Homework 9
Reliability-Based Design
1. RBD with direct reliability analysis
The design margin of a beam is given by
where F is the external force, T is the external torque, and S is the yield strength. The equation represents the difference between the yield strength and the maximum equivalent stress.
The distributions of random variables and the lower and upper bounds of design variables are given in the following table.
|
Variables |
Mean |
Std |
Distribution |
Lower bound |
Upper bound |
|
b |
Deterministic design variable |
0.1 in |
0.4 in |
||
|
h |
Deterministic design variable |
0.1 in |
0.8 in |
||
|
l |
Deterministic design variable |
2 in |
20 in |
||
|
F |
300 lb |
30 lb |
|
--- |
--- |
|
T |
450 lb-in |
50 lb-in |
|
--- |
--- |
|
S |
100 kpsi |
10 kpsi |
|
--- |
--- |
Minimize the volume of the beam with required reliability 0.999. Use FOSM for reliability analysis.
(1) Provide the RBD model.
(2) Provide the result.
(3) Attach your source code.
2. RBD with inverse reliability analysis
Solve the above problem using inverse reliability analysis.
(1) Provide the RBD model.
(2) Provide the result.
(3) Attach your source code.