3D實體結構分析 Analysis of 3D Structural Solids Chapter 8 3D實體結構分析 Analysis of 3D Structural Solids

Contents 8.1 SOLID45: 3D實體結構元素 8.2 實例: 六角板手靜力分析 8.3 3D實體元素瀏覽 SOLID45: 3D Structural Solid Element 8.2 實例: 六角板手靜力分析 Example: Static Analysis of an Allen wrench 8.3 3D實體元素瀏覽 Overview of 3D Solid Elements 8.4 練習題: Allen Socket的扭轉剛度 Exercise: Torsional Stiffness of an Allen Socket

SOLID45: 3D實體結構元素 SOLID45: 3D Structural Solid Element 第8.1節 SOLID45: 3D實體結構元素 SOLID45: 3D Structural Solid Element

8.1.1 SOLID45元素描述

8.1.2 SOLID45 Input Data (1/5) Element Name SOLID45 Nodes I, J, K, L, M, N, O, P Degrees of Freedom UX, UY, UZ Real Constants None Material Properties EX, NUXY, GXY, ALPX, DENS, DAMP, etc. Surface Loads Pressure face 1 (JILK), face 2 (IJNM), face 3 (JKON), face 4 (KLPO), face 5 (LIMP), face 6 (MNOP) Body Loads Temperature -- T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) Special Features Plasticity, Creep, Stress stiffening, Large deflection, Large strain, etc. KEYOPT(1) Key to include extra shapes: 0 -- Include extra displacement shapes 1 -- Suppress extra displacement shapes KEYOPT(2) Key for reduced integration: 0 -- Full integration 1 -- Uniform reduced integration with hourglass control KEYOPT(4) Key for element coordinate system: 0 -- Element C.S. is parallel to the global C.S. 1 -- Element C.S. is based on the element I-J side KEYOPT(5) Key for element solution KEYOPT(6)

8.1.2 SOLID45 Input Data (2/5) Material Properties EX, EY, EZ NUXY, NUYZ, NUXZ (or PRXY, PRYZ, PRXZ) GXY, GYZ, GXZ ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ) DENS DAMP

8.1.2 SOLID45 Input Data (3/5) Loads Surface Loads Pressure face 1 (JILK), face 2 (IJNM), face 3 (JKON), face 4 (KLPO), face 5 (LIMP), face 6 (MNOP) Body Loads Temperature T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) Etc.

8.1.2 SOLID45 Input Data (4/5) KEYOPT(1): Extra Displacement Shape 0 -- Include extra displacement shapes 1 -- Suppress extra displacement shapes

8.1.2 SOLID45 Input Data (5/5) KEYOPT(2): Reduced Integration 0 -- Full integration 1 -- Uniform reduced integration with hourglass control

8.1.3 SOLID45 output Data Name Definition EL Element Number NODES Nodes - I, J, K, L, M, N, O, P MAT Material number VOLU: Volume XC, YC, ZC Location where results are reported PRES Pressures P1 at nodes J, I, L, K; P2 at I, J, N, M; P3 at J, K, O, N; P4 at K, L, P, O; P5 at L, I, M, P; P6 at M, N, O, P TEMP Temperatures T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P) S:X, Y, Z, XY, YZ, XZ Stresses S:1, 2, 3 Principal stresses S:INT Stress intensity S:EQV Equivalent stress Etc. …

ETABLE and ESOL Command Input 8.1.4 Item/Sequence Number ETABLE, SEQVJ, NMISC, 10 ETABLE, S1P, NMISC, 36 Output Quantity Name ETABLE and ESOL Command Input Item I J K L M N O P P1 SMISC 2 1 4 3 - P2 5 6 8 7 P3 9 10 12 11 P4 13 14 16 15 P5 18 17 19 20 P6 21 22 23 24 S:1 NMISC 26 31 36 S:2 27 32 37 S:3 28 33 38 S:INT 29 34 39 S:EQV 25 30 35 40

實例：六角扳手靜力分析 Example: Static Analysis of an Allen Wrench 第8.2節 實例：六角扳手靜力分析 Example: Static Analysis of an Allen Wrench

8.2.1 Problem Description

8.2.2 ANSYS Procedure (1/8) Set Up 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 FINISH /CLEAR /TITLE, Static Analysis of an Allen Wrench /UNITS, SI ! Reminder only *AFUN, DEG ! Units for angular functions   ! Define parameters ... EXX = 2.07E11 ! Yung's modulus NU = 0.3 ! Poisson's ratio W_HEX = 0.01 ! Width of hex flats W_FLAT = W_HEX*TAN(30) ! Width of flat L_SHANK = 0.075 ! Length of shank L_HANDLE = 0.20 ! Length of handle BENDRAD = 0.01 ! Bend radius L_ELEM = 0.0075 ! Length of elements NO_D_HEX = 2 ! No. of div. on a flat TOL = 25E-6 ! Selection Tolerance

8.2.2 ANSYS Procedure (2/8) Attribute Tables 20 21 22 23 24 25 26 /PREP7   ! Element types and material properties... ET, 1, SOLID45 ! 8-node brick element ET, 2, MESH200, 6 ! Mesh-Only Element MP, EX, 1, EXX ! Young's modulus MP, NUXY, 1, NU ! Possion's ratio

8.2.2 ANSYS Procedure (3/8) Solid/Analysis Models 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 ! Wrench bottom end...   RPOLY, 6, W_FLAT ! Hexagonal area L, 4, 1 ! Middle of hex shape ASBL, 1, 7,, DELETE, KEEP ! Cut into two areas CM, BOTAREA, AREA ! Group two areas /PNUM, KP, ON /PNUM, LINE, ON /PNUM, AREA, ON /TITLE, Fixed End (Viewed from Below) APLOT LESIZE, 1,,, NO_D_HEX LESIZE, 2,,, NO_D_HEX LESIZE, 6,,, NO_D_HEX TYPE, 2 ! Mesh-Only Elements MSHAPE, 0, 2D ! Quadrilaterial shapes MSHKEY, 1 ! Mapped meshing AMESH, ALL ! Mesh all two areas /TITLE, Meshed Fixed End EPLOT

8.2.2 ANSYS Procedure (4/8) Solid/Analysis Models 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77  ! Middle line of the wrench...   /VIEW,, 1, 1, -1 ! Isometric view /VUP,, -Z ! -Z axis as view-up K, 7, 0, 0, 0 K, 8, 0, 0, -L_SHANK K, 9, 0, L_HANDLE, -L_SHANK L, 7, 8 L, 8, 9 LFILLT, 8, 9, BENDRAD /TITLE, Middle Line of the Wrench LPLOT /PNUM, DEFAULT ! Drag the 2D mesh to produce 3D elements... TYPE, 1 ! SOLID45 is used ESIZE, L_ELEM ! Default to L_ELEM VDRAG, 2, 3,,,,, 8, 10, 9 ! Drag to create 3D mesh /TITLE, 3D Mesh of the Wrench EPLOT FINISH

8.2.2 ANSYS Procedure (5/8) Solve: Load Step 1 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 /SOLU   ! Load step 1... CMSEL, S, BOTAREA ! Fixed end areas LSEL, S, EXT ! Exterior lines NSLL, S, 1 ! Nodes on those lines D, ALL, ALL, 0 ! Fix those nodes ALLSEL ASEL, S, LOC, Y, BENDRAD, L_HANDLE ASEL, R, LOC, X, W_FLAT/2, 99 NSLA, S, 1 NSEL, R,LOC,Y,L_HANDLE-3*L_ELEM-TOL,L_HANDLE+TOL *GET, MINYVAL, NODE,, MNLOC, Y ! Min Y of nodes *GET, MAXYVAL, NODE,, MXLOC, Y ! Max Y of nodes PTORQ = 100/(W_HEX*(MAXYVAL-MINYVAL)) SF, ALL, PRES, PTORQ /PBC, U,, ON /PSF, PRES,, 2 /TITLE, Load Step 1 EPLOT SOLVE

8.2.2 ANSYS Procedure (6/8) Solve: Load Step 2 107 108 109 110 111 112 113 114 115 116 117 118 119 ! Load step 2...   PDOWN = 20/(W_FLAT*(MAXYVAL-MINYVAL)) ASEL, S, LOC, Z, -(L_SHANK+W_HEX/2) NSLA, S, 1 NSEL, R,LOC,Y,L_HANDLE-3*L_ELEM-TOL,L_HANDLE+TOL SF, ALL, PRES, PDOWN ALLSEL /TITLE, Load Step 2 EPLOT SOLVE FINISH

8.2.2 ANSYS Procedure (7/8) Results: Load Step 1 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 /POST1   ! Results for load step 1 /PBC, DEFAULT /PSF, DEFAULT /TRIAD, OFF SET, 1 /TITLE, Deformed Shape for Load Step 1 PLDISP, 2 /Title, Stress Intensity for Load Step 1 /ANGLE,, 120, YM ! Rotate about model axis PLNSOL, S, INT

8.2.2 ANSYS Procedure (8/8) Results: Load Step 2 137 138 139 140 141 142 143 144 145 146 ! Results for load step 2   SET, 2 /TITLE, Deformed Shape for Load Step 2 /ANGLE, 1, 0, YM PLDISP, 2 /Title, Stress Intensity for Load Step 2 /ANGLE, 1, 120, YM PLNSOL, S, INT

3D實體元素瀏覽 Overview of 3D Solid Elements 第8.3節 3D實體元素瀏覽 Overview of 3D Solid Elements

8.3.1 General 3D Structural Solids

8.3.2 Large Strains

8.3.3 3D Solids with Rotations

8.3.4 P-Elements

8.3.5 Explicit Dynamics

8.3.6 Hyperelasticity

8.3.7 Viscoelasticity and Viscoplasticity

8.3.8 Anisotropic and Composite Materials

8.3.9 Thermal Solids

8.3.10 Fluid Elements

8.3.11 Electrostatic Fields

8.3.12 Magnetic Fields

8.3.13 Coupled-Field Elements

8.4 Exercise: Torsional Stiffness of an Allen Socket