Linear Static Analysis of a Spring Element (CELAS)

Transcription

1 Linear Static Analysis of a Spring Element (CELAS) Objectives: Modify nodal analysis and nodal definition coordinate systems to reference a local coordinate system. Define bar elements connected with a spring element. (CBAR and CELAS1) Submit the model to MSC.Nastran. a rigid body constraint to account for the extra DOF on a bar element. (SPC) Re-submit the model to MSC.Nastran. Compare results with a hand calculation. MSC.Nastran 120 Exercise Workbook 20-1 Model Description: The Figure in the title page shows a cantilever beam with a spring connection in between two elements. The spring is highlighted for clarification. The left end is fixed into the wall, and a tensile load of 100 lbf is applied to the right end of the model. Figure 20.1 shows two user defined coordinate systems. Nodes on the left half of the beam will reference Coordinate System 11 for displacements and location. Nodes on the right half will reference Coordinate System 13. Figure Coordinate Frames Figure Grid Coordinates and Element Connectivities 20-2 MSC.Nastran 120 Exercise Workbook MSC.Nastran 120 Exercise Workbook 20-3

2 Figure Loads and Boundary Conditions Table Material Properties Elastic Modulus = 10E6 lb/in 2 Poisson s Ratio = 0.3 A spring element is attached at the midpoint of the assembly. Properties for the spring, and bar elements are shown in Table 20.1 and Table The material properties for the model are shown in Table Because the spring attaches the beams in the Global X direction, the model is properly connected for a hand calculation. However, for MSC.Nastran, all DOF of the model have to be constrained against rigid body motions. When the model is first submitted for analysis, a fatal error message will be returned. Because the right half of the bar elements also have DOF in the UY, UX, RX, RY, and RZ, an additional constraint needs to be applied. After adding the constraints and re-running the job, compare the deflection results with the hand calculation. Table Spring Properties Spring Constant = 100 lb/in Table Element Properties A 1 in 2 I in 4 I in 4 Torsional Constant MSC.Nastran 120 Exercise Workbook MSC.Nastran 120 Exercise Workbook 20-5 Suggested Exercise Steps: Open a new database. Define the coordinate systems. Create Curves to define bar elements. Mesh the Curves and define the nodal coordinate systems for each half of the model. Define the spring element. Define material properties. Define spring and bar properties. the first constraint and load on the model. Submit the model to MSC.Nastran. Review the model for fatal messages. a constraint to account for rigid body motions. Re-submit the model to MSC.Nastran. Compare the results with a hand calculation. Exercise Procedure: 1. Create a new database called workshop20.db. File/New Database New Database Name In the New Model Preferences form set the following: Tolerance Analysis code: 2. Activate the entity labels by selecting the Show Labels button on the toolbar. 3. Also, activate the Node Size button. 4. Create coordinate frames. Show Labels Node Size workshop20 Default MSC/NASTRAN Geometry Action: Create Object: Coord Method: 3 Point Coord ID List: 11 Origin: [0, 0, 0] Point on Axis 3: [0, 1, 0] Point on Plane 1-3: [0, 0, 1] Coord ID List: MSC.Nastran 120 Exercise Workbook MSC.Nastran 120 Exercise Workbook 20-7

3 Origin: [21, 0, 0] Point on Axis 3: [22, 0, 0] Point on Plane 1-3: [21, 0, -1] 5. Create parent geometry. Geometry Object: Curve Method: XYZ Refer. Coordinate List: Coord 11 Vector Coordinates List: <0, 20, 0> Origin Coordinates List: [0, 0, 0] Refer. Coordinate List: Coord 13 Vector Coordinates List: <0, 0, 20> Origin Coordinates List: [0, 0, 0] 6. Create the nodes (GRID) and connectivities (CBAR) by meshing the curves previously created. Finite Elements Object: Mesh Type: Curve Global Edge Length: 10 Element Topology: Bar2 Node Coordinate Frames... Analysis Coordinate Frame: Coord MSC.Nastran 120 Exercise Workbook Refer. Coordinate Frame: Coord 11 Curve List: Curve 1 Node Coordinate Frames... Analysis Coordinate Frame: Coord 13 Refer. Coordinate Frame: Coord 13 Curve List: Curve 2 7. Create the spring. Finite Elements Object: Element Method: Edit Shape: Bar Node 1 = Node 3 Node 2 = Node 4 7a. Define spring properties. Properties Object: 1D Type: Spring Property Set Name: spring Input Properties... Spring Constant 100 MSC.Nastran 120 Exercise Workbook 20-9 DOF at Node 1 DOF at Node 2 (hint: To select the element on the screen, use the Beam element option from the entity selection menu.) Beam element 8. Clean up the display. Refresh the display using the brush icon on the Top Menu Bar. The display should resemble Figure Figure Nodal and Element Locations MSC.Nastran 120 Exercise Workbook UY UZ Select Members Elm 5 Display/Plot/Erase... Geometry Erase Refresh Graphics 9. Define a material using the specified modulus of elasticity and Poisson s ratio. Materials Object: Isotropic Method: Manual Input Material Name: alum Input Properties... Constitutive Model: Linear Elastic Elastic Modulus = 10e6 Poisson Ratio = Define element properties for the analysis model. Properties Dimension: 1 D Type: Beam Property Set Name: beam Option(s): General Section Input Properties... Material Name m:alum Bar Orientation < 0, 1, 0 > Area 1 [Inertia 1,1] 10 [Inertia 2,2] 10 [Torsional Constant] 0.1 MSC.Nastran 120 Exercise Workbook 20-11

4 Select Members: Elm 1:4 Figure Boundary Condition. 11. Shrink the elements by 15% for clarity; this allows us to easily assess the element connectivities. Use the Display/Finite Elements... option. Display/Finite Elements... FEM Shrink: Create the displacement constraints and apply them to the analysis model. Loads/BCs Object: Displacement Type: Nodal New Set Name: fixed Input Data... Translations < T1 T2 T3 > <0, 0, 0> Rotations < R1 R2 R3 > <0, 0, 0> Analysis Coordinate Frame: Coord 11 Select Application Region... Geometry Filter: FEM Select Nodes: Node 1 The display should resemble Figure MSC.Nastran 120 Exercise Workbook 13. Create the load. Loads/BCs Object: Force Method: Nodal New Set Name: load Input Data... Force < F1 F2 F3 > <100, 0, 0> Moment < M1 M2 M3 > < > Select Application Region... Geometry Filter: FEM Select Nodes: Node 6 To view both the coordinate frames and the load easier, change the view to Isoview_1 by selecting the following icon: Iso 1 View MSC.Nastran 120 Exercise Workbook Figure Load. 14. Generate an input file for analysis. Analysis Action: Analyze Object: Entire Model Method: Analysis Deck Job Name: workshop20 A MSC.Nastran input file called workshop20.bdf will be generated. This process of translating your model into an input file is called the Forward Translation. The Forward Translation is complete when the Heartbeat turns green MSC.Nastran 120 Exercise Workbook SUBMITTING THE INPUT FILE FOR MSC.Nastran and MSC.Patran USERS: 15. Submit the input file to MSC.Nastran for analysis. 15a. To submit the MSC.Patran.bdf file, find an available UNIX shell window. At the command prompt enter nastran workshop20.bdf scr=yes. Monitor the run using the UNIX ps command. 15b. To submit the MSC.Nastran.dat file, find an available UNIX shell window and at the command prompt enter nastran workshop20 scr=yes. Monitor the run using the UNIX ps command. 16. When the run is completed, edit the workshop20.f06 file and search for the word FATAL. The model will return a fatal message because the model needs additional constraints. Each bar element has six D.O.F. at every node. The spring element only supports one degree of freedom. Because of this, the model will fail. 17. Create additional constraints to avoid a fatal error. Loads/BCs Object: Displacement Type: Nodal New Set Name: constraint Input Data... Translations < T1 T2 T3 > <0, 0, > Rotations < R1 R2 R3 > <0, 0, 0> Analysis Coordinate Frame Coord 13 Select Application Region... Geometry Filter: FEM Select Nodes: Node 4 MSC.Nastran 120 Exercise Workbook 20-15

5 Figure Load and Boundary Conditions. SUBMITTING THE INPUT FILE FOR MSC.Nastran and MSC.Patran USERS: 19. Submit the input file to MSC.Nastran for analysis. 19a. To submit the MSC.Patran.bdf file, find an available UNIX shell window. At the command prompt enter nastran workshop20.bdf scr=yes. Monitor the run using the UNIX ps command. 19b. To submit the MSC.Nastran.dat file, find an available UNIX shell window and at the command prompt enter nastran workshop20 scr=yes. Monitor the run using the UNIX ps command.when the run is completed, edit the workshop20.f06 file and search for the word FATAL. 18. Generate an input file for analysis. Analysis Action: Analyze Object: Entire Model Method: Analysis Deck Job Name: workshop20 A MSC.Nastran input file called workshop20.bdf will be generated. This process of translating your model into an input file is called the Forward Translation. The Forward Translation is complete when the Heartbeat turns green MSC.Nastran 120 Exercise Workbook MSC.Nastran 120 Exercise Workbook Comparison of Results: 20. Compare the results obtained in the.f06 file with the results on the previous page: Also compare the results in the.f06 file with the following hand calculations applicable to node #6. Deflection from the axial load: P L T1 = = A E 6 T 1 = 5.15E 4 in 0.97 ( ) 21.MSC.Nastran Users have finished this exercise. MSC.Patran Users should proceed to the next step. 22. Proceed with the Reverse Translation process, that is, attaching the workshop20.xdb results file into MSC.Patran. To do this, return to the Analysis form and proceed as follows: Analysis Action: Attach XDB Object: Result Entities Method: Translate Select Results File... Selected Results File workshop20.xdb Reset the graphics by click on the Reset Graphics icon: Deflection from the bending moment: M L T2 = = I E 6 T 2 = 9.43E 3 in 2 ( 2.65) ( ) Rotation at the end: M L R3 = = E I 6 R 3 = 3.77E 4 rad ( ) ( 2.65) 23. When the translation is complete and the Heartbeat turns green, bring up the Results form. Find the maximum deformation. Results Object: Deformation Select Result Case(s) Select Deformation Result Show As: Reset Graphics Default, Static Subcase Displacements, Translational Resultant MSC.Nastran 120 Exercise Workbook MSC.Nastran 120 Exercise Workbook 20-19

6 Figure Deformation. Note: Compare the results to what was found in the.f06 file. Quit MSC.Patran after fininshing this exercise MSC.Nastran 120 Exercise Workbook