Engineering | Finite Element Analysis | Stress
© Copyright Value Design Consulting Ltd
Value Design
Consulting
Sharp discontinuities can greatly increase stress, if there are particular areas
of interest in a model, then the finer details should be included.
The usual rule
of thumb is to start with a simple representation of the component, analyse it and
see if it is behaving as expected. If it is, then more detail can be added in stages,
repeating the analysis each time to gain an appreciation of the amount of detail
that is required. However, attention should be given to the effect of detail exclusion
before any analysis is carried out.
Discretisation Errors.
Discretisation error results from the FEM's approximation of the continuous domain (design) with a finite number of finite elements, as well as the size and shape of the elements. If the mesh is coarse, the elements will not be able to capture the behaviour of the structure and is said to suffer from descretisation error. On the other hand, if the mesh is too dense, solution time will be too high. The graph to the right shows how the solution converges with an increase in elements (no element numbers are included on the x-axis as they vary according to the application). An ideal mesh would use just enough elements to arrive at 100% convergence.
To explain descretisation error, lets consider the analysis of a rectangular plate with a central hole. If the engineer meshes the model with straight sided triangular elements, the circular hole will be approximated by a series of connected straight lines. In a coarse mesh, using a small number of elements, the discretisation error will be greater than in the case of a finer mesh, using a large number of smaller elements. The only trade off against using a very dense mesh, is that the analysis will take a considerable time longer, due to the extra nodes that are required to be solved for.
An alternative is to refine the mesh at the local details. This requires specialist
knowledge on how the results will vary over the model domain. Computed values such
as stress and strain, are evaluated at locations on the element known as Gauss points.
These points are always well inside element boundaries. Values at other positions
are interpolated or extrapolated. If this is done across a boundary between two elements,
then it should be reasonably accurate, but extrapolating to the edge of an element
on the edge of a structure, where the stresses will probably be at the highest and
of most interest, can lead to significant errors in rapidly changing stress fields
if the mesh density or the element order is too low.
Errors in FEA - discretisation
Navigate the knowledge base
