Torsion stiffness and St. Venant’s principle
Torsion stiffness is a very important characteristic in chassis design. A stiff chassis has more cornering torque and the suspension can handle it more easily. This post presents results of torsion test performed at Idra Simulation using code_aster.
To perform the test, a simplified beam elements model is built. The loads are applied at the front suspension mounting points, while the displacements are fixed at the rear suspension. To have a realistic distribution of loads, a-arms, kingpin and springs are represented by truss elements.
Such simple model is not only useful to estimate and compare different design; it can also be used to obtain detailed results on a region of interest by using the sub-modeling technique.
To do so, the displacements calculated at a certain location inside the beam model are specified as boundary conditions for the solid sub-model.
This technique is based on St. Venant’s principle, which states that if an actual distribution of forces is replaced by a statically equivalent system, the distribution of stress is altered only near the region of load application (1).
So let say we want a more accurate estimation of the stresses on the upper part of the roll cage. We first “cut” the structure in the middle of the roll cage to retrieve the displacements at those nodes. Then, we apply those values on the solid element model.
Since the beam elements have translations and rotations degrees of freedom, those values cannot be applied directly on the solid elements. For this reason, a node is created at the center of the cut tubes, and rigid beams link it to the solid structure. That way, translations and rotations can be applied:
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(1) Mac Donald. Practical Stress Analysis with Finite Element. Glasnevin Publishing, 2011.