The document describes a finite element analysis of a block made of isotropic material subjected to loading and temperature changes. The objectives are to determine displacements, stresses, strains, and principal values at midpoints due to loading and temperature increments from 0-25 degrees C. MATLAB is used to calculate the values. Results show coefficients for displacement, strains, stresses, and how octahedral stress changes with temperature. The bottom and top edges are most sensitive to temperature change.

1. By
Ahmad Abo-Mathkoor 6145531
Asmita Dubey 9796924
Daniel Modric 6062539
Rohit Katarya 6306160

2. PROBLEM STATEMENT
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 Point Co-ordinates Before Loading Co-ordinates After Loading
stresses at the midpoint of each edge due to A 0,0,20 0.0001, 0.0002, 20
temperature change. B 30, 0, 20 30.0001, 0.0, 20.0004
C 30, 10, 20 29.9997, 10.0003, 19.9996
 To evaluate the most sensitive edge of the
block due to temperature change. D 0, 10, 20 0.0004, 10.0009, 19.9995
Plot and discuss the results with increment of E 0, 0, 0 0, 0, 0.0
temperature by 5 degree in the range of 0-25
F 30, 0, 0 30.0009, 0.0001, 0.00026
degrees.
G 30,10,0 29.9996, 10.00033, 0
 Analyse the effect of temperature with H 0, 10, 0 0.00011, 9.9996, 0.00021
increment of 20 degrees on change in I 0, 0, 10 0.00019, 0.00027, 9.9998
octahedral stress of constraints (a) The bottom
J 30, 5, 20 30.0006, 4.9997, 20.0005
edge at the front face and (b) the top edge of
the block at the rear face. K 15, 10, 20 15.0007, 9.9998, 20.0003

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.

4. Basic definitions and equations used
•

5. MATLAB programing for finding stress, strains with
or without temperature effects
• The programming software MATLAB was used to calculate all of the objectives.
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
Coefficien Value ( * 10-3) Coefficient Value ( * 10-3) Coefficient Value ( * 10-3)
t D0 0
C0 0 D1 -0.1033 E0 0
C1 0.1167 D2 0.0036 E1 0.1087
C2 -0.0029 E2 -0.0033
D3 -0.2200
C3 0.2910 E3 0.2210
D4 0.0180
C4 -0.0280 E4 -0.0200
D5 0.0440
C5 0.0330 E5 -0.0400
D6 -0.0017
C6 -0.0014 E6 0.0020
D7 0.0021
C7 -0.0047 E7 -0.0016
D8 -0.0005 E8 0.0002
C8 -0.0015
D9 0.0055 E9 -0.0035
C9 0.0010
D10 -0.0002 E10 0
C10 0.0001
Coefficients in the u direction Coefficients in the v direction Coefficients in the w direction

7. STRAINS
•

8. Stress
•

9. Change in Octahedral Stress
Change in Octahedral Stress
25
20
15
10
5
0
AB BC CD DA BF FG GC GH HE EF DH AE
Change in Equivalent Stresses (TRESCA)
100
90
80
70
60
50
40
30
20
10
0
AB BC CD DA BF FG GC GH HE EF DH AE

10. Variation of Temperature (0-25°C) in 5°C
Increments

11. strains

12. Change in Octahedral Stress

13. Comparison

14. Two Constrained Edges

15. • No Temperature Change
• To compare the effect of temperature change, it must first be calculated
without a temperature change. The figures in annex VIII show the principle
stresses the principle strains and the octahedral stresses.
• 20°C Temperature Change
• The figures in annex IX show the principle stresses the principle strains
and the octahedral stresses after the thermal loading.
• Comparison of Octahedral Stress
• The following figure shows the change in octahedral stress.