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1. Purbanchal University
School of Engineering
M.E. Earthquake
“Plane Problems in Polar
Coordinates”
Presented by:
Uttam Karki
Roll No: 18
First Semester

2. Introduction
In any elasticity problem the proper choice of the co-ordinate system is extremely
important since this choice establishes the complexity of the mathematical
expressions
employed to satisfy the field equations and the boundary conditions.
In order to solve two dimensional elasticity problems by employing a polar co-
ordinate reference frame, the equations of equilibrium, the definition of Airy’s Stress
function, and one of the stress equations of compatibility must be established in
terms of Polar Co-ordinates.

3. STRAIN-DISPLACEMENT RELATIONS
Case 1: For Two Dimensional State of Stress
Deformed element in two dimensions

4. (Cont.)

5. (Cont.)

6. Cont.

7. Cont.

8. (Cont.)

9. (Cont.)

10. (Cont.)
`

11. Cont
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12. Conclusion
In polar coordinates, solving problems involving planes typically
involves expressing the equation of the plane in terms of polar
coordinates.

13. Doubt and Discussion?????

14. References
• https://www.sciencedirect.com/topics/engineering/seismic-wave-
propagation
• https://www.usgs.gov/media/images/earthquake-early-warning-basics-
0#:~:text=Earthquake%20early%20warning%20systems%20like,to%203%20mi
les%20per%20second).
• https://www.researchgate.net/publication/280764638_Innovative_Mathema
tical_Model_for_Earthquake_Prediction#:~:text=From%20the%20data%20ta
ble%2C%20the,Identifier%20is%20determined%20as%202.99.&text=The%20
angle%20theta%20from%20the%20prediction%20was%2040%20degrees.&te
xt=So%20in%20the%20first%20100,occur%20from%20the%20last%20earthq
uake.
• Slide on chatgpt

15. Thank you