![]() ![]() The rotation around the y-axis is once more constrained, but this is not a problem.įinally, the symmetry condition on the xz-parallel face imposes the additional constraint of no displacement in the y direction. Next, the symmetry condition on the yz-parallel face imposes the additional conditions that there can be no displacement in the x direction and no rotation about the z-axis. Thus, the symmetry condition applied on the face parallel to the xy-plane will impose the condition that this face has zero displacement in the z direction, and that there can be no rotations about the x-axis and the y-axis. The symmetry condition imposes that there be no displacement in the normal direction to the selected (planar) boundaries. Let’s think about exactly how these three symmetry conditions constrain the part. In addition, this has the beneficial side effect of reducing the computational size of our model.Įxploiting symmetry along three orthogonal planes fully constrains the model. We apply the symmetry condition to the three faces along these planes, and this will have the effect of completely constraining our part. This reduces our model to a 1/8 submodel of our original model. We can draw the part aligned with the global Cartesian coordinate system and use partitioning along workplanes parallel to the xy-, yz-, and xz-planes. ![]() Using Symmetry Planesįor this geometry, the experienced structural analyst will immediately see that there are three planes of symmetry that can be exploited. This blog post will describe various ways in which this can be achieved, depending on the geometry that we’re dealing with. To get a solution for the deformations, we do need to introduce a set of constraints on the displacement field, and these must be sufficient to constrain all free-body displacements and rotations, but they cannot affect the stresses and strains. For the purposes of this blog post, it is sufficient to address solely the linear case, but if you’re interested in some more advanced topics, see the following blog posts: The stresses and strains are computed from the displacement field. Instead, we solve for the displacements (or deformations) from the undeformed state. Now, when we solve a solid mechanics problem via the finite element method, we aren’t directly solving for the stresses or strains. ![]() That is, the applied forces could be aligned with any arbitrary direction and the solution in terms of the stresses and strains would still be the same. That is, we can say with confidence that a stationary solution to this problem exists, even if we don’t know where the part is or how it is oriented. Now, we intuitively know that a part with equal and opposite forces on it will not experience any accelerations, so although the part will deform, it won’t be in motion. We really just want to focus our analysis on this one part of a larger system, so it makes sense to approximate all of these other parts as a boundary load that is normal to the ends of the plate. Imagine, perhaps, that this part is connected to some cables via some fixturing and put in tension.įree-body diagram of a flat plate with a hole in the center, under a tension load.Īlthough we could build a model of the fixturing and the cables, and a model of whatever the cables are connected to, this is likely much more effort than we want to expend. Let’s assume that there are equal and opposite forces applied at the top and bottom. We will start by considering a simple model of a flat plate with a hole through it - a classic problem in solid mechanics. Let’s look at how to use these different approaches and their nuances. There are a number of different strategies that we can employ in such cases, depending on the geometry. When building models in solid mechanics, we often have a part where there are prescribed loads but no constraints that we can reasonably apply. ![]()
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