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FEM Loads and d'Alembert Principle.

The joint force vector is resolved into its axis and side components. The axis component is the component along the hinge rotation axis. The side component is the perpendicular component, resting on the plane perpendicular to the hinge rotation axis.

Each of the joint force components (axis and side) results in one set of FEM loads. The axis joint force component derives in FEM loads acting on the pendulum and pin "shoulders", and are distributed following a linear profile. The shoulders are the annular faces on both parts, which make contact and prevent the relative displacement along the hinge axis. The side force component derives in FEM loads applied to the nodes belonging to the cylindrical faces, and follow a sinusoidal profile.

The joint torque leads to four sets of FEM loads, two acting on the two annular faces (up and down shoulders), and two acting on the cylindrical faces. These FEM loads follow both a sinusoidal and a linear profile along the adequate planes.

The videos below depict the action FEM loads applied to the pendulum mesh (left), and the reaction FEM loads acting on the pin mesh1 (right). The software ensures all these FEM loads are always in compression, as the hinge is not capable of applying tension loads.

In the videos below, the weight and d'Alembert force vectors are shown only for a representative sample of all the volume elements in the mesh1. This facillitates the visualization of the joint force FEM loads. These loads are applied in compression, to the adequate nodes of the bearing surfaces. The heads of the arrows are depicted by a white line.

  1. FEM loads derived from MbD joint force are always depicted by red lines, while FEM loads derived from MbD joint torque are shown in blue.
  2. From now on, to facilitate the visualization of the joint force/torque FEM loads; d'Alembert and weight body forces are either shown only for a small set of all the mesh volume elements, or not shown at all. However, the underlaying principle of the simulation remains the same for all the cases: the dynamic problem is reduced into a set of static problems by the application of the d'Alembert principle, this is, by canceling the inertial forces acting at the center of mass of each volume in the mesh.
Next: von-Mises stress.