MEC10120/MEC10720 - Mechanics and Computational Modelling
Tutorial 8 - Stress singularities and stress concentrations
Dr Chennakesava Kadapa, Email: c.kadapa@napier.ac.uk
Edinburgh Napier University
Question 1:
(i)
The top surface is fixed and the point load is applied in the vertical downward direction.
So, the free end of the part should bend downwards. This is exactly what we observe in
the deformation plot in Figure Q.1(c). Therefore, FE results are valid.
(ii)
The stress is maximum at the fillet and a higher stress is also observed in the reentrant
corner. The maximum stress value is 174.9 MPa which is quite close to the yield stress of
200 MPa. Therefore, the structural integrity of the component is poor. The part is highly
likely to fail if the load is increased further. We have to redesign the component to
minimise the maximum stress, for example, by adding fillets.
Question 2:
a.
In FEA, we have three main stages:
1. Preprocessing stage
2. Solution stage
3. Postprocessing stage
In the preprocessing stage, we create the model, assign material properties, specify
boundary conditions and loads, and generate the mesh.
In the solution stage, the computer solves for the unknowns. Usually, displacement DOFs
are the unknowns in stress analysis.
In the postprocessing stage, we plot the results, for example, deformations, strains,
stresses and energy. We also generate graphs and tables for preparing the reports. We
calculate the strains from displacements and then calculate stresses from strains.
b.
In FEA, stress recovery is the process of extrapolating the stresses (or strains) from
Gauss points to nodes.
c.
Nodal stresses are the stresses extrapolated from Gauss points to nodes. In short, nodal
stresses are the values of stresses at the nodes.
Element stresses are the stresses per element. Element-wise stresses can be calculated
by averaging the stresses either at nodes or Gauss points. Different software different
options. Element stresses calculated from their values at Gauss points are more accurate.
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d. and e.
We use both nodal and element stresses to
(i) choose the appropriate element size we need in a particular location, especially the
locations where the stresses are higher,
(ii) identify convergence range, and
(iii) assess solution accuracy.
Studying both nodal and elemental stresses for different meshes is nothing but a meshindependent study.
Usually, we choose the mesh for which the difference between nodal and element
stresses is about 10%. In critical applications, for example, in aerospace, nuclear and
biomedical, we use lower percentages.
For more details, please follow the YouTube video https://www.youtube.com/watch?
v=wkzGRIuphdc
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Question 3
a.
Stress singularities are the locations where the theoretical stress value is infinite. At stress
singular points, the stress increases monotonously with mesh refinement.
Stress concentrations are the locations where the stress is usually higher than when
compared with other locations. At stress concentrations, the approaches a constant value
with mesh refinement.
b.
Stress singularities can be distinguished from stress concentrations by conducting mesh
refinement study and observing whether the stress values increases monotonously or
reaches a constant value. If the stress increases with mesh refinement, then the location
is a stress singularity but if the stress converges to a constant value, then the location is a
stress concentration location.
c.
Stress singularities can be remedied by smoothing out the corners, for example, by
adding fillets.
d.
Stress concentration zones experience higher stress values compared to other locations
of a component. Therefore, stress concentration zones reduce the maximum load that a
component can withstand. To account of stress concentration zones we use factors of
safety in the designs.
Please refer to the blog posts for additional details.
http://www.acin.net/2015/06/02/stress-singularities-stress-concentrations-and-meshconvergence/
https://help.solidworks.com/2020/english/SolidWorks/cworks/r_assessing_stress_hot_spots.htm
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