ME 3255 Final Project

Part A

Central finite difference approximation for gradient of 3x3 interior nodes of w.

[w] = membrane_solution3(T,P);

Part B

T = 0.006 uN/um P = 0.001 MPa

[w] = membrane_solution3(0.006,0.001);

Part C

General central finite difference approximation for gradient of nxn interior nodes of w.

[w] = membrane_solution(T,P,n)

Part D

• T = 0.006 uN/um
• P = 0.001 MPa
• n = 10 nodes

[w] = membrane_solution(0.006,0.001,10)

Part E

Function that calculates the difference in the strain energy and the work done by pressure for n-by-n elements.

[pw_se,w] = SE_diff(T,P,n)

Part F

Root-finding Method used to find tension in the Membrane, given:

• P = 0.001 MPa
• n = [20:5:40]

Error

|number of nodes |Tension (uN/um) |rel. error |
|---|---|---|
|3 |0.059 |n/a|
|20|0.0618|4.5%|
|25|0.0616|0.3%|
|30|0.0614|0.3%|
|40|0.0611|0.3%|

Part G

Pressure v. Maximum deflection (MPa v. um)