 ## ME 465 Project 1

### Introduction  机械工程作业代写

In this project, we will focus on building models in Excel that can be used in an automated optimization study.

Determine the optimal cross‐sectional shape of the cantilever I‐beam shown below. Independently develop the entire analytical model in Excel and link this to HEEDS to perform the optimization (see the note at the end of this assignment regarding your model).  机械工程作业代写

Remember to use the Excel portal. The input and output files will be the same, but you still must tag the variables in the input file and the responses in the output file.

The primary goal is to minimize the mass of the beam, while satisfying constraints on the maximum bending stress (σ ≤ 5,000 psi) and the maximum transverse deflection (ð ≤ 0.1 inches). Use E=1.0e7 psi, P=1000 lbs and L=36 inches. The four cros‐sectional variables have the following ranges (note that h1 is discrete, and all dimensions are given in inches):

h1 from the set {0.1, 0.25, 0.35, 0.5, 0.65, 0.75, 0.9, 1}

2.0 ≤ b1 ≤ 12.0

0.1 ≤ b2 ≤ 2.0

3.0 ≤ H ≤ 7.0

### Turn In

Your project report should be typed. Use a 12 pt font and 1 inch margins. Your report should be very thorough, but not necessarily lengthy. As always, use lots of figures to explain the problem and to justify your conclusions. Refer to all figures within the body of the report. Figures are not included in the page length recommendations below.

On the first page, include the pledge:

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

1. Results of the optimization designstudy

a.Explain briefly (~ 0.5 page) the goals of the optimization study in paragraph form. Also include a clear and concise statement of the objectives, constraints and design variables (this statement should not be in paragraph form, but rather in the form that we discussed in class and that you have used in otherassignments).

b.Explainbriefly (0.5‐1.0 pages) your analysis  Provide justification for the type of model used. Describe the equations and all terms in them. Include your Excel model (or a picture of it) in the report.  机械工程作业代写

c.Write a brief (0.5‐1.0 pages) description of the study results, including any interesting observations you can find regarding trends, relationships among the variables and responses, etc. In other words, describe what you learned from the study in addition to the optimal values of the parameters. Include appropriate figures (cut and paste) to justify your conclusions. These figures do not count toward the length recommendation. At the very least, include and discuss the following plots:

• A history plot of the objective versus evaluationnumber
• A 2D relation plot of the objective versus each of the constraints (twoplots)
• A parallel plot containing only the top 10 designs from thestudy
1. Based on this design study, provide answers to the following questions in paragraph format. When possible, use figures to justify your answers.

a.How many evaluations did you use to obtain the optimal solution? How did you determine thisnumber?

b.Which of the constraints are active in this problem? How could you reduce the mass evenfurther?

c.Does the optimized beam shape agree with your intuition? Why or whynot?

### Note regarding the analytical model  机械工程作业代写

Your analytical model should be based on the following beam mechanics equations.

Bending Stress: , where M is the maximum bending moment, c is the distance from the beam cross‐sectional centroid to the outer surface of the beam (H/2), and I is the second area moment of inertia of the beam cross‐section.  机械工程作业代写

Tip Deflection: , where P is the point load at the tip of the beam, L is the length of the beam, E is the modulus of elasticity of the beam material, and I is the second area moment of inertia of the beam cross‐section.

The second area moment of inertia I is calculated as follows: 