite Element Analysis Codes

Question

I am trying to replicate a finite element analysis given in a research paper titled On the Detection of Stress Singularities in Finite Element Analysis 1 by G.B.Sinclair et. al.

The geometry of the problem is given in Figure 1.

and boundary conditions are $$ (x, y) = (D/2 < x < L + D/2) \hspace{0.5in} \sigma_y = -p, \tau_{xy} = 0 $$ and the left-most bolt hole is clamped.

Typically, in finite element analysis codes such as Patran/MSC Nastran, ANSYS, and FEMAP, we can apply displacement, force, and distributed loads as boundary conditions. The boundary conditions given in this problem specify stresses. How can I apply them in commercial FEA codes?

Answer 1

First, let us properly describe the boundary conditions of your problem. You have the following:

1. Fixed/encastre. The left hole is fixed and displacements are zero there. These boundary conditions are termed (homogeneous) Dirichlet conditions.

2. Free boundaries. All, except the right segment on top, have traction boundary conditions. That is, both components of the traction vector are specified and are zero. These are called (homogeneous) Neumann conditions.

3. Traction boundary. The segment with traction on the upper part of your model has one component of the traction vector (vertical) different from zero. The horizontal one is also zero. These are called (in-homogeneous) Neumann conditions.

To summarize, you can have displacements or traction boundary conditions in elasticity models. You might also have concentrated forces... but it can be seen as traction described by a Dirac's delta. Internally, all of these boundary conditions are integrated to obtain nodal forces, but that's a different story.

Also, check this previous answer.