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Matt,
Please provide an image with labeled edges and verticies and a table with three columns that has a row for each joint. The columns are Joint Name, Reference scope and Mobile scope. Do this for a few of the joints that share entities. Then we will have a specific example to suggest changes.
Without seeing that, I will describe a trivial example for you to consider. Imagine three line bodies meshed with beams that meet at a common point in space. You want to know the forces and moments on each of the three beams, but a Fixed Joint only has two sides, the Reference and Mobile side, so one side will have two beams while the other has one. A probe of the Joint will accurately show the forces going into the one beam that is on its own, but can’t separate the forces between the two beams that are on the other side of the joint. Creating three Fixed Joints so that each joint has one beam on one side doesn’t work because that is a redundant set of constraints and the warning message will issue telling you that. You could solve the model 3 times and redefine the joint between each solve to switch between the three beams to output three sets of forces.
The above example is ridiculous because what you would do instead is to simply Node Merge or Share Topology at the node where the beams intersect so that there is no Joint and extract forces and moments from the beam using Beam Results (or is it Beam Tool?). However, reimagine the same problem with three edges of three plates that come together. Now you have to do more work to get the forces and moments from each of the three plates. Review this discussion to see how to extract forces and moments on any plane.
Another way to solve the problem is to add a “connection body” at the intersection location. In the three way example I mentioned above, cut back each of the three entities around a small radius of the intersection point and create a connection body with three legs at the intersection point. Now you can have three joints that have only a single entity on each side of the joint so you get no warning messages and the correct values of forces and moments.