Modelling

We already know that for creating a FE model we need to mesh a mathematical model.

Mathematical model = CAD data (3D or 2D) + Boundary conditions

There for the importance of the creation of mathematical model and using reliable modelling techniques is crucial to the FE analysis. The best mathematical model is the one which represent our area of interest adequately and help us to make assertive design decisions with reliable results.

Steps in modelling

• Define the objective of analysis

The purpose should be to understand what we require from the results and prepare the simplest model for analysis. For Example: A model required for frequency analysis is different from the one required for stress analysis.

This also applies for all stages of the FE analysis, like a non-linear material should not be used if a linear material can be used.

• Consistent measurement units

One must make sure that the unites of measurements stay consistent in the CAD model for the properties of dimensions in “mm” and the material characteristics like density in “Kg/m³”. All units in the FEA model should also be use consistent results to avoid erratic results.

One should take help of the units’ manager in FEA soft wares and make sure that the measurement units are consistent.

• Geometry creation

The mathematical model is meshed to create the FE model. The math model should capture all important features and avoid complexities at the same time mesh correctly.

A common mistake is meshing the CAD model as it is. This often may lead to unreliable results due to element insufficiency or element distortion. Also if it works it is an expensive model to solve with little benefit to quality of results. Choice of meshing element like 3D element, shells, 2D elements etc. should also be a factor to consider.

• Define material properties

Material properties like elastic modulus can be automatically assigned to the FE model from the material library provided in the FE software. Material properties can also be provided to the mathematical model in the CAD software after which it is meshed and the properties are transferred to the FE model. However there may be chance of data lose if some elements are deleted, so it is preferred to give material properties through the FE software where possible.

• Define Boundary conditions

Boundary conditions i.e. loads and restraints can be applied to either the CAD model or the element entities. It is easier to apply loads on the FE model that restraints, loads should be verified by checking the reaction on the FE model. Applying restraints is trickier and errors can be made. Restraints can be verified by checking the displacement plot.

Restraining is the most uncertain part in creation of an FE model for analysis and sufficient care and verification should be made for the same.

Useful Modelling Techniques

• Symmetry and Anti Symmetry

These boundary condition are useful techniques to reduce the model size and structure analysis. Care must be used in using them in modal analysis.

• Axial Symmetry

When the geometry and boundary condition share an axial relationship (along 360^o) the FEA model can be simplified to for axisymmetric analysis which is a type of 2D analysis included in the FE analysis. Using Axis symmetry only a planer cross section must be meshed and solved.

Other symmetries like cyclic or repetitive and combination of different forms of symmetries can be depending if the FE software is capable of analyzing them.

• Realignment of Degree of Freedom

FE elements depending on its type have a certain degree of freedom. E.g a 2D plate elements have two in-plane translational degree of freedom, 3-D shell element have six degree of freedom i.e. three translational and three rotational. Solid element have 3 translational degree of freedom.

The degree of freedom for all the element are connected to the global coordinate system of the model. However it is sometimes required to change this reference for easy application of boundary conditions and interpretation of results.