Transcript
Transcript
In this lesson, we will set up and run the two-step simulation process for homogenization using the same simple lattice example. Again, we’ll apply compression loading to the top plate and fix the bottom plate. You can download the starter file below to follow along with this video. We’ll start by creating sections in the notebook to help organize our thought process a little bit. The first section will be for the first stage of homogenization and the second one will be for the bulk lattice volume.For homogenization, we’ll need the homogenized unit cell block, so I’ll add it to that section and also add the Static Analysis block to the other section. These will be our end goal for each stage of the process. Let’s fill everything out that we need for homogenization. This works very similarly to the Static Analysis block, except you don’t define any boundary conditions and just give it the design volume that it needs. We’ll see what this is in a little bit. So I’ll double click and fill out the FE Model, choosing a solid component which needs a mesh. So we’ll double click and choose this FE Volume Mesh as well, and make it a variable called Unit Cell Mesh. Then fill out the standard meshing workflow there, which is Volume Mesh, Remesh Surface, then Mesh from Implicit Body.It needs a body, so this is where we’ll create our unit cell. We’ll start by adding a box, which will be this design volume that will be repeated across the representative structure, and our unit cell will have to fit in this box. So let’s also add a unit cell. We’ll change the length, width, and height of this box to the size of our unit cell. To do that, I’ll go back up to our lattice, open it up, and make the cell size a variable called Unit Cell Size. Then we can come back here to our box and type in the name of the variable, and then choose that length X component. Same thing for each of the other ones, Y component, and then press enter or click outside the box to choose it. Then Z, and then we’ll call this the unit cell volume.For the unit cell, we’ll want to make sure that all the parameters are the same as in our lattice structure. So I’ll go back up and make into variables the type and call it unit cell type, the orientation as well. Bring that into our inputs. Then we’ll need the Periodic Lattice Body block, and we’ll put that unit cell inside, as well as add a Rectangular Cell Map that will need to be the size of the unit cell. We’ll use the unit cell volume box we created earlier, as well as the unit size parameter that we’ve made into a variable.In here, we’ll also grab the beam thickness variable for our unit cell parameter one, which is for thickness. If we click on this block, we can see the unit cell we’ve created highlighted on the screen. I’ll make this variable called Unit Cell and collapse this. Now if we isolate this unit cell and turn on the visibility of the box as well, we can see that some parts of it are coming outside of the box, and we can get rid of all of this because the unit cells will be repeated across the structure and they’ll have neighboring units. So these parts are negligible. So we’ll trim it to the box using the Boolean intersect, and the unit cell will homogenize, will look like this. I’ll name this appropriately so we know what is what: Unit Cell Trimmed. Then we’ll drag this into the meshing workflow, and I’ll use the second overload and the tolerance of 0.3 mm, which is 30% of my beam thickness. Then add a sharpen iteration of one. Let’s take a look at what we have. That looks good. So I’ll move on to the next block. I’ll give it an edge length of 0.25 and triangle shape. That also looks good, and we have closed and manifold true and self-intersecting false. So we can keep going here. I want to use the same edge length. So let’s make this a variable called Mesh Size to reuse it, and then I’ll choose linear geometric order. Then if we isolate this and check our section cut, the mesh looks good.So we have that mesh complete, and so we can grab that material and fill that in as well. For the design volume, we’ll use this unit cell volume that we created earlier. We’ll call this homogenization result. It’s already completed running very quickly. So we can go into the properties under material and linear elastic property to see the compliance and stiffness Matrix coefficients. If you open each of these, you’ll find the constant value. To visualize the result, we can isolate this block and use the heads-up display here to the right. The directional option will give you the stiffness Matrix visualization, and we’ll just have to zoom to fit here. If you want to export the result, you can either right click and choose Export to take this out as text or CSV file of the 6×6 elasticity matrix, or you can also use the Export Material block. Put in this whole block, choose your unit system that you want to export with, and be able to export into different file types for other external software as well. That’s it for the first stage. All we have left to do now is use that result that we got as the material for this next static analysis.So let’s fill in our FE Model, and we’ll need two components for this. So I’ll add another item to the list. Both of these will be solid components, one for the bulk lattice volume and one for the plate. So let’s choose FE Solid Component for both. We will need the mesh for these, so choosing the FE Volume Mesh block, I’ll make this into a variable calling this Lattice Volume Mesh. Then we’ll fill it out with the Volume Mesh block, and for this, if we turn back on the visibility of our plates as well as for our lattice region here, they’re both nTop geometry. So we can skip the Remesh block and go straight to using Mesh from Implicit Body. For the body, it will be that lattice region implicit, so I can type that in and choose that implicit body. I’ll use 0.5 mm as tolerance. If we isolate this block, we can see some rounding happening. So I’ll change the overload to the second one and add a sharpen iteration of one to sharpen the whole mesh. The edge length will be 0.25 mm, and if we isolate this as well and look at that cross-section, the volume mesh looks fine enough. So I’ll choose linear here, and we have our lattice volume mesh for that first solid component, and I’ll just go ahead and put in the material here really quickly and also label this component FE Lattice Volume, so that we know what we’re working with. FE Plates component. Then we’ll do the exact same process for the plates as well with the same input values, starting with that FE Volume Mesh, making it a variable called Plates Mesh, filling it out with Volume Mesh, and then Mesh from Implicit Body. Body will be those plates implicits. All the values I’ll keep the same as in the previous step. Then I’ll use that same material here as well.Then the next step is to create that connection using a connector. So we’ll grab the Tie Constrained block and then fill this out with the independent and dependent boundaries. I’ll use the Boundary by Body block, and this independent component will be the plates. So we’ll use that plates mesh, as well as that implicit, to choose that whole region. The same thing for dependent, but this time with that lattice volume mesh. If we look at that, the nodes that were selected, it seems like it’s not catching all the nodes that I want. So I’ll try increasing the tolerance, and now it is getting all of those nodes. Then I’ll make this a variable and then put that into the connector input. I’ll also rename this analysis result.The last thing we’ll have to do here is define our boundary conditions, and we’ll need two, one for force and the other for the restraint. So I’m bringing this outside of that nested block and adding those, and adding those different blocks. We’ll select the boundary on the mesh by right-clicking on that face and choosing Flood Fill. So the top phase for the force, we’ll put that into our boundary, choose nodes, and the vector will be 0, 0, and 1,000 Newtons for that downward in the Z direction. Then we’ll do the same for that bottom face, using right-click and choosing Flood Fill and putting that into our displacement restrained boundary. Then we can let the analysis run since everything is now complete. Once that’s done, we can click on that block, isolate it to be able to see that result, and also be able to look inside the properties tab to get the analysis results.