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# ME 3255 Final Project | |
## Part A | |
Central finite difference approximation for gradient of 3x3 interior nodes of w. | |
```matlab | |
[w] = membrane_solution3(T,P); | |
``` | |
## Part B | |
T = 0.006 uN/um | |
P = 0.001 MPa | |
```matlab | |
[w] = membrane_solution3(0.006,0.001); | |
``` | |
![Fig. 1](./figures/PartB.png) | |
## Part C | |
General central finite difference approximation for gradient | |
of nxn interior nodes of w. | |
```matlab | |
[w] = membrane_solution(T,P,n) | |
``` | |
## Part D | |
- T = 0.006 uN/um | |
- P = 0.001 MPa | |
- n = 10 nodes | |
```matlab | |
[w] = membrane_solution(0.006,0.001,10) | |
``` | |
![Fig. 2](./figures/PartD.png) | |
## Part E | |
Function that calculates the difference in the strain energy and the work done by pressure for n-by-n elements. | |
```matlab | |
[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) |