Homework 6
FORM and MPP-Based MCS
1. The limit-state function of a shaft in a speed reducer is defined by the difference between the strength and the maximum equivalent stress. It is given by
where
mm, the diameter of
the shaft
mm, the length of the
shaft
the external force
the external torque
the yield strength
The distributions of the independent random variables are given below.
Table 1 Distributions
|
Variables |
Mean |
Std |
Distribution |
|
External force |
2000 N |
220 N |
Normal |
|
Torque |
450 N·m |
50 N·m |
Normal |
|
Strength |
250 MPa |
30 MPa |
Normal |
Use FORM to calculate the probability of failure. Please tabulate the MPP search process in the table shown below.
2. Use the MPP-based MCS to compute the probability of failure for the above problem. Attach your source code.