Idealisation Error Within SOLIDWORKS Simulation by Applications Engineer Tom McHale

Idealisation
Error Within SOLIDWORKS Simulation

Introduction

It doesn’t matter how accurately a model is discretised
or how good a solver is, if a mathematical model is poorly idealised, the
solver will always converge on an incorrect solution.

Idealisation errors normally account for the largest source
of error in any simulation and, ironically, they are introduced before Finite Element
Analysis (FEA) is even applied to the model. The good news is that we typically
engineer components with a Factor of Safety large enough to mitigate all three
types of error within simulation. Nevertheless, reducing the magnitude of these
errors will allow component design to be optimised to a greater degree of
accuracy.

Generally, all simulation errors can be attributed to one
of three categories and are introduced at different stages of the analysis
process:

While idealisation errors occur before FEA is introduced,
the creation and preparation of the mathematical model is still heavily reliant
upon both the SOLIDWORKS CAD and SOLIDWORKS Simulation environments. Good
engineering judgement is often required for appropriate idealisation of the mathematical
model and also for interpretation of the results.

Types of Idealisation Error

Idealisation errors typically emerge when the geometry is
created, the material model is defined and when boundary conditions are applied.
All three areas control the degree of resemblance between the mathematical
model and reality.

1. Geometric Representation
and Simplification

Geometric simplification is often unavoidable and is
usually necessary for acceptable computation times. It is best practice to
initially use an overly simplified model for any analysis in order to ensure
that the model is behaving as expected. The degree of simplification should
then be reduced: especially in areas of interest in order to get meaningful and
representative results.

Typical simplifications include the removal of features
not important to the analysis – defeaturing. Fillets are a good example of
this. When removed, the mesh will be simpler and therefore will result in
quicker computation times. However, a sharp edge will result in a singularity
so the stresses in the immediate vicinity will be wrong. This is fine if the
stresses in this area are not of interest.

It is also worth noting that defeaturing will often
add/remove material which will affect the stiffness of the model. Again, this
is acceptable if the stiffness in the area of interest is accurate.

Simplification doesn’t have to come in the form of
defeaturing. One of the best ways to simplify a model is to take advantage of
symmetry or to represent a 3D model as 2D. This can significantly reduce
computation time due to the large reduction of elements needed to discretise
the model.

2. Material Model Definition

SOLIDWORKS has a material library containing a sample of
typical materials. It is sometimes easy to take this for granted as many
dedicated simulation packages do not provide this information. SOLIDWORKS materials
will be more than sufficient for many simulations when used correctly. However,
occasionally, the material model may need to be tweaked or a new material
created from scratch using experimental data if an unusual material is required
or it is used in a special situation. For example, consider the points below:

·
If a material is designed to operate below yield
then a plasticity model is not needed
·
If a fatigue cycle is ‘zero based’ then an S-N
curve for a ‘fully reversed’ cycle may not be representative
·
If a material is to operate in a high
temperature environment then the stress-strain curve should be representative
of that temperature
·
Material definitions are unlikely to account for
imperfections

3. Boundary Conditions

Boundary conditions include: fixtures, loads and
contacts. It is normally the poor idealisation of fixtures that will cause the
biggest error in any simulation. In reality, loads will always have some degree
of eccentricity, fixtures are never rigid and contacts can often have some
degree of slide and friction. Constraining too many degrees of freedom is easy
to do and can result in over stiffening.

For example, we know from Euler that the type of fixtures
applied to struts under a buckling condition can result in very different
critical buckling loads. These loads can be calculated by hand in the two cases
below: Fixed-Fixed and Pinned-Pinned. Note that the respective descriptions of
each buckling condition do not correlate to an exact representation of fixtures
applied; the degrees of freedom constrained are stated at each end of the strut
and the respective differences shown in red.

The difference in critical buckling load is significantly
different between the two buckling conditions, yet this difference is entirely
due to how just one degree of freedom has been handled at each end of the beams.
This is an extreme case but it is easy to see how important it is to consider
every degree of freedom when constraining and loading your model.

Again, consider the thoughts below:

·
Is it appropriate to fix an entire face when it
is the edges that are welded in place?

·
Does the applied load always act in the same
direction or does it follow the deformation of the geometry?

·
Using remote mass / distributed mass is a great
way to simplify a model for analysis but they will not account for the
additional stiffness that would have been provided by the missing geometry –
only mass.

Conclusion

The main point to take home from this blog is to always
be perceptive when transitioning between reality and the mathematical model. It
is easy to make quick decisions in the set-up of a study when it should really
be the part of the analysis where most time is spent. By ensuring that simplification
has been achieved intelligently, and that the material model and the boundary
conditions are accurate, the degree of idealisation error will be minimised.

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