 ## Project 2

### Note:

This is an independent assignment. You may not discuss or share information regarding any aspect of this assignment with anyone except the instructor. The use of outside resources other than relevant textbooks is not allowed.

Pledge: I have neither given nor received any unauthorized assistance on this exam.

Signature: __________________________________  Print Name: ________________________

The thin, flat plate below has an elliptical cutout with dimensions 2a x 2b. The area of the cutout is required to be 20 in2 . The inplane loading is as shown, and you may assume that =1psi.

Assuming the dimensions of the plate are much larger than the largest radius of the elliptical cutout, the tangential stresses at points A and B are given by:

### Optimize the shape of the elliptical cutout to find the best values of a and b. Use the following five (5) approaches:

(a) Analytical: Assume that the optimal shape is one in which the tangential stresses at points A and B are equal. Derive the values of a and b by hand. Show all work.

(b) Graphical: Use the following problem statement. This graph must be done by hand. 代写机械工程

Minimize: ݂f=|σAB |

Such that:  h=area=20

For a and b, use a variable range of (1.0, 6.0). Show all work and create clear graphs. You must show the h function and at least three contours of f on the graph. Denote the

optimal solution point on the graph.

(c) Numerical: Use the following summed objectives problem statement with no constraint.

Minimize: f = [max(oÆ, oB)] + [abs_value(Area — 20)]

Use SHERPA. For a and b, use a variable range of (1.0, 6.0).

### (d) Numerical: Use the following pareto optimization problem statement with multiple  代写机械工程

objectives.

Minimize: ݂

f1 = [max(oÆ, oB)]

f2 = [abs_value(Area — 20)]

Use SHERPA. For a and b, use a variable range of (1.0, 6.0).

(e) Numerical: Use a different problem statement (representation) of your choice. In other words, how else can you represent and solve this problem? For a and b, use a variable range (1.0, 6.0).

### Results and Discussion:代写机械工程

(i)For each of the solutions above, briefly describe your problem statement and show all work in your formulation and solution. Include any necessary tables and plots to provide a complete description and assessment of your solutions.

(ii)Create a table to compare the results of the five solutions in terms of the numerical results and the overall effort (manual or computational). Discuss the pros and cons of each approach.