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

Contents 11.1 BEAM3: 2D樑元素 BEAM3: 2D Elastic Beam Element 11.2 實例: 腳踏車架設計 Example: Design of a Bicycle Frame 11.3 實例: 鋼弦的震動分析 Example: Vibration of a String Under Tension 11.4 實例: 升降平台結構分析 Example: Structural Analysis of a Lift Platform 11.5 樑元素瀏覽 Overview of Beam Elements 11.6 練習題 Exercises

BEAM3: 2D樑元素 BEAM3: 2D Elastic Beam Element 第11.1節 BEAM3: 2D樑元素 BEAM3: 2D Elastic Beam Element

11.1.1 BEAM3元素描述

11.1.2 BEAM3輸入資料 Element Name BEAM3 Nodes I, J Degrees of Freedom UX, UY, ROTZ Real Constants AREA, IZZ, HEIGHT, SHEARZ, ISTRN, ADDMAS Material Properties EX, NUXY, GXY, ALPX, DENS, DAMP Surface Loads Pressure face 1, face 2, face 3, face 4 Body Loads Temperature -- T1, T2, T3, T4 Special Features Stress stiffening, Large deflection, etc. etc.

11.1.3 BEAM3輸出資料

實例: 腳踏車架設計 Example: Design of a Bicycle Frame 第11.2節 實例: 腳踏車架設計 Example: Design of a Bicycle Frame

11.2.1 問題描述 31 10 18 32 36 12 15

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

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

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

實例: 鋼弦的震動分析 Example: Vibration of a String Under Tension 第11.3節 實例: 鋼弦的震動分析 Example: Vibration of a String Under Tension

11.3.1 問題描述

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

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 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

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   /WINDOW, 2, OFF   SET, 1, 3   /WINDOW, 3, -1, 1.67, -1.0, -0.4

實例: 升降平台結構分析 Example: Structural Analysis of a Lift Platform 第11.4節 實例: 升降平台結構分析 Example: Structural Analysis of a Lift Platform

11.4.1 問題描述 72 32 24 30 300 lb 400 lb 6

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

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

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

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

樑元素瀏覽 Overview of Beam Elements 第11.5節 樑元素瀏覽 Overview of Beam Elements

11.5.1 Elastic Beams

11.5.2 Plastic Beams

11.5.3 Finite Strain Beams

11.5.4 Unsymmetric Beams

11.5.5 Elastic Pipes

11.5.6 Plastic Pipes

11.5.7 Explicit Dynamics

第11.6節 練習題 Exercises