Types of finite element analysis

Thermal Analysis

FE analysis thermal analysis is much simpler than structural analysis considering from the calculation point of view. This is considering a steady state condition i.e. the heat flow does not change with time. Also temperature is a scaler quantity and only one degree of freedom needs to be specified to the nodes in both 2D and 3D cases.

 

We can therefore compare the linear static analysis to a steady state thermal analysis. And a dynamic structural analysis to a transient thermal analysis.

 

Analogies between the structural and thermal analysis are as below.

 

Heat Flow due to set temperature

Like stresses are induced due to induced load, heat flow can be induced by heat load or temperature difference. Heat flow is set about by the temperature gradient across the temperature boundaries. In such a case we consider that the part under analysis is completely insulated and no heat is lost or transferred to any other part. This can denote the heat transfer by conduction.

 

Heat Flow by heat load and convection

Heat load applied to a part by means the application of heat flux E.g. To a surface. The analysis can then be continued by providing the convective coefficients to the surface which dissipate heat. The heat flow and temperature across the FE model can then be studied from the analysis.

Attempt to run a thermal analysis with heat loads but without specifying the convection coefficients/temperatures to remaining surfaces result in an error like cause by absence of support on structural analysis.

Modelling symmetry can be utilized in thermal analysis to simply the problem.

 

Non Linear analysis

Linear analysis is defined by the assumption that the stiffness of the material does not change during the analysis. This means the stiffness matrix [K] is does not change during the analysis. Certain problems like a material entering the plastic stage (Stress-strain curve) has a change in its stiffness and therefor the stiffness matrix [K] changes and therefore require non-liner analysis.

 

Non Linear material

For a linear material the inputs required for FE analysis are the Elastic modulus and the Poisson’s ratio. The elastic modulus is constant for a linear analysis, but for a non-linear the elastic modulus is not constant and must be recalculated during the FE analysis.

The Elasto-Plastic material model is the commonly used non-linear analysis model. This model assumes a linear relationship between the stress and strain to a defined limit “Yield point stress”. Beyond this the stress in material constant regardless of the strain level.

Additional information about the “Yield point stress” is required for this analysis.

The use of elasto-plastic stress can eliminate singularities like those by sharp re-entrant corners as an upper limit is set to the value of stress i.e. yield point stress the stress value cannot diverge to infinity.

 

Non Linear geometry

Non-linear geometry analysis, also known as “large deformation” analysis. During this analysis the stiffness matrix changes due to change in the shape of the part under analysis. An example where non-linear analysis is applicable with small deformation is when linear analysis evaluates for the bending case in a flat, however due to some deformation in the flat shape, membrane stiffness is added to the beam in addition to the bending stiffness. Neglecting this membrane stiffness, i.e continuing with linear analysis gives high margins of errors for displacement results.

For the above condition the linear analysis cannot evaluate a stiffness matrix which exist prior to load application.

Non-linear analysis should always be considered for structures that show large deformation. This is recommended as not only the stiffness changes but also the orientation of loads change with respect to the new shape of the model. Load that retains its absolute direction with reference to global coordinates is “non-following load”. Load which retains its direction with respect to its new shape is called “following load”.