Homework 8 Optimization

1. MPP search by optimization

Find the MPP using optimization for the problem in Homework 5. The original problem is stated as follows:

Consider the limit-state function of a shaft in a speed reducer defined by

(1)

where d = 39 mm is the diameter of the shaft, l = 400 mm is the length of the shaft, F is the external force, T is the external torque, and S is the yield strength.

Distributions of Random Variables

Variables	Mean	Std	Distribution
External force F	2000 N	220 N	Normal
Torque T	450 N×m	50 N×m	Normal
Strength S	250 MPa	30 MPa	Normal

2. Optimization

(1) Solve the following optimization problem graphically.

(2) Solve the above problem by a numerical method. You may use any optimization software. Attach the code you used.

3. Optimization for worse case analysis

If the three variables , , and in problem 1 are interval values. Find the range of defined in Eq. (1). Use the following lower and upper bounds for the interval variables:

,

where X is , , or .