The d'Alembert's principle is employed to reformulate the dynamic problem into an equivalent set of static problems suitable for processing by the FEM solver, a procedure commonly referred to as a "quasi-static" simulation1. The MbD solver provides the joint forces and torques, as well as the position, velocity and acceleration vectors defined at the origin coordinate system2 of each part in the assembly. These MbD joint forces and torques are distributed as Concentrated LOADs (CLOADs)3, following a sinusoidal profile; across the appropriate FEM nodes located on the bearing surfaces of each part.
The mass of each volume element in the FEM mesh is determined from its volume and the user-prescribed material density. The total acceleration at the center of mass of each volume element is obtained as the sum of the centripetal, transverse, and translational contributions. Subsequently, the d'Alembert forces4 for each volume element are computed as the negative product of total accelerations at element center of mass (CM) and the corresponding element masses.
The videos below depict the distribution of the joint forces among the FEM nodes, as well as the weight and d'Alembert force vectors at the center of mass of each FEM mesh volume element (tetrahedrons in this example). Joint FEM loads and d'Alembert forces are shown using red lines. Weight vectors are depicted by white lines5.
As mentioned, the pin is grounded. For the FEM simulation, all the nodes belonging to the top and bottom circular faces of the pin are grounded.
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 mesh. 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.