Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ Chapter Exercises Many of the exercises in this text are mini projects that allow students to integrate concepts You will see that the exercises have several subparts This is different from exercises in other texts that have a single correct answer These mini projects focus on investigation and integration Consequently, they are time consuming both for the students to complete and for the instructor to grade, as they require students to think and analyze instead of simply putting numbers into an equation As such, it is suggested not to assign all of the exercises at the end of a chapter in one week 1.1 Locate a peer-reviewed journal article about an application of Finite Element Analysis (structural, mechanical, fluid, heat analyses, etc.) and summarize it Include a complete reference to the article using a proper format and punctuation Use correct technical writing style and format I use this exercise to reinforce and connect to instruction in previous courses at CSM In a first and second year course sequence called EPICS (Engineering Practices Introductory Course Sequence), students learn how to gather information and research literature They also learn technical writing skills that include proper format for referencing literature The following is one example of a paper and one way of formatting the answer Your institution may have different formatting preferences Romeo G, G Frulla, and E Cestino, 2007, Design of a high-altitude long-endurance solarpowered unmanned air vehicle for multi-payload and operations, Proc IMechE Vol 221 Part G: J Aerospace Engineering, p 199-217 1.2 State your career goals and describe how the application in Exercise 1.1 relates to them I like to encourage students to think about their future I find that many of them not have a very clear idea of their career goals Consequently, I accept a wide range of answers as correct 1.3 Analyze the model shown in Figure A Use MMGS dimensions and SI units The purpose of this exercise is to give students practice with the FEA process Another objective is to get students to review the prerequisite course in mechanics of materials This is a mini-project exercise with several parts You will notice that the mechanics of materials calculations, done in a Mathcad worksheet, are equivalent to several traditional single answer problems in other texts In addition to one equation, the worksheets contain several concepts â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ and the relations between them, but an even greater integration occurs when the equation is integrated with 3D solid model FEA That level of integration leads to more complex situations that approach real-world application and a much higher level of thinking a Create a 3D solid model The solid model should look just like the figure: A B C Students should follow the directions in Appendix A to sketch the outer perimeter on the Front Plane with connected horizontal and vertical lines Appendix A sketched the end of the I beam, but students should sketch the side of this bar, not the end Their sketch should be fully defined Then, they should add the fillets to prevent stress intensities The sketch should be similar to the one below: Next, they should extrude the thickness of the bar to create the 3D object Then, create the three planes (at 60, 130, and 200 mm from the left end) and the split lines Use SW Help to learn how to create the planes and split lines Create a plane using “Insert>Reference Geometry>Plane” to open the “Plane” property manager For this model, choose a plane parallel to the end surface from the “Flyout Menu,” for the “First Reference” box, and then enter the offset distance Select “Insert>Curve>Split Line” from the menu bar to open the “Split Line” property manager to create the split lines at the three planes â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ b Create an FEA model for the CAD model from part a Use ASTM A36 steel material, a fixed geometry restraint on the left-end face, a 5000 N load applied uniformly over the right-end face in the –y direction, and the default mesh Create von Mises (vM) stress and Xdisplacement plots Your results might differ, depending on the computer and software version used c Use the probe tool to generate three graphs of the X-direction stresses along the split lines in the CAD model Split lines 1, 2, and are shown below along with the probe configuration © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ Split Line Split Line Split Line â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ Split lines and have negligible variations of approximately 0.03 MPA and 0.01 MPa respectively, but split line has a 55 MPA variation due to its proximity to the geometric discontinuity d Explain why the X-direction stresses along the split lines and appear to vary rapidly when they should be essentially constant according to mechanics of materials fundamentals The variations are enhanced by the automatic scaling of the SWS probe plots e Calculate the x-normal stress using mechanics of materials fundamentals in segment AB at the x section 60 mm from the left end (split line 1) and in segment BC at the x section 200 mm from the left end (split line 3) Identify all stresses as compressive (negative) or tensile (positive) Compute the percent difference with the FEA results Define the percent difference as = ∗ |ሺ࣌ࡹࡹ − ࣌ࡿࢃࡿ ሻ/࣌ࡿࢃࡿ | , where MoM = mechanics of materials and SWS = SOLIDWORKS Simulation © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ The average values of the x normal stresses from the probe plots are: Considering rounding and resolution, the percent differences are essentially zero f Use mechanics of materials fundamentals to calculate the deformation δAC in the X direction and compute the percent difference with the FEA results FEA results from 1.b â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ g Determine the stress concentration factor for the model from a mechanics of materials reference, and use it to calculate the maximum normal stress at the transition from width of 30 mm to width of 15 mm (at the fillets) Compute the percent difference between the maximum x-normal stress and the FEA results The factor is about 1.8 Using it, the stress concentration would be 1.8 * the average x normal stress = 1.8 * 83.333 MPa = 150 MPa The max stress from the x normal FEA plot in SWS is 174 MPa The percent difference is 100 * 24/174 = 13.8 % h Calculate the x-deformation using mechanics of materials (MOM) in segment AB at the x section 60 mm from the left end (split line 1) and in segment BC at the x section 200 mm from the left end (split line 3) Compute the percent difference with the FEA results If the FEA results are rounded to 0.017 to match the resolution of the MOM calculations, there is no difference â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ difference = 100 * 0.001/0.076 = 1.3% 1.4 Investigate the effect of adding a 10-mm diameter circular hole, centered at 60 mm from the left-hand end and half way across the width to the bar from Exercise 1.3, as shown in the figure a Create the 3D solids model Save the model from Exercise 1.3 with a new name Create the model by opening a new sketch on the Front Plane Sketch a 5-mm radius circle at the location noted above Then use the Features menu to create an Extruded Cut through the thickness (Through All) of the model © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ b Perform a static FEA on the modified bar with the same configuration as part a for the bar without a hole Probe and plot the X-normal stress across the bar and through the hole along one side of split line (The hole divides the split line.) Before running, right click on the study and choose Update All Components Then run Since the hole breaks the split line, the probe points as shown below Node 15412 was probed by mistake Delete errors by right clicking and choosing Delete â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ After deleting node 15412, the following plot can be displayed: 10 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ c Calculate the maximum stress using mechanics of materials fundamentals and a stress concentration factor Determine the percent difference with the maximum x-normal stresses from the FEA results The stress concentration factor is about 2.4 Using MOM, the maximum x-normal stress is: 2.4 * 55.556 MPA = 133.33 MPa Difference = 100 * (189.9 – 133.33)/189.9 = 29.8% d Explain the effect of the hole on the change in the maximum x-normal stress from the analysis of the bar model without a hole The hole reduces the cross section area, and the stress distribution changes Note that the minimum stress in 1.4.b is negative 1.5 Analyze an extruded aluminum strut shown in the figure This was chosen because students often use these materials in their senior design project prototypes and graduate students use them in research project fixtures Parts of this exercise will be used in Chapter 11 © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ 12 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ a Create the 3D solid model by downloading the profile twelve, 120 mm X 60 mm crosssection profile from Item America You can this step for the students and give them the file, but it is important for them to learn how to access information from corporate websites They will have to it frequently in their professional engineering careers They can figure it out on their own, or you can lead them through it Make sure they have good security software Extrude the cross section so L = 1200 mm The origin is at the center of the cross-section sketch Do not use a weldment profile, as that will automatically create beam elements instead of 3D tetrahedral elements Points A and B are at the left end, and points A’ and B’ are at the right end Points C, D, E, F, and G are at 120 mm from the left end Coordinates of points: A = (0.0, 60.0, -8.0) mm, A’ = (1200.0, 60.0, -8.0) mm B = (0.0, 38.0, 30.0) mm, B’ = (1200.0, 38.0, 30.0) mm C = (120.0, 60.0, -8.0) mm, D = (120.0, 30.0, -8.0) mm, E = (120.0, 0.0, -26.5) mm, F = (120.0, -30.0, -8.0) mm, G = (120.0, -60.0, -8.0) mm 13 © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ b Create a static study of the strut model Use 6063-T6 aluminum alloy material Apply a 1000-N external load in the negative y direction uniformly distributed on the right-end face Apply a fixed geometry restraint to the left-end face (the face at the origin) Run the study with the default mesh configuration Create a contour plot of UY in mm Probe it along A – A’ on the upper-back corner of the strut Choose “on selected entities” in the probe window and choose the edge closest to A- A’ for the entity Then choose update Create a probe plot of UY in mm You may have to check the Flip Edge Plot box to place the LHE displacement at x = mm on the left side of the plot c To investigate the FEA model configuration and to better understand the deformation probe plot shape and amplitude, use mechanics of materials fundamentals to create a graph of Uy(x) from A – A’ Use Mechanics of Materials (MoM) fundamentals to create a graph in a Mathcad worksheet of Uy(x) from A to A’ Use the section properties in SW to check the values for area and moment of inertia of the area, I Select the end face of the part Choose Section Properties in the Tools drop down menu 14 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ d Investigate further by comparing the FEA results for Uy @ x = mm and Uy @ x = 1200 mm with the mechanics of materials fundamentals results i Explain any significant difference The difference is not significant ii Is the probe plot of Uy linear? Explain No The equation for y (x) is cubic 15 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ iii Does the probe plot of Uy vary with x (distance from the left end)? Explain Yes The equation for δy depends on x e Investigate the St Venant’s effects Create a contour plot of the x-normal FEA stress results Probe it along A – A’ on the upper-back corner of the strut Notice St Venant’s effect on stress at the left end fixture At what value of x does the St Venant’s effect first become negligible? Choose “on selected entities” in the probe window and choose the edge closest to A- A’ for the entity Then choose update Create a probe plot You might have to check the Flip Edge Plot box to place the LHE stress on the left side of the plot Notice St Venant's effect on stress at the LHE fixture The effect becomes negligible at 60 mm from the fixture f Investigate the stresses outside of the region affected by the St Venant’s principle Using the x-normal stress results plot from FEA, create a section clipping plot 120 mm from the left end to avoid St Venant’s effect at the fixture Probe at points C, D, E, F, and G Coordinates of C = (120.0, 60.0, -8.0) mm, D = (120.0, 30.0, -8.0) mm, E = (120.0, 0.0, -26.5) mm, F = (120.0, -30.0, -8.0) mm, and G = (120.0,2 -60.0, -8.0) mm Plot on the section only Use the right view Consider using “save as sensor” to facilitate probing in later questions Don’t show the deformed shape 16 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ g Further investigate the configuration and the x-normal stress section clipping-plot probe values, use mechanics of materials fundamentals to calculate the normal stress values at points A’, D, and F Compare the values with the FEA results from part f Explain any significant differences 17 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ h Investigate shear stresses Create a τxy shear-stress contour plot from the FEA results Create a section clipping plot 120 mm from the left end to avoid St Venant’s effect from the fixture Probe at points A’, D, and F Don’t show the deformed shape Hide the fixture and the load symbols i Further investigate shear stresses Use mechanics of materials fundamentals to calculate the shear stress values Compare the values with the FEA results from part h Explain any significant differences j Investigate the effect of changing the applied load to 1000 N in the positive z direction uniformly distributed on the right-end face Maintain the remaining configuration items, like the fixed geometry restraint on the left-end face and the default mesh Create a contour plot of Uz(x) in mm Probe it along B – B’ on the upper-back corner of the strut and create a probe plot of Uz Coordinates of B = (0.0, 38.0, 30.0) mm and B’ = (1200.0, 38.0, 30.0) mm 18 â 2019 Cengage Learningđ All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ k Investigate the deformation probe plot shape and amplitude by using mechanics of materials fundamentals to create a graph of Uz(x) Compare with the FEA results probe plot and explain any differences Compare the values of Uz @ x = mm z and Uz @ x = 1200 mm with the FEA results and explain any differences l Investigate the probe plot of Uz Compare its linearity with what you expect from mechanics fundamentals The equation for the deflection is cubic m Investigate the deformation in the z direction of the Z-load model Is it significantly different from the deformation in y direction of the Y-load model? Explain Yes Deflection is inversely proportional to the area moment of inertia, which is different with respect to the y- and z-axis 19 © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/ Solution Manual for Finite Element Analysis 1st Edition by King Full file at https://TestbankDirect.eu/ 1.6 Investigate the effect of adding a hole in the strut Extrude a 10-mm diameter hole completely through the strut 120 mm from the left end in the 3D solids model as shown in the figure a Create an FEA study with the same loads and fixture as the Y-load model Execute the study and create an x-normal contour plot b How did the location of the maximum x-normal stress change after adding the hole? The maximum stress is located around the newly added hole instead of at the restraint c What effect does adding a slot have on the magnitude of the load that can be applied safely to the strut? It decreased the maximum load The max stress increased from 18.1 to 44.9 MPa d What happens to the magnitude of the load that can be applied safely if the hole is located at the center of the strut? (Specifically, if the 10-mm vertical dimension is increased to 25 mm.) Explain The magnitude of the load that can be applied will increase if the slot is located on the neutral axis because stress is proportional to the distance from the neutral axis 20 © 2019 Cengage Learning® All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part Full file at https://TestbankDirect.eu/