Aspects of Singularities

Daniel Weschke

October 13, 2017

1 Outline

After conducting a finite element analysis we can face singularities which we may like to avoid.

2 Supports

One possibility of singularities is a ’wrong’ support condition. For example imagine in the field of elastostatics a square plate with constant thickness, fix supported one-sided and on the other side loaded with tensile stress. In numbers a 100 MPa tension load. Will lead to a singularity on the corners of our fixed support constrain. Which means the more elements or the finer the mesh is the higher is the stress at the corners of the supported edge. We will not find a mesh independent result for these corners.

Stress at the corner of a one-sided fixed supported square plate which is loaded on the other side with a tensile stress of 100 MPa

No. of elements	Max. normal stress
1	100.00
2	104.86
4	111.42
8	124.34
16	143.16
32	167.60
64	197.67
128	233.76

The problem is that the fixed support disallow the transverse strain under the action of a longitudinal stress. If we allow the body to contract at the boundary condition in the transverse or lateral direction then there will be no singularities.