Structures Mike McKenzie Structures Ansys is being used to do the stress and weight analysis on the HAB. Ansys is a commercial program that can do linear and non-linear stress analysis. Other programs that were considered were Catia, ProE, IDEAS, ABAQUS, and professor Doyle’s program, Stadyn. Ansys was chosen because a few professors in the AAE department (Professors Doyle and Kim) are familiar with the program, and it is loaded on all ECN machines and PUCC labs. It can also do both the modeling and FEA of the s/c. Our group used a HAB design similar to last semester’s HAB. The HAB is cylindrical with a hemisphere on top. Counting the top and bottom of the cylinder, there are 5 floors. There is a hollow pillar in the center of the HAB that runs the length of the cylinder. The pillar was added to constrain the motion of the floors in their center to keep the bending stresses from the supplies down. Frames were added as rings between the floors on the sides of the cylinder to help keep the hoop stress down. There is a approximately 60,000 kg of supplies that need to be in the HAB. I distributed the mass evenly onto the 5 floors for now. I will more accurately model the supplies when I get a more exact mass per floor from Randy. An internal pressure of 1 atm (101,325 Pa) was applied to the walls of the shell. The internal pressure was not applied to the floors or pillar of the HAB. Sandwich materials were used on all HAB surfaces to keep the stresses and weight down. The sandwich material being used is 5.2cm thick. Such a thick sandwich decreases the hoop stress, and increases the flexural rigidity (EI). A large flexural rigidity keeps the bending stresses down, and increases the buckling stiffness. The equation for hoop stress is: H Pd 2t (1) where P is the internal pressure, d is the diameter, and t is the wall thickness. The hoop stress is significant for such a large diameter of cylinder. Using a sandwich structure and having a large t significantly reduces the hoop stress. The HAB is bigger than last semester’s. See table 1 for a breakdown of the HAB’s dimensions, and Figure 1 for a schematic of the HAB. Figure 2 shows a cut-away view to give a better view of the inside of the HAB. Notice the frames and pillar in Figure 2. The cutting plane for figure 2 is rotated an angle from the symmetry axis to give a better depth of field. That is why the pillar isn’t shown running the length of the cylinder, even though it physically does. Dia [m] Length [m] # floors Mass [kg] tface plates [mm] tcore [cm] Last semester 8.75 13.625 5 8,500 2 3 This semester 13 16.5 5 14,200 2 shell 3 shell 1 other 5 other Table 1: Values for HAB from last semester and this semester. Figure 1: Front and side view of HAB modeled in Ansys. Figure 2: Cut-away view of HAB in Ansys. A script is used to input the Finite Element Model (FEM) into Ansys. I included the script file, structure.log, on the zip disk. Using a script file allows parametric studies to be done on the model. Any aspect of the model can be changed in the script to see the effect on the results. The script is necessary since Ansys is not really a parametric modeler like many commercial CAM packages, and it’s GUI is not as advanced as many CAM programs either. Once the areas were drawn in Ansys, they had to be ‘glued’ together to simulate them being fastened together. The supply masses were input into the model as pressures. Adding the supplies as pressures is not a problem since only the g loading (more on this later) will be studied, and this is in the (-)z direction. In the script file, it is possible to define 8 different sandwich thicknesses for the various surfaces of the s/c. It is also possible to have a different mass of supplies on each of the five floors. The sandwich faceplates are made of a Graphite/Epoxy composite. The core of the sandwich is a honeycomb material. More will be said of the materials later. The sandwich material was modeled in Ansys using a sandwich shell element called linear layer 99. This particular element can have a total of 250 different layers, but our sandwich structure only has 3. The thicknesses of the sandwich components can be seen in table 1. The properties of the sandwich components are easily specified by entering their material properties into a table. The only properties necessary to completely describe the materials are: thickness, density, Young’s modulus, and Poisson ratio. Graphite/Epoxy was chosen for the faceplates because it is strong and light. Titanium and Aluminum were the other materials being considered for the faceplates. See Table 2 for a listing of properties for these 3 different materials. [kg/m3] Specific Modulus (E/) [Pa/] Specific max (max/) Tmax [°K] [Pa/] Graphite/Epoxy 1600 40.9e6 159.4e3 450 Aluminum 2600 26.9e6 173.1e3 933 Titanium 4500 22.2e6 177.8e3 1940 Table 2: Properties of 3 materials considered for the faceplates. Material properties for the metal are taken from reference 1, material properties for the composite can be found in reference 2. From the table above, it can be seen that Titanium had the highest specific strength, but the composite material had the highest Specific Modulus. A high specific modulus adds to the flexural rigidity of the structure (EI). The composite material had the lowest Tmax. Using more TPS to keep the temperature of the composite low uses less mass than using Ti with less TPS. This will be verified later with the trade studies. The thickness of the faceplates should not be less than 1mm to avoid local buckling of the material. Using 1mm of the Graphite/Epoxy meets the stress and buckling requirements. Less than 1mm of Titanium would be needed to meet the stress requirements, but since the thickness should not be less than 1mm, 1mm of Ti would have to be used anyway. Therefore, using Ti would raise the structural mass considerably because its density is so much greater than that of Graphite/Epoxy. An important difference between the composite being used and structural metals is that the composite doesn’t have a yield strength like the metals. The composite only has an ultimate strength. This is why a safety factor (SF) is being used when designing the structure. The composite is from the [0/±45/90]s family of composites. The s means the composite is symmetric. Therefore, each layer of the composite is made from 8 bonded plies in the 0°, ±45° and 90° directions. This means 25% of the plies are in the 0° direction, 50% of the plies in the ±45° directions, and 25% in the 90° direction. Using this arrangement lets the composite be modeled as a Quasi-Isotropic material. This means material direction doesn’t need to be taken into account when specifying material properties. A carpet plot is used to find material properties based on the % of 0°, and ±45° plies. The carpet plot used to find the Young’s Modulus (E) for the Graphite/Epoxy is shown in Figure 3 below. For 25% 0° plies, and 50% ±45° plies, E is found to be ~9.5 Msi, or 65.5 Gpa. Other properties are found in the same manner using similar carpet plots, see reference 3. Figure 3: Carpet plot used to find E for the Graphite/Epoxy composite. As can be seen from the figure, E is dependent on the # and % of directions of the plies. If the plies could be placed on the structure in the direction of the loading (which is currently possible in industry), then a higher stiffness could be attained. Because this wasn’t taken into account when designing the HAB, the values found in this structural report are conservative. A honeycomb material made by the Hexcel Corporation was chosen for the sandwich core material. The particular honeycomb material is HRH-327 vented Glass Reinforced Polyimide Honeycomb. HRH-327 was chosen because of it’s high tmax and because it is an insulator. An insulator needs to be used between the face sheets to keep the heat out of the s/c. A vented honeycomb needs to be used so that the core isn’t pressurized in space. Properties of the honeycomb are listed in table 3 below. The material properties listed were taken from reference 4 page 6. Note that E is in units of Mpa (E for the face sheets is ~66 Gpa). Also note how light the core material is compared to the face sheets. HRH-327 Tmax [°K] E [Mpa] [kg/m3] max [Mpa] 773.15 870 128 6.9 Table 3: Material properties of the core material. The flexural rigidity of the sandwich material is Etot=E1I1 + E2I2 (2) Where material 1 is the composite and 2 is the honeycomb, I1=8*t*d2 I2=1/12*h3 (3) (4) Where d is the distance between the face sheets, t is the thickness of the face sheets, and h is the thickness of the core. The width of the sandwich is taken to be unity in the above equations. This is not the case, but allows for comparison of equations 3 and 4. During my trade studies, I am going to use equation 2 to find the optimum thickness for the face sheets and the core to get the maximum Etot while keeping the weight to a minimum. Equations 1, 2, and 3 are taken from reference 1, p397-9. The only loads that will be modeled are the launch loads. An eigen-value buckling analysis will also be done on the s/c for the launch loads. Jon gave a gload at launch of ~4g’s. I input a gravity field of 4g’s in Ansys to simulate the launch loads, along with the supply masses on the floors and the internal pressure. The combination of these three aspects of loading gives a good representation of the loads incurred by the s/c during launch. If a metal had been used for the s/c, a Von Mises max stress criterion could be used. But, since composites are used this can’t be done. To make sure the composite doesn’t fail, each axial and shear stress must be checked to make sure it is not over the limit of the material. Figure 4 below is one example of this. In this figure the maximum stress in the z-dir (perpendicular to the axis of symmetry) is graphed. Figure 4: Max stress in the z direction. From the figure it can be seen that the max stress of 255 Mpa has not been exceeded. For this sample case, the stress in the z direction is the largest of the stresses. Therefore, the structure can withstand the g loading with a SF of about 1.6. The ability of Ansys to cut away a part of the s/c makes it possible to see the stresses in the floors as you can see in Figure 4. The launch loads are the greatest loads the s/c will encounter during its mission. If there was more time, I would’ve also modeled the pressure on the s/c during aero braking and the loads during the parachute deployment. But, since the s/c holds up so well to the launch loads, it will not fail during the other loading. An Eigen buckling analysis was also done on the s/c during launch. It was found from Ansys that the Eigen value is 81. This means that the applied loads during the launch are only 1 of the loading required to make the s/c buckle. 81 The value is so high because of the rigidity of the s/c from the thick walls of the sandwich structure. Eigen-value buckling was chosen because it takes much less computer time than doing a non-linear buckling analysis. When doing a non-linear buckling analysis, the shape history of the structure is found after the buckling has occurred to see if it is stable buckling. This is not necessary for a preliminary analysis of the s/c. Several analytical calculations were carried out to test the accuracy of the Ansys program. The hand calculations were: stress in the x direction (x) for the s/c, an eigen value buckling analysis of a simple beam, hoop stress (H) of the s/c, and the mass of the s/c. The buckling problem was taken from section 7.6 in the Ansys help files. The results of these hand calculations are listed in Table 4. x (from weight of s/c only) [MPa] Mass of s/c only [kg] H [MPa] By hand In Ansys 1.7 1.7 51,000 51,000 14.90074 15.3 w/ floors 14.9 w/o floors Eigen-value Buckling Numbers agreed to 99.999% Table 4: Comparison of analytical and Ansys calculations. A convergence test needs to be done during the trade studies to be sure the data Ansys gives is accurate. During a convergence test the mesh is refined. As the mesh is refined, stresses and the Eigen value should approach some number (a different number for each individual stress and buckling value). If this is not the case than the model must be meshed differently to make it more accurate. The buckling analysis is the most sensitive to mesh quality. Other people in the group depend on data from me: Damon needs the thickness and materials of the shell for his heating code, Randy needs the cg of the structure to combine with his cg of the supplies to give to Giles, and Tami needs the mass of the structure to enter into her trajectory code. For this sample case I told Tami the mass was 14,500kg. But, I found an error in my script file and the mass is actually 14,200kg. I depend on other people in the group for certain numbers. They are: Randy for the distribution of the supply masses in the s/c, and Jon for the launch loads. When a student does the structural analysis next time, more can be analyzed. It took a great amount of time learning the ropes with Ansys, so there was less time for analysis. Next time the following should be considered in the analysis: a vibration analysis (this is a must next time), a more accurate model of the s/c (having reinforced joints and adding a bulkhead are two examples), analyzing more of the loading conditions, and analyzing other parts of the s/c (like the landing gear). Using the manual that will be written from Shin and I’s experience with Ansys, the next student should have a much easier time modeling the vehicle. References: 1. Gere, and Timoshenko, Mechanics of Materials, Fouth Edition 1997. 2. http:www.structures.ucsd.edu/casl/data_analysis/carpet_plots.htm 3. I got the carpet plots from Professor Kim. He is trying to find out what book he got them out of, He said Prof Sun would know, but he is on sabbatical. 4. Hexcel Corporation, The basics on bonded sandwich construction TSB124, 1987.