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# Validation Case: Bonded Contact on a Quarter Shaft

This bonded contact validation case belongs to solid mechanics. This test case aims to validate the following parameter:

• Bonded contact

The simulation results obtained with SimScale were compared to the analytical results presented in [Roark]$$^1$$.

## Geometry

Two geometries are used for this bonded contact validation. The first one consists of a quarter shaft. Radius is 0.1 $$m$$ and length is 0.5 $$m$$:

The second geometry has the same dimensions, however, it is split exactly in half, between the ABC and A’B’C’ planes:

The 3D geometry is a 90$$^0$$ section of a cylinder with dimensions as tabulated below:

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Linear static

Mesh and Element Types: The meshes for Cases A through D were created in SimScale. The standard algorithm was used.

Find below the mesh used for Case D. It is a standard mesh with second-order tetrahedral cells.

## Simulation Setup

Material:

• Steel (linear elastic)
• $$E$$ = 208 $$GPa$$, $$v$$ = 0.3
• Therefore, the shear modulus is 80 $$GPa$$.

Boundary Conditions:

• Constraints
• Fixed support on face ABC
• Face A’B’C’ is rotated with an angle $$(\theta)$$ of 2e-4 $$rad$$
• Contacts
• Single part shaft
• Cyclic symmetry: face AA’B’B is tied to face AA’C’C. Rotation axis: z-axis. Sector angle: 90º
• Split shaft
• Cyclic symmetry: face AA”B”B is tied to face AA”C”C. Rotation axis: z-axis. Sector angle: 90º
• Cyclic symmetry: face A”A’B’B” is tied to face A”A’C’C”. Rotation axis: z-axis. Sector angle: 90º
• Bonded contact: both parts are bonded at A”B”C”.

## Reference Solution

The analytical solution for maximum shear stress $$\tau_{max}$$ given below is based on Roark$$^1$$.

$$\large{\tau _{max}}=\frac {\theta.G.r}{l} = 3.2 \ [MPa]$$

## Result Comparison

The results obtained from SimScale for the maximum shear stress $$\tau_{max}$$ at point B’ are compared with the analytical solution by [Roark].

Inspecting the Cauchy stress magnitude for Case B in the post-processor: