ME 475 FEA of a Composite Panel
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1 ME 475 FEA of a Composite Panel Objectives: To determine the deflection and stress state of a composite panel subjected to asymmetric loading. Introduction: Composite laminates are composed of thin layers (plies) consisting of reinforcement and a matrix. The reinforcement are typically a strong, stiff material, in the form of long fibers. The matrix is typically a material that is applied in a liquid form and then cured and hardened. The matrix is applied to support the reinforcement, and to distribute the load through the reinforcement and plies. It is common to have plies with fibers in one direction, also called unidirectional, or in several directions in a weave. The orientation of the fibers and stacking sequence has a large effect on the deformation and stress throughout the laminate. The stress in a laminate is more complex to characterize than that for linearly elastic, homogeneous, isotropic (LEHI) materials. It is discontinuous through the plies, and thus must be evaluated differently. Failure, consequently, is also much more complex than for LEHI materials, and will not be discussed in this class. In this lab, a foam core between two laminates will be utilized. This is a common practice, since it puts the fibers farther from the center of the plate. This increases the bending stiffness of the laminate, while only adding a small amount of mass (ρ foam << ρ laminate ). Analysis Problem Statement: A composite panel made of four plies of carbon/epoxy above and below a foam core. The panel is cantilevered, and has a point load applied to one corner, as shown in Figure 1. 1
2 10000 N Carbon/epoxy unidirectional laminate: E 1 = 147 GPa, E 2 = E 3 = 10.3 GPa ν 12 = ν 13 = 0.27, ν 23 = 0.54 G 12 = G 13 = 7 GPa, G 23 = 3.7 GPa ρ = 1,600 kg/m 3 1 m 0.4 m Polypropylene foam: E = 0.3 GPa, ν = 0.43 ρ = 400 kg/m 3 Figure 1. Geometry, material and loading for the composite panel. The top and bottom surfaces have four plies of unidirectional carbon/epoxy, each with a thickness of m. The core is made of polypropylene foam. The thickness of the foam is 0.04 m, while the total thickness of the carbon/epoxy lamina is m for the section on both the top and bottom (this makes the panel a total of 0.05 m thick). Mathematical Idealization: Mathematical Representation The foam is too thick to model with shells, thus 3D solid elements must be used. The carbon/epoxy sections are very thin, so they will be modeled with shells. Geometrical Representation Perfect bonding between the foam and the laminates will be assumed, so skinning will be used to section the geometry. Boundary Conditions One side is fixed, and a load is applied to one of the free corners. This induces both a bending moment and torsion in the panel. 2
3 Material Model The foam is linearly elastic, homogeneous and isotropic. The laminate is orthotropic, and linearly elastic. The individual constituents (carbon fibers and epoxy) of the laminate are homogeneous, but the laminate itself is not. Analysis Procedure: 1. Create a new part. It should be a 3D, deformable part, created by Solid Extrusion. 2. Sketch a rectangle with height 0.4 m and length 1 m. 3. Assign an extrusion thickness of 0.04 m. 4. Partition the top face using the Partition Face: Sketch tool. a. Create two sides of a square in the bottom right corner of the face. They should have a side length of 0.05 m. When finished, the part should look like Figure 2. Be sure the long side is aligned with the 1-direction. Figure 2. Plate after part creation and partitioning. 3
4 5. In the Property Module, create a material called Comp_Carbon_Epoxy. Create a density property, and an elastic property. For the latter, change the type to Engineering Constants. Enter the data as shown in Figure Create a second material called Polyprop Foam. Create both a density and an elastic property, as in previous labs for LEHI materials. Enter the data shown in Figure Next, the part will be skinned. The important consequence of this is that when meshed, the part has solid elements and shell elements that share the same nodes. This enforces the same displacement at the boundary of the foam and lamina, which agrees with the perfect bonding assumption made earlier. a. Choose the Create skin tool. Choose the top surface, including the partitioned region. Click Done. b. Choose the bottom surface. Click Done. The top and bottom surfaces have now been skinned. 8. Create a solid, homogeneous section for the foam. 9. Assign the section to the plate. 10. Choose the Create Composite Layup tool. Use a conventional shell with 4 plies. Name it CompositeLayup-Top. Create a layup the same as that shown in Figure 3. a. To choose the region for each ply, double click in the corresponding box. b. Click on the Show/Hide selection options button. c. Change the Select from box to Skins. d. Select the top surface. 4
5 Figure 3. Layup for top surface. 11. On the Offset tab, choose the Bottom Surface radio button. By default, Abaqus puts half the thickness of shell elements above and below the actual elements. In this case, the thickness should all be above the surface for the top layer, and below the surface for the bottom layer. 12. Create another layup, called CompositeLayup-Bottom. It should be very similar to the first layup, but the plies are in reverse order, as shown in Figure 4. Remember to choose the bottom skin for the region. 5
6 Figure 4. Layup for bottom surface. 13. On the Offset tab, choose the Top Surface radio button. Once this is finished, the property definition and assignment is complete. 14. Create an instance of the part in the assembly. 15. Create a Static, Linear Perturbation step. 16. In the field output requests, be sure the strain ( E ) is requested. 17. In the load module, create a boundary condition on the back face that constrains all 6 DOF (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0). 18. Create a pressure load on the partitioned region of the plate with magnitude 4 MPa. This is to apply the 10,000 N load over a small area to prevent stress concentrations. After steps 15 and 16 are complete, the part will look like Figure 5. 6
7 Figure 5. Plate with boundary conditions applied. 19. In the mesh module, apply a global mesh seed of In mesh controls, mesh with Hex elements, and use the Advancing Front algorithm with mapped meshing where appropriate turned on. 21. Assign an element type of C3D8 to the solid region. Assign an element type of S4 to the skinned regions. For the latter, you will need to use the same procedure as for assigning the regions during the layup defintion. 22. Mesh the plate. 23. Create a job, and run the analysis. View the layup orientations and thicknesses. 1. Start in the Property module. 2. Choose Tools Query Ply Stack Plot 3. Choose the surface you wish to view (you will need to choose Skins from the selection filter). 7
8 In this procedure, a layup with orientations [0/90/45/-45] on top and [-45/45/90/0] on bottom was used (Layup #1, below). Analyze the plate with Layup #2 and Layup #3, listed below. It may be useful give each of these a different input deck name. Note the report requirements. 1. [0/90/45/-45] on top and [-45/45/90/0] on bottom 2. [-35/-35/45/0] on top and [0/45/-35/-35] on bottom 3. [10/0/90/-15] on top and [25/0/0/-35] on bottom Model Validation: Set all the plies to have an orientation of 0. Compare the deflection of the plate (average the deflection of the free corners on the bottom surface) to that of a uniform LEHI cantilevered beam with E = E 1. The beam should have a moment of inertia equal to that of the plate, neglecting the stiffness of the foam, but not the position of the laminates. Since the plate does not meet the all the requirements of beam theory (width << length is not true here) there will not be great agreement between the FEA and hand calculations. An order of magnitude comparison is really all that can be drawn from this calculation. If you can find an analytical solution for a plate with these boundary conditions, then a better comparison could be made. Report Requirements: A full report is required for this lab (see ME 475 Lab Report Format Guidelines). Include the following in your report: 1. A plot of the deformed plate with Max Principal strain contours displayed for the layup used in the procedure (Layup #1). 2. Plots of the ply stack plot for Layup #1 (top and bottom surfaces). 3. A plot of the deformed plate with Max Principal strain contours displayed for Layup #2. 4. Plots of the ply stack plot for Layup #2 (top and bottom surfaces). 5. A plot of the deformed plate with Max Principal strain contours displayed for Layup #3. 6. Plots of the ply stack plot for Layup #3 (top and bottom surfaces). 7. Report the maximum principal strain for each of the layups analyzed. 8. Report the maximum z-component of displacement (U3) of the plate for each of the layups analyzed. 8
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