1. 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

2. 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

3. 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

4. SOLID45元素描述

5. 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)

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

7. 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. 8.1.2 SOLID45 Input Data (4/5) KEYOPT(1): Extra Displacement Shape
0 -- Include extra displacement shapes
1 -- Suppress extra displacement shapes

9. 8.1.2 SOLID45 Input Data (5/5) KEYOPT(2): Reduced Integration
0 -- Full integration
1 -- Uniform reduced integration with hourglass control

10. 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. …

11. ETABLE and ESOL Command Input
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

12. 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

13. Problem Description

14. 8.2.2 ANSYS Procedure (1/8) Set Up01 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 = 2.07E ! Yung's modulus
NU = ! Poisson's ratio
W_HEX = ! Width of hex flats
W_FLAT = W_HEX*TAN(30) ! Width of flat
L_SHANK = ! Length of shank
L_HANDLE = ! Length of handle
BENDRAD = ! Bend radius
L_ELEM = ! Length of elements
NO_D_HEX = ! No. of div. on a flat
TOL = 25E ! Selection Tolerance

15. 8.2.2 ANSYS Procedure (2/8) Attribute Tables20 21 22 23 24 25 26
/PREP7
! Element types and material properties...
ET, 1, SOLID ! 8-node brick element
ET, 2, MESH200, ! Mesh-Only Element
MP, EX, 1, EXX ! Young's modulus
MP, NUXY, 1, NU ! Possion's ratio

16. 8.2.2 ANSYS Procedure (3/8) Solid/Analysis Models28 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, ! 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, ! Mesh-Only Elements
MSHAPE, 0, 2D ! Quadrilaterial shapes
MSHKEY, ! Mapped meshing
AMESH, ALL ! Mesh all two areas
/TITLE, Meshed Fixed End
EPLOT

17. 8.2.2 ANSYS Procedure (4/8) Solid/Analysis Models53 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, ! 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, ! 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

18. 8.2.2 ANSYS Procedure (5/8) Solve: Load Step 179 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, ! Nodes on those lines
D, ALL, ALL, ! 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

19. 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

20. 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

21. 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

22. 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

23. 8.3.1 General 3D Structural Solids

24. Large Strains

25. 8.3.3 3D Solids with Rotations

26. P-Elements

27. Explicit Dynamics

28. Hyperelasticity

29. 8.3.7 Viscoelasticity and Viscoplasticity

30. 8.3.8 Anisotropic and Composite Materials

31. Thermal Solids

32. Fluid Elements

33. Electrostatic Fields

34. Magnetic Fields

35. 8.3.13 Coupled-Field Elements

36. 8.4 Exercise: Torsional Stiffness of an Allen Socket