Chapter 11 樑與鋼架結構分析 Analysis of Beams and Frames.

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  • Slide 1
  • Chapter 11 Analysis of Beams and Frames
  • Slide 2
  • 2/31 Contents 11.1BEAM3: 2D BEAM3: 2D Elastic Beam Element 11.2 : Example: Design of a Bicycle Frame 11.3 : Example: Vibration of a String Under Tension 11.4 : Example: Structural Analysis of a Lift Platform 11.5 Overview of Beam Elements 11.6 Exercises
  • Slide 3
  • 3/31 11.1 BEAM3: 2D BEAM3: 2D Elastic Beam Element
  • Slide 4
  • 4/31 11.1.1 BEAM3
  • Slide 5
  • 5/31 11.1.2 BEAM3 Element NameBEAM3 NodesI, J Degrees of Freedom UX, UY, ROTZ Real ConstantsAREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS Material PropertiesEX, NUXY, GXY, ALPX, DENS, DAMP Surface LoadsPressure face 1, face 2, face 3, face 4 Body LoadsTemperature -- T1, T2, T3, T4 Special FeaturesStress stiffening, Large deflection, etc. etc.
  • Slide 6
  • 6/31 11.1.3 BEAM3
  • Slide 7
  • 7/31 11.2 : Example: Design of a Bicycle Frame
  • Slide 8
  • 8/31 11.2.1 31 10 31 18 32 36 1215
  • Slide 9
  • 9/31 11.2.2 ANSYS Procedure (1/3) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 FINISH /CLEAR /UNITS, BIN D = 1! Outer Diameter T = 1/16! Thickness PI = 4*ATAN(1) PSEAT = 150*2.5! Load on seat PHANDLE = 25*2.5! Load on handle /PREP7 ET, 1, BEAM3 MP, EX, 1, 30E6 MP, NUXY, 1, 0.3 AREA = PI*(D**2-(D-T)**2)/4 IZZ = PI*(D**4-(D-T)**4)/64 R, 1, AREA, IZZ, D
  • Slide 10
  • 10/31 11.2.2 ANSYS Procedure (2/3) 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 K, 1, 0, 0 K, 2, 18, 0 K, 3, 36, 0 K, 4, 10, 15 K, 5, 31, 15 K, 6, 32, 12 L, 1, 2 L, 4, 5 L, 1, 4 L, 2, 4 L, 2, 6 L, 5, 6 L, 6, 3 ESIZE, 2 LMESH, ALL FINISH 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 /SOLU NLEFT = NODE(0,0,0)! Left support NRIGHT = NODE(36,0,0)! Right support NSEAT = NODE(10,15,0)! Seat NHANDLE = NODE(31,15,0)! Handle D, NLEFT, UX, 0 D, NLEFT, UY, 0 D, NRIGHT, UY, 0 F, NSEAT, FY, -PSEAT F, NHANDLE, FY, -PHANDLE /PBC, ALL,, ON EPLOT SOLVE FINISH
  • Slide 11
  • 11/31 11.2.2 ANSYS Procedure (3/3) 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 /POST1 PLDISP, 2 ETABLE, MFORX, SMISC, 1 ETABLE, MFORY, SMISC, 2 ETABLE, MMOMZ, SMISC, 6 ETABLE, SDIR, LS, 1 ETABLE, SBYT, LS, 2 ETABLE, SBYB, LS, 3 ETABLE, SMAX, NMISC, 1 ETABLE, SMIN, NMISC, 2 PRETAB, MFORX, MFORY, MMOMZ PRETAB, SDIR, SBYT, SBYB, SMAX, SMIN PLETAB, SDIR PLETAB, SBYT PLETAB, SMAX PLETAB, SMIN
  • Slide 12
  • 12/31 11.3 : Example: Vibration of a String Under Tension
  • Slide 13
  • 13/31 11.3.1
  • Slide 14
  • 14/31 11.3.2 ANSYS Procedure (1/3) 01 02 03 04 05 06 07 08 09 10 11 12 13 FINISH /CLEAR /TITLE, VM53 (lb-in-s) D = 1/16! Diameter PI = 4*ATAN(1)! Constant AREA = PI*D**2/4! Cross section IZZ = PI*D**4/64! Moment of inertia ISTRN = 0.00543228! Initial strain E = 30E6! Steel NU = 0.3! Steel RO = 0.00073! Steel L = 100! Length of string
  • Slide 15
  • 15/31 11.3.2 ANSYS Procedure (2/3) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 /PREP7 ET, 1, BEAM3 R, 1, AREA, IZZ, D,, ISTRN MP, EX, 1, E MP, NUXY, 1, NU MP, DENS, 1, RO N, 1, 0, 0 N, 14, L, 0 FILL E, 1, 2 EGEN, 13, 1, -1 FINISH /SOLU D, 1, ALL, 0 D, 14, ALL, 0 PSTRES,ON SOLVE FINISH 37 38 39 40 41 42 43 44 45 46 47 48 49 /POST1 ETABLE, STRESS, LS, 1 PRETAB, STRESS FINISH /SOLU ANTYPE, MODAL MODOPT, SUBSP, 3 PSTRES, ON SOLVE FINISH
  • Slide 16
  • 16/31 11.3.2 ANSYS Procedure (3/3) 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 /POST1 SET, LIST /TRIAD, OFF /COLOR, PBAK, OFF SET, 1, 1 /WINDOW, 1, -1, 1.67, 0.4, 1.0 PLDISP, 2 /NOERASE /WINDOW, 1, OFF SET, 1, 2 /WINDOW, 2, -1, 1.67, -0.3, 0.3 PLDISP, 2 /WINDOW, 2, OFF SET, 1, 3 /WINDOW, 3, -1, 1.67, -1.0, -0.4 PLDISP, 2
  • Slide 17
  • 17/31 11.4 : Example: Structural Analysis of a Lift Platform
  • Slide 18
  • 18/31 11.4.1 72 32 24 30 300 lb 400 lb 300 lb 24 30 6
  • Slide 19
  • 19/31 11.4.2 ANSYS Procedure (1/4) 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 FINISH /CLEAR /TITLE, Lift Platform (lb-in-s) B = 1! Width for all members E = 30E6! Steel NU = 0.3! Steel /PREP7 ET, 1, BEAM3 MP, EX, 1, E MP, NUXY, 1, NU R, 1, B*8, B*8**3/12, 8! Arms R, 2, B*4, B*4**3/12, 4! Platform R, 3, B*2, B*2**3/12, 2! Connector R, 4, B*2, B*2**3/12, 2! Actuator
  • Slide 20
  • 20/31 11.4.2 ANSYS Procedure (2/4) 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 N, 101, 0, 0 N, 102, 0, 24 N, 103, 32, 24 N, 104, 32, 48 N, 105, 72, 54 N, 106, 72, 78 N, 201, 72, 54 N, 202, 72, 78 N, 203, 102, 54 N, 204, 102, 78 N, 205, 132, 54 N, 206, 132, 78 N, 301, 32, 24 N, 302, 32, 48 N, 401, 32, 24 N, 402, 62, -6 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 REAL, 1 E, 101, 103 E, 103, 105 E, 102, 104 E, 104, 106 REAL, 2 E, 201, 203 E, 203, 205 E, 202, 204 E, 204, 206 E, 201, 202 E, 203, 204 E, 205, 206 REAL, 3 E, 301, 302 REAL, 4 E, 401, 402
  • Slide 21
  • 21/31 11.4.2 ANSYS Procedure (3/4) 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 CP, 1, UX, 105, 201 CP, 2, UY, 105, 201 CP, 3, UX, 106, 202 CP, 4, UY, 106, 202 CP, 5, UX, 103, 301, 401 CP, 6, UY, 103, 301, 401 CP, 7, UX, 104, 302 CP, 8, UY, 104, 302 D, 101, UX, 0 D, 101, UY, 0 D, 102, UX, 0 D, 102, UY, 0 D, 402, UX, 0 D, 402, UY, 0 F, 202, FY, -300 F, 204, FY, -400 F, 206, FY, -300 74 75 76 77 78 79 80 81 82 /PNUM, NODE, ON EPLOT /PNUM, DEFAULT FINISH /SOLU SOLVE FINISH
  • Slide 22
  • 22/31 11.4.2 ANSYS Procedure (4/4) 84 85 86 87 88 89 /POST1 PLDISP, 2 ETABLE, MFORX, SMISC, 1 ETABLE, MFORY, SMISC, 2 ETABLE, MMOMZ, SMISC, 6
  • Slide 23
  • 23/31 11.5 Overview of Beam Elements
  • Slide 24
  • 24/31 11.5.1 Elastic Beams
  • Slide 25
  • 25/31 11.5.2 Plastic Beams
  • Slide 26
  • 26/31 11.5.3 Finite Strain Beams
  • Slide 27
  • 27/31 11.5.4 Unsymmetric Beams
  • Slide 28
  • 28/31 11.5.5 Elastic Pipes
  • Slide 29
  • 29/31 11.5.6 Plastic Pipes
  • Slide 30
  • 30/31 11.5.7 Explicit Dynamics
  • Slide 31
  • 31/31 11.6 Exercises

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