2. PROBLEM STATEMENT
Point Co-ordinates Before Loading Co-ordinates After Loading
A 0,0,20 0.0001, 0.0002, 20
B 30, 0, 20 30.0001, 0.0, 20.0004
C 30, 10, 20 29.9997, 10.0003, 19.9996
D 0, 10, 20 0.0004, 10.0009, 19.9995
E 0, 0, 0 0, 0, 0.0
F 30, 0, 0 30.0009, 0.0001, 0.00026
G 30,10,0 29.9996, 10.00033, 0
H 0, 10, 0 0.00011, 9.9996, 0.00021
I 0, 0, 10 0.00019, 0.00027, 9.9998
J 30, 5, 20 30.0006, 4.9997, 20.0005
K 15, 10, 20 15.0007, 9.9998, 20.0003
A block made of an isotropic material with dimensions of 30 mm X 20 mm X 10 mm is shown.
The coordinates of each corner before and after loading with the addition two extra points (J
and K)
The aim of the project
To determine displacements, stresses, strains,
principle stresses and strains at the mid-point
of each edge of the block.
To determine the change in stress distribution,
principle stresses and strains, octahedral
stresses at the midpoint of each edge due to
temperature change.
To evaluate the most sensitive edge of the
block due to temperature change.
Plot and discuss the results with increment of
temperature by 5 degree in the range of 0-25
degrees.
Analyse the effect of temperature with
increment of 20 degrees on change in
octahedral stress of constraints (a) The bottom
edge at the front face and (b) the top edge of
the block at the rear face.
3. Property of an Isotropic material
An Isotropic material, has the same properties in every direction. Most material
have mechanical properties which are independent of particular coordinate
directions, and such material are called the isotropic material. When a solid body
or a structure made of isotropic material possesses elastic symmetry that is the
symmetric directions exist in the solid body.
5. MATLAB programing for finding stress, strains with
or without temperature effects
• MATLAB was used to calculate all objectives. There are various functions that
the main program calls upon, followed by a flow chart to help the reader
understand how the main program works.
6. RESULTS
Displacement
Coefficient Value ( * 10-3)
C0 0
C1 0.1167
C2 -0.0029
C3 0.2910
C4 -0.0280
C5 0.0330
C6 -0.0014
C7 -0.0047
C8 -0.0015
C9 0.0010
C10 0.0001
Coefficients in the u direction
Coefficient Value ( * 10-3)
D0 0
D1 -0.1033
D2 0.0036
D3 -0.2200
D4 0.0180
D5 0.0440
D6 -0.0017
D7 0.0021
D8 -0.0005
D9 0.0055
D10 -0.0002
Coefficients in the v direction
Coefficient Value ( * 10-3)
E0 0
E1 0.1087
E2 -0.0033
E3 0.2210
E4 -0.0200
E5 -0.0400
E6 0.0020
E7 -0.0016
E8 0.0002
E9 -0.0035
E10 0
Coefficients in the w direction
11. Change in Octahedral Stress
0
5
10
15
20
25
AB BC CD DA BF FG GC GH HE EF DH AE
Change in Octahedral Stress
0
10
20
30
40
50
60
70
80
90
100
AB BC CD DA BF FG GC GH HE EF DH AE
Change in Equivalent Stresses (TRESCA)
17. • No Temperature Change
• To compare the effect of temperature change, it must first be calculated
without a temperature change.
• 20°C Temperature Change
• Then the principle stresses, the principle strains and the octahedral
stresses were calculated after the thermal loading.
• Comparison of Octahedral Stress
• The following figure shows the change in octahedral stress.
