Modelling and Analysis Laboratory Manual
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Modelling and Analysis Laboratory Manual

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Modelling and analysis laboratory manual prepared by Hareesha N G, Asst. Prof., Dept of Aerospace, DSCE, Bangalore, for BE Students under VTU

Modelling and analysis laboratory manual prepared by Hareesha N G, Asst. Prof., Dept of Aerospace, DSCE, Bangalore, for BE Students under VTU

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Modelling and Analysis Laboratory Manual Modelling and Analysis Laboratory Manual Document Transcript

  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 1
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 2 ,QWURGXFWLRQ WR WKH )LQLWH (OHPHQW 0HWKRG In thermo mechanical members and structures, finite-element analysis (FEA) is typically invoked to compute displacement and temperature fields from known applied loads and heat fluxes. FEA has emerged in recent years as an essential resource for mechanical and structural designers. Its use is often mandated by standards such as the ASME Pressure Vessel Code, by insurance requirements, and even by law. Its acceptance has benefited from rapid progress in related computer hardware and software, especially computer-aided design (CAD) systems. Today, a number of highly developed, user-friendly finite-element codes are available commercially. The purpose of this chapter is to introduce finite-element theory and practice. The next three chapters focus on linear elasticity and thermal response, both static and dynamic, of basic structural members. After that, nonlinear thermo mechanical response is considered. In FEA practice, a design file developed using CAD is often “imported” into finite element codes, from which point little or no additional effort is required to develop the finite-element model and perform sophisticated thermo mechanical analysis and simulation. CAD integrated with an analysis tool, such as FEA, is an example of computer-aided engineering (CAE). CAE is a powerful resource with the potential of identifying design problems much more efficiently and rapidly than by “trial and error.” A major FEM application is the determination of stresses and temperatures in a component or member in locations where failure is thought most likely. If the stresses or temperatures exceed allowable or safe values, the product can be redesigned and then reanalyzed. Analysis can be diagnostic, supporting interpretation of product-failure data. Analysis also can be used to assess performance, for example, by determining whether the design-stiffness coefficient for a rubber spring is attained. OVERVIEW OF THE FINITE-ELEMENT METHOD Consider a thermo elastic body with force and heat applied to its exterior boundary. The finite-element method serves to determine the displacement vector u(X,t) and the temperature T( X,t ) as functions of the un deformed position X and time t . The process of creating a finite-element model to support the design of a mechanical system can be viewed as having (at least) eight steps: 1. The body is first discretized, i.e., it is modeled as a mesh of finite elements connected at nodes. 2. Within each element, interpolation models are introduced to provide approximate expressions for the unknowns, typically u(X,t) and T(X,t), in terms of their nodal values, which now become the unknowns in the finite-element model. 3. The strain-displacement relation and its thermal analog are applied to the approximations for u and T to furnish approximations for the (Lagrangian) strain and the thermal gradient. 4. The stress-strain relation and its thermal analog (Fourier’s Law) are applied to obtain approximations to stress S and heat flux q in terms of the nodal values of u and T. 5. Equilibrium principles in variational form are applied using the various approximations within each element, leading to element equilibrium equations. 6. The element equilibrium equations are assembled to provide a global equilibrium equation
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 3 7. Prescribed kinematic and temperature conditions on the boundaries ( constraints ) are applied to the global equilibrium equations, thereby reducing the number of degrees of freedom and eliminating “rigid-body” modes. 8. The resulting global equilibrium equations are then solved using computer algorithms. The output is post processed. Initially, the output should be compared to data or benchmarks, or otherwise validated, to establish that the model correctly represents the underlying mechanical system. If not satisfied, the analyst can revise the finite-element model and repeat the computations. When the model is validated, post processing, with heavy reliance on graphics, then serves to interpret the results, for example, determining whether the underlying design is satisfactory. If problems with the design are identified, the analyst can then choose to revise the design. The revised design is modeled, and the process of validation and interpretation is repeated. MESH DEVELOPMENT Finite-element simulation has classically been viewed as having three stages: preprocessing, analysis, and post processing. The input file developed at the preprocessing stage consists of several elements: 1. control information (type of analysis, etc.) 2. material properties (e.g., elastic modulus) 3. mesh (element types, nodal coordinates, connectivities) 4. applied force and heat flux data 5. supports and constraints (e.g., prescribed displacements) 6. initial conditions (dynamic problems) In problems without severe stress concentrations, much of the mesh data can be developed conveniently using automatic-mesh generation. With the input file developed, the analysis processor is activated and “raw” output files are generated. The postprocessor module typically contains (interfaces to) graphical utilities, thus facilitating display of output in the form chosen by the analyst, for example, contours of the Von Mises stress. Two problems arise at this stage: Validation and interpretation. The analyst can use benchmark solutions, special cases, or experimental data to validate the analysis. With validation, the analyst gains confidence in, for example, the mesh. He or she still may face problems of interpretation, particularly if the output is voluminous. Fortunately, current graphical-display systems make interpretation easier and more reliable, such as by displaying high stress regions in vivid colors. Postprocessors often allow the analyst to “zoom in” on regions of high interest, for example, where rubber is highly confined. More recent methods based on virtual-reality technology enable the analyst to fly through and otherwise become immersed in the model. The goal of mesh design is to select the number and location of finite-element nodes and element types so that the associated analyses are sufficiently accurate. Several methods include automatic-mesh generation with adaptive capabilities, which serve to produce and iteratively refine the mesh based on a user-selected error tolerance. Even so, satisfactory meshes are not necessarily obtained, so that model editing by the analyst may be necessary. Several practical rules are as follows: 1. Nodes should be located where concentrated loads and heat fluxes are applied.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 4 2. Nodes should be located where displacements and temperatures are constrained or prescribed in a concentrated manner, for example, where “pins” prevent movement. 3. Nodes should be located where concentrated springs and masses and their thermal analogs are present. 4. Nodes should be located along lines and surface patches, over which pressures, shear stresses, compliant foundations, distributed heat fluxes, and surface convection are applied. 5. Nodes should be located at boundary points where the applied tractions and heat fluxes experience discontinuities. 6. Nodes should be located along lines of symmetry. 7. Nodes should be located along interfaces between different materials or components. 8. Element-aspect ratios (ratio of largest to smallest element dimensions) should be no greater than, for example, five. 9. Symmetric configurations should have symmetric meshes. 10. The density of elements should be greater in domains with higher gradients. 11. Interior angles in elements should not be excessively acute or obtuse, for example, less than 45°or greater than 135°. 12. Element-density variations should be gradual rather than abrupt. 13. Meshes should be uniform in subdomains with low gradients. 14. Element orientations should be staggered to prevent “bias.” In modeling a configuration, a good practice is initially to develop the mesh locally in domains expected to have high gradients, and thereafter to develop the mesh in the intervening low-gradient domains, thereby “reconciling” the high-gradient domains. There are two classes of errors in finite-element analysis: Modeling error ensues from inaccuracies in such input data as the material properties, boundary conditions, and initial values. In addition, there often are compromises in the mesh, for example, modeling sharp corners as rounded. Numerical error is primarily due to truncation and round-off. As a practical matter, error in a finite-element simulation is often assessed by comparing solutions from two meshes, the second of which is a refinement of the first. The sensitivity of finite-element computations to error is to some extent controllable. If the condition number of the stiffness matrix (the ratio of the maximum to the minimum eigen value) is modest, sensitivity is reduced. Typically, the condition number increases rapidly as the number of nodes in a system grows. In addition, highly irregular meshes tend to produce high-condition numbers. Models mixing soft components, for example, rubber, with stiff components, such as steel plates, are also likely to have high-condition numbers. Where possible, the model should be designed to reduce the condition number.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 5 Types of supports Degrees of Freedom to be Restricted Sl. No Type of support Tx Ty Tz Rx Ry Rz 1 Fixed ¥ ¥ ¥ ¥ ¥ ¥ 2 Roller x-y plane ¥ ¥ ¥ ¥ 3 Hinged Or pinned x-y plane ¥ ¥ ¥ ¥ ¥ 4 Simply support x-y plane ¥ ¥ ¥ ¥
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 6
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 7 TRUSS Determine the force in each member of the following truss. Indicate if the member is in tension or compression. The cross-sectional area of each member is 0.01 mand the Young’s modulus is 200x109 N/m2 . Step1: Start Algor – Start- Program files-Algor22- Fempro Step2: Select the "File: New" command. The "New" dialog will appear. Select the "FEA Model" icon and press the "New" button. Step3: Select Linear – Statics Stress With Linear Material model Step4: Select the New Button on the lower right corner
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 8 Step5: Create a new Analysis file truss1 and save-this will open us the Working environment Step6: Go for Plane 1 <XY-Top> , right click it and select Sketch. Now the Drawing Environment opens. Step7: Go for Geometry in the menu bar for the creation of line element.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 9 Step 8: uncheck the USE AS CONSTRUCTION box.. Step9: Start the line by pressing enter i.e start from 0,0. Then Y=2.8– Enter Then X=1.5 and Y=2.0- Enter Then X=0 , y=0 Step 10: Go for Plane 1 <XY-Top> , right click it and select Sketch again to come out of the Drawing Environment.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 10 Step 11: A New Part 1 Will be generated. In Part1 kindly select Element type and right click to define it . Select Truss from the list. Step 12: Select the Element Definition, right click for Modify Element Definition, A new dialog box opens give cross-sectional area as 0.01m2 . Step13: Select Material, right click to modify material and select AISI !005 Steel from the List to assign it to the truss
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 11 Step14: Defining boundary condition: Select the Vertices from Selection-Select from menu bar Move the cursor to near the A node and select it. The Node will highlight, then right click in the screen and select Nodal Boundary condition and select fixed.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 12 Select Node C and right click for applying Force . Select Y Direction and give -2800 as nodal force – ve sign for force acting downwards
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 13 Move the cursor to near the C node and select it. The Node will highlight, then right click in the screen and select Nodal Boundary condition and select all expect TY. Step15: Go for Analysis in the menu bar and select Parameters. Select all in the output tab. Step 15: Go for Analysis in the menu bar and select Perform Analysis.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 14 Step16: After analysis completes, Go for Results Element Force And moments –Axial Forces. The Model will show the results. Select Nodes from selection-select menu bar Select all nodes and right click to add probe to selection: FORCE ACTING ON AB=1700 AC=2000 BC=-2500(Compression) Step17: After analysis completes, Go for Reaction Vector –Reaction Forces-Y. The Model will show the results.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 15 Reaction Force FY: 2800 Repeat for X Direction FX: 1500 -1500 Step 18: Select Automatic result generation to complete the tutorial
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 16 Exercises on Truss 1) Determine the reaction force, displacement and elemental stress for the truss shown below. Given: Material : Mild steel E = 209X103 N/mm2 A= 100mm2 2) Determine the reaction force displacement and elemental stress for the truss shown below. Given: Material : Mild steel E = 209X103 N/mm2 Section A –A : 10X10 Sq 3) Determine the reaction force displacement and elemental stress for the truss shown below Given: E = 209X103 N/mm2 A = 0.01m2 100
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 17 BARS Determine the Displacement in the direction of force applied for a bar of constant cross Section area. Step1: Start Algor – Start- Program files-Algor22- Fempro Step2: Select the "File: New" command. The "New" dialog will appear. Select the "FEA Model" icon and press the "New" button. Step3: Select Linear – Statics Stress With Linear Material model Step4: Select the New Button on the lower right corner
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 18 Step5: Create a new Analysis file Bar 1 and save-this will open us the Working environment. Step6: To create the bar we need to draw line in YZ plane, to go to drawing environment right Click the YZ plane and select sketch. Step 7: To create Line go for geometry – add line Step 8: Remove the construction only and press enter to start line and enter the value 1m in Y direction to complete the Line. Step 9: To come out of the drawing double Click the YZ plane. Step 10: Assign Beam Element for the Line by right Clicking the Element type. Step 11: To assign the Cross section, right click the Element definition, select the colum value –the Cross-Section Libraries iron will appear. Press this icon to get the library. Select round from the List and assign value 0.1m. Click ok to accept.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 19 Step12: Select Material, right click to modify material and select AISI 1005 Steel from the List to assign it to the truss Step13: Defining boundary condition: Select the Vertices from Selection-Select from menu bar
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 20 Click on the left side end vertices and right Click to add the constraints. Select Fixed. Click on the Right side end vertices and Right click to add force Assign the value 1000N.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 21 With this step we conclude the boundary condition assigning. Step14: Go for Analysis in the menu bar and select Parameters. Select all in the output tab. Step 15: Go for Analysis in the menu bar and select Perform Analysis.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 22 Step 16: Now the result window opens. Select the Results- displacement -magnitude to know the displacement Select Automatic result generation to complete the tutorial
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 23 Exercises on Bars Case 1: Bars with uniform cross section 1) A circular rod of dia 20 mm and 500 mm long is subjected to a tensile force of 45 KN. The modulus of elasticity for steel may be taken as 200 KN/mm2 . Find stress, strain and elongation of the bar due to applied load. ( Ans: A=314.159 mm2 , stress = 143.24 mm2 , strain = 0.0007162 , Elongation = 0.358 mm) 2) A bar of 800 mm length is attached rigidly at A and B as shown in figure. Force of 30KN and 60 KN act as shown on the bar. If E= 200GPa, determine the reactions at the two ends. If the bar dia is 25 mm, Find the stresses and change in length of each portion. A C D B 275 150 375 (Ans: RA = 8.4375KN, RB = 21.5625KN) Case 2: Bars with cross section varying in steps 3) For the bar shown below, determine total extension, Max and Min stress developed in the bar, Max and Min strain in the bar and reaction force. E= 198714.72 N/mm2 P P 160 240 160 (Ans: Deformation = 0.285 mm) 4) The composite bar shown in fig is subjected to a tensile force of 30kN. Young’s modulus of brass and steel are 99777.6N/mm2 and 2x 105 N/mm2 respectively. Find the extension of the bar. (Ans: 0.186mm) P = 30KN 400 300 D1=25mm D2 = 20mm D3 = 25mm 60KN 30KN D1=30mm, Steel D2= 20mm, Brass
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 24 Case 3: Compound bars 5) A compound bar of length 500 mm consists of a strip of Aluminum 50 mm wide X 20 mm thick and a strip of steel 50 mm wide X 15 mm thick rigidly joined at ends. If the bar is subjected to a load of 50KN, find the stress developed in each materials and extension of the bar. Take EAl = 1x105 N/mm2 and ESteel = 2x105 N/mm2 ( Ans: Deformation = 0.1 mm) 50KN 500mm 6) A compound bar consist of a circular rod of steel of dia 20 mm rigidly fitted into a copper tube of internal dia 20 mm and thickness 5 mm. If the bar is subjected to a load of 100 KN, find the stresses developed in two materials. Take Esteel 2X105 N/mm2 and Ecopper = 1.2 X105 N/mm2 . Length of both the bars is 100 mm. Case 4: Bars with taper cross section 7) A 1.5 meter long steel bar is having uniform dia of 40 mm for a length of 1 m and in the next 0.5 m its dia gradually reduces from 40 mm to 20 mm. Determine the elongation of this bar when subjected to an axial tensile load of 160 KN. Given: E = 200GPa. 8) Find the extension of the bar shown in figure under an axial load of 20KN. Take E= 2GPa. (Ans: extension=0.444mm) Aluminum Steel
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 25 Beams 1) Determine the maximum bending stress and strain developed in the beam and Maximum deflection of the beam due to applied load. Also plot SFD and BMD for the cantilever beam shown below. Material used is Steel AISI 4130. Step1: Start Algor – Start- Program files-Algor23- Fempro Step2: Select the "File: New" command. The "New" dialog will appear. Select the "FEA Model" icon and press the "New" button. Step3: Select Linear – Statics Stress With Linear Material model Step4: Select the New Button on the lower right corner Step5: Create a new Analysis file : Cantilever BEAM and save-this will open us the Working environment.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 26 Step6: To create the bar we need to draw line in XY plane, to go to drawing environment right Click the XY plane and select sketch. Step 7: To create Line go for geometry – add line Step 8: Remove the construction only and press enter to start line and enter the value 1m in X direction to complete the Line, then enter 2 m in X direction , again enter 3.5 m in X direction, press ESC twice to exit from sketch. Or Step 9: To come out of the drawing double Click the XY plane. Step 10: Assign Beam Element for the Line by right Clicking the Element type. Step 11: To assign the Cross section, right click the Element definition, and select the column value –the Cross-Section Libraries icon will appear. Press this icon to get the library. Select Rectangular section and enter the values as below. b=.01m h=.008m
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 27 Press Ok. Again OK. Step12: Select Material, right click to modify material and select AISI 4130 Steel from the List to assign it to the beam. Step13: Defining boundary condition: Select the Vertices from Selection-Select from menu bar Click on the left side end vertices and right Click to add the constraints. Select Fixed.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 28 Click on the 2nd and 3rd vertices and Right click to add force. Assign the value -20KN in Y direction. Similarly select 4th vertices assign -10KN load in Y direction. With this step we conclude the boundary condition assigning. Step14: Go for Analysis in the menu bar and select Parameters. Select all in the output tab. Step 15: Go for Analysis in the menu bar and select Perform Analysis. Step 16: Now the result window opens. Select the Results- displacement -magnitude to know the displacement
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 29 ANSWERS Displacement: 0.326395m Bending stress in local 3 direction=-2.3841E-6N/m2
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 30 Max strain about axis 3= -6.938E-18m/m Min Value” -0.00430442m/m Reaction forces: RA=50000N Procedure To Draw SFD and BMD: i) For SFD 1) Keep the displacement plot in the results area. 2) Results options> Deselect Show displaced model 3) Right click >select vector plot. 4) With Rectangular select on select elements- select complete line.( Selection>shape> rectangle and selection> select> Elements)
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 31 5) With elements selected go to Inquire >Add shear diagram( axis 2) to get SFD. 6) To get the magnitude of Shear force at required points….. Results>Element forces and Moments>Local 2 force 7) With rectangular selection ON and Vertices selection ON, Select all vertices >right click> Add probes to selection. 8) View >display >features. 9) Inquire > clear beam diagram For BMD 1) Keep the displacement plot in the results area. 2) Results options> Deselect Show displaced model 3) Right click >select vector plot. 4) With Rectangular select ON, select elements- select complete line- (Selection>shape> rectangle and selection> select> Elements) 5) With elements selected go to Inquire >Add Moment diagram (axis 3) to get BMD. 6) To get the magnitude of bending moment at required points….. Results>Element forces and Moments>Local 3 moment 7) With rectangular selection ON and Vertices selection ON, Select all vertices >right click> Add probes to selection. 8) View >display >features. 9) Inquire > clear beam diagram
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 32 2) Determine the maximum stress and strain developed in the beam and Maximum deflection of the beam due to applied load. Also plot SFD and BMD for the beam shown below. Material used is Steel AISI 4130. 3) Determine the maximum stress and strain developed in the beam and Maximum deflection of the beam due to applied load. Also plot SFD and BMD for the beam shown below. Material used is Steel AISI 4130. 4) Determine the maximum stress and strain developed in the beam and Maximum deflection of the beam due to applied load. Also plot SFD and BMD for the beam shown below. Material used is Steel AISI 4130. 5) Plot SFD and BMD for the beam shown below. 6) Plot SFD and BMD for the beam shown below.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 33
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 34
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 35 1) Stress Analysis of a Rectangular Plate with a Circular Hole Determine the maximum stress for a rectangular plate of 50mm x 80mm with hole of 10mm diameter in the center is loaded in axial tension. Thickness of the plate is 10mm. Take E = 200GPa Theoretical calculation: Results Comparison FEM Theoretical Deformation 0.009284 mm - Stress 59.99 N/ mm2 62.5 N / mm2 Procedure: Steps to create geometry: 1) Select XY plane > Sketch 2) Select>Create rectangle> Press enter to define one corner of the rectangle( 0, 0,0) 3) Type X and Y coordinate of opposite corner of the rectangle ( 80, 50,0) 4) To crate hole: Select>circle by center and radius> Type center point of the circle (40, 25, 0)> press Enter. To define radius: check use relative> Enter DX= 5 mm( Radius of circle) 5) Exit from the sketch. Steps to solve the problem: 1) To generate 2-D mesh: Right click >1< XY top> > Create 2D mesh> Enter 500 in the mesh density tab > Apply,
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 36 2) Define Element type (Plate), Element definition >Check design variable> Enter thickness (10 mm) and Material type (200GPa). 3) To Apply BC and Load: select all nodes in left side > Apply fixed BC > Select all nodes in right side> Apply Nodal force as shown below. (1000N/ No of nodes)> OK. 4) Perform Analysis. 5) Find out displacement, Maximum stress etc…
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 37 Exercises: Determine the maximum stress for a rectangular plate of 50mm x 80mm with hole of 10mm diameter in the center is loaded in axial tension. Thickness of the plate is 10mm. Take E = 210GPa. Take Axial Load P = 100KN. Validate your results with theoretical results. PP
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 38 2) Thermal Analysis -2D problem with conduction and convection boundary conditions Determine Temperature Distribution in a Plate. Material Alumina, 99.9%, AL203. Assume thickness of the plate 10mm. Plot temperature distribution curve. Solution: Step1: Start Algor – Start- Program files-Algor23.1- Fempro Step2: Select the "File: New" command. The "New" dialog will appear. Select the "FEA Model" icon and press the "New" button. Step3: Select –Thermal- Steady State Heat Transfer Step4: Select the New Button on the lower right corner Step5: Create a new Analysis file THERMAL 1 and save-this will open us the Working environment Step6: Go for Plane 1 <YZ-Right>, right click it and select Sketch. Now the Drawing Environment opens. Step7: Go for Geometry in the menu bar for the creation of rectangle element. Uncheck the USE AS CONSTRUCTION BOX. Create a rectangle by pressing enter for the starting corner and enter the values Z=20 and Y=10 and press enter to complete the rectangle. Step8: Double click the YZ plane to come out of the drawing environment. Step9: Right Click the element type and Select Plate. Step 10: Right Click Element definition and assign 0.1m for the thickness of the plate. Step11: Right Click Material and assign Alumina material from the material List. Step 12: Right Click the YZ plane and select create 2D Mesh option and create Mesh; you can modify the mesh also.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 39 Step 13: Select ---Selection-Shape-Rectangle. Step 14: Select ---Selection-Select -Vertices Step 15: Window the left side edge nodes and right Click to add Nodal Applied temperature. Give value 100. Repeat the procedure for all other sides. Steps 16: Select –Analysis- perform Analysis Step 17 : Your window will change to Result window to show the results Step 18: Select Automatic result generation to complete the tutorial
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 40 Exercises: 1) A furnace wall is made of inside silica brick (k = 1.5 W/mK) and outside magnesia brick (k = 4.9 W/mK), each 10 cm thick. The inner and outer surfaces are exposed to fluids at temperatures of 820°C and 110°C respectively. The contact resistance is 0.001 m2 K/W. The heat transfer coefficient for inner and outside surfaces is equal to 35 W/m2 K. Find the heat flow through the wall per unit area per unit time and temperature distribution across the wall. Theoretical calculation: 2) A rod of 6 cm dia with k= 98 W/mK and 125 cm long is attached to an evaporation chamber maintained at -15°C. The film coefficient of heat transfer is 40 W/m2 K and the ambient temp is 28°C. Compute and plot the temperature distribution along the length of the fin and Find the length up to which there will be ice formation.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 41 Dynamic analysis 1) Modal Analysis of Cantilever beam Determine the natural frequency and different modes of vibration (Simple Modal Analysis) of a cantilever beam as shown below. Given: E=2e11 N/m2 , I = 8.33e-06 m4 Area A = 0.01 m2 , Density = 7830 Kg/m3 Manual calculation: Mode FEM (Frequency) Theory (Frequency) 1 81.1569 81.70 2 491.593 510.63 3 1263.48 1432.10 For hand calculation: Step1: Start Algor – Start- Program files-Algor23- Fempro Step2: Select the "File: New" command. The "New" dialog will appear. Select the "FEA Model" icon and press the "New" button. Step3: Select Linear –Natural frequency (Modal) Step4: Select the New Button on the lower right corner Step5: Create a new Analysis file : Cantilever BEAM and save-this will open us the Working environment. Step6: To create the bar we need to draw line in XY plane, to go to drawing environment right Click the XY plane and select sketch. Step 7: To create Line go for geometry – add line Step 8: Remove the construction only and press enter to start line and enter the value 1m in X direction to complete the Line, press ESC twice to exit from sketch. Or Step 9: To come out of the drawing double Click the XY plane. Step 10: Assign Beam Element for the Line by right Clicking the Element type. Step 11: To assign the Cross section, right click the Element definition, and select the column value –the Cross-Section Libraries icon will appear. Select Rectangular section and enter the values as below. b=0.1m h=0.1m Press Ok. Again OK. Step12: Select Material, right click to modify material, create custom material with following properties.
  • Computer Aided Modeling and Analysis Laboratory Department Of Mechanical Engineering, Don Bosco Institute of Technology 42 E=2e11 N/m2 Density = 7830 Kg/m3 Step13: Defining boundary condition: Select the Vertices from Selection-Select from menu bar Click on the left side end vertices and right Click to add the constraints. Select Fixed. Step 15: Go for Analysis in the menu bar and select Perform Analysis. Step 16: Now the result window opens. To get the modes of vibration click the icon as below. To animate the results: use the icons as shown below. Results: Mode FEM (Frequency) 1(2) 81.1569 3(4) 491.593 5 1263.48 Exercises: Determine the natural frequency and different modes of vibration (Simple Modal Analysis) of truss shown below. Given: E=2e11 N/m2 , Area A = 0.01 m2 , Density = 7830 Kg/m3 Results: Mode Frequency 1 57.1109 2 107.986 3 141.601 4 196.702 5 231.16