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# Have Initial Stress? Relax, We Can Work with It!

July 10, 2015 By: Patrick Cunningham

I was recently working on a finite element model that included multiple loading conditions.  This is not uncommon, but in this case the finite element mesh needed refinement in different regions of the model that were specific to each load.  Initially, I needed to evaluate the stress distribution in one region due to assembly loads.  Subsequent to this, I was interested in the contact stress at a stop that could occur in an overload condition.   Since this was a path dependent problem I needed to have the stress state from the assembly load included in the stop load.

Consider a simple analogy where the model consists of parts A, B and C.  Part B has a fixed support for both load cases.  In the first load step, I need to evaluate a contact stress between parts A and B.  In the second load step, the contact stress is evaluated between parts B and C. The result of load step two is dependent on the stress state from load step one but there is no interaction between parts A and C.

The common approach is to define a mesh in part B that would accommodate both loading conditions.  This is not convenient for several reasons:
1.    It requires that I use a single model of the entire assembly for both load cases.
2.    My mesh refinement studies would become lengthy because I need to refine the mesh in two stages.  I cannot begin the mesh refinement for the second load step until the required mesh for the first step is determined.
3.    Each refinement of the second load step would have to include the refined mesh from the first load step as well.

An alternative approach is to use two different models – one to evaluate the stresses between parts A and B, and a second to do the same between parts B and C. To use two models,  I will need to get the stresses from model AB into model BC as an initial condition.  Defining initial stress has traditionally been limited to either a constant state throughout the structure or a non-uniform stress state that is defined per element.  To use this approach, I would need to construct a table of the normal and shear stresses from model AB to be assigned to each element in model AC using format like the one shown in Figure 1.

This approach will also be very time consuming as I need to keep the mesh the same in part B for both models.  Each mesh refinement in model BC will require a re-run of model AB to regenerate the initial stress.   At this point, any sane person would have to ask why I bothered to divide the structure into two models in the first place.

The good news is that there are tools available that can interpolate the initial stress distribution between two different meshes.   The ANSYS Mechanical tool can export the normal and shear stresses in tabular form with a click of the mouse.   The ANSYS Workbench environment can read a tabular definition of stress versus location and map the data onto a different mesh of the same part.   The interpolated initial stress can be evaluated visually and analytically verified.

To illustrate this a bicycle hand brake is fastened to the handlebar with a bolt preload prior to any braking loads being applied.  When the brake handle is squeezed the total stress on the component should include the initial stress of the bolt preload.   A model consisting of the preloaded part of the grip is used to generate the initial stress illustrated in Figure 2.

Figure 2 - Initial stress resulting from fastening the brake to the handlebar.

## initial stress 1.png

The initial stress is exported from the preload model and mapped onto a model of the grip assembly where the braking loads are applied.   Note that a different mesh is used in the assembly model.  An illustration of an imported stress mapped onto the assembly model with source point verification is shown in Figure 3.

Figure 3 - Imported Initial Stress with Source Point Validation

## initial stress 2.png

Together, these tools enabled me to refine the mesh in the two models as needed and keep my computing requirements and solution times within reason.   If you are interested in more information about this you can view the CAE Associates eLearning presentation "Advanced Loads in Workbench."