Homework Assignment 2 – Fusion of Engineering, Control, Coding, Machine Learning, and Science

Problem Description:

Half of the 2D cross-section of a cylindrical object is shown in the figure below. All the units are in millimeters.

Figure 1: Half of the cross-section of the object. All the units are in millimeters.

Force $F= 5\cdot 10^{5} [N]$ and the boundary condition are introduced in the following figure.

Figure 2: Force $F$ and boundary conditions.

The action of the force $F= 5\cdot 10^{5} [N]$ is localized at the circular region with a radius of $10 [mm]$ .

Perform the following tasks.

Model this objection in Fusion 360, assign boundary conditions and force, and perform static stress analysis. Assume that the object is made of a structural steel (default fusion 360 option).
For every segment (defined by cross sections with constant diameters), analytically compute normal stress using the formula
(1) $\begin{align*}\sigma = \frac{\text{internal force}}{\text{cross-section area}}\end{align*}$

Compare these results with Fusion 360 results. Use the “slice plane” option and “point probes” in Fusion 360 to read the stress value at a cross section.
Why the normal stress value peaks at the points that are close to the action region of the force $F$ ? Use the textbook to provide a solid and scientifically justified explanation.
Using the analytical formula
(2) $\begin{align*}\text{deformation} = \frac{\text{internal force} \cdot \text{length}}{\text{modulus of elasticity} \cdot \text{cross-section area}}\end{align*}$

compute the deformation of every segment. Compare these results with Fusion 360 results. Do results match? Explain the difference?
Can the current design of the object safely carry force $F$ ? Provide a scientifically justified explanation?
Identify the regions of stress concentrations. How would you modify the design such that stress concentration is decreased? To answer this question use the textbook.
Modify the design to introduce significant stress concetration. That is, introduce worst-case stress concentration. Show the 3D model of the modified design. To answer this question use the textbook.

Submission instructions:

Submission deadline is Monday, September 20, at 11 AM (after the class).
Only printed copies should be submitted in person. I do not accept electronic submissions.
Please do not copy solutions from other students. This should be your original work.
Hand-written solutions will not be accepted. You are not allowed to write text and graphs using handwritting. Graphs should be made using appropriate software. You are allowed to write equations using handwritting.
Extra points will be given to students who write everything (equations + text+graphs) using software. A good program for writting engineering homework assignments is Latex. You will get extra points if you use Latex. You can use different Latex editors, a good choice is given here. Below, you can find a video tutorial on how to start with Latex.

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