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by: Paige Cruickshank


Paige Cruickshank
GPA 3.95

Nam Kim

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About this Document

Nam Kim
Class Notes
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This 8 page Class Notes was uploaded by Paige Cruickshank on Friday September 18, 2015. The Class Notes belongs to EML 4500 at University of Florida taught by Nam Kim in Fall. Since its upload, it has received 10 views. For similar materials see /class/206706/eml-4500-university-of-florida in Engineering Mechanical at University of Florida.

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Popular in Engineering Mechanical




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Date Created: 09/18/15
Tutorial Plane beam bending analysis using Rectangular elements V F l 2 3 4 5 1m L F cl Consider a plane beam in the figure which is modeled using 5 rectangular elements When a 100kNm couple is applied at the tip by two equal and opposite force F 100 kN calculate 1 the tip deflection 2 stress along the top surface 2 stress along the bottom surface and 4 stress along the neutral axis In addition check if other components of stresses 039yy and TXy vanish The thickness of the beam is 10 cm and Young s modulus and Poisson s ratio are respectively 200 GPa and 03 Assume plane stress condition Compare the solution with exact solution from Euler beam theory amax 60 MPa vmax 00075 m 1 Start Nastran FX with new model file and use SI units Select File a New from the menu In Analysis Setting window select 2D for model type Select N m J sec for unit system Click OK to close Analysis Setting window 2 Create material and property Select Analysis a Material from the menu In the Material Manager window select downarrow next to Create button and select Isotropic In the CreateModify Isotropic Material window type 20E11 for Elastic Modulus and 03 for Poisson s Ratio Click OK to close CreateModify Isotropic Material window and click Close to close Material Manager window Select Analysis a Property from the menu In the Property Manager window select downarrow next to Create button and select 2D In the CreateModify 2D Property window select quotquot 39 tag quotquot 39 is 39 39 to plane stress rarerial and t me 001 for thickness TTl and click Close uow 3 Create a rectangular face Select Geometry gt Curve gt Create on WP gt Rectangle Input 00 for Location select ABS x y for method and click Apply lnput 51 for d dy for Method and rlirk nnl Click Cancel to close the window 4 Create rectangular elements Select Mesh gt 20 Mesh gt Auto Mesh Face i in In Mesh Size column check Elem ent Size and type 10 for element size Click Apply to generate ve elements Click Cancel to close the window In auto mesh the user 5 Applying displacementboundaryconditions Select Analysis gt Boundary Condition gt Set from the menu I ma RF fnr set Click Close to close the Boundary Condition Set window Select Analysis gt Boundary Condition gt Constraint from the menu When the Constraint window appears select Node 2 Lower left corner from the graphic window and check T1 and T2 in the DOF column in the Constraint window Click Apply button Two small triangular arrows will appear at Node 1 Select Node 1 Upper left corner from the graphic window and check T1 in the DOF column in the Constraint window In fact T2 should be unchecked Click Apply button One small triangular arrow will appear at Node 2 Click Cancel button to close Constraint window 6 Apply couple at the tip Select Analysis a Static Load a Set from the menu In the Load Set window type Couple for name and click Add to add Couple to the load set Click Close to close the Load Set window Select Analysis a Static Load a Force from the menu When the Force window appears select Node 7 Lower right corner from the graphic window and type 100000 for F1 field in the Components column in the Force window Click Apply button An arrows will appear at Node 7 Select Node 8 Upper right corner from the graphic window and type 100000 for F1 field in the Components column in the Force window Click Apply button An arrows will appear at Node 8 Click Cancel button to close Force window H 39x 7 ngure 4 Dwsp acEmEnt bnundary candmnns and apphEd Dads 7 Create Ana ysws Case SE E Ana ysws aAna ysws Case hum the menu nthe Ana ysws Case ManagEr Wmduw thAdd duck C Dsetn c DsE Ana ysws Case ManagEr Wmduw SavEthE madE usmg we gt Save cummand fmm the menu TypE ReciiBEam fDrME name a SDWEthemndE SE E Ana ysws esmvefmm the menu Chck OK nme that the BEndmgAnaWsws s sE E Ed by dEfauk appEarat the End Dfsmutmn s TOTAL wmmwcs n SDmEUmEs nuntrmca Wammgs can be aHDWEd s wommmmons n s Pustpmcessmgmmpmspxacement TD gu a puslpmcEssmg mndE th Resuns tag To read the tip deflection at Nodes 7 and 8 right click on T2 TRANSLATION and select Table popup menu and click OK The tip deflection can be obtained by averaging deflections at these two nodes In this case the deflections of both nodes are identical to 75 mm which is the same as exact solution In NASTRAN special shape functions are added to make the element works accurately under bending Z O O D T2 TRANSLATIONV 0000000 0000000 0000300 0001200 0002700 0004800 0007500 0007500 RDOOVOHU39IbUJNH 0004800 10 0002700 11 0001200 12 0000300 11 Postprocessing for element stress Expand 2D Element Stresses Too see 039 double click SHELL NORMALX TOP Too see o w double click SHELL NORMALY TOP Too see Txy double click SHELL SHEARXY TOP Note that the maximum 039 on the bottom surface is 60 MPa which is exact Again using an additional shape function NASTRAN rectangular element can represent the pure bending problem accurately Note that there are small values of cryy and TXy due to numerical noise SHELL NORMAL smsss gtlt aor Wm J J EDEJkDDE J 72wqu SW 1 2 IESeDHY CHAP 5 FINITE ELEMENTS FOR HEAT TRANSFER PROBLEMS EML 4500 FINITE ELEMENT ANALYSIS AND DESIGN NamHo Kim Spring 2009 HEAT CONDUCTION ANALYSIS Analogy between Stress and Heat Conduction Analysis Structural problem Displacement Temperature scalar Stressstrain Heat flux vector Displacement 80 Fixed temperature 80 Surface traction force Heat flux 80 Body force Internal heat generation Young s modulus Thermal conductivity Infinite element viewpoint two problems are identical if a proper interpretation is given More Complex Problems Coupled structuralthermal problems thermal strain Radiation problem


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