Lab 1 Solid Modeling

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University of Minnesota-Twin Cities *

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5221

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Mechanical Engineering

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Feb 20, 2024

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docx

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Name: Smile Tongkaw Course: ME5221 Lab 1: Solid Modeling Task 1: Plate with Through Hole For a structure to be mechanically idealized and modeled as a beam needs the relation between the cross- section and the beam. It needs to be a long structure. The length is high compared to the cross-section dimensions. In this lab the width was set up to be half of the length. For this to be an actual beam the width must be much smaller. Plate models with dimensions: Figure I. Plate Hole Model 1 Figure II. Plate Hole Model 2

Name: Smile Tongkaw Course: ME5221 Figure III. Plate Hole Model 3. Creo Program to Alter Variables: Figure IV. Creo Program for Plate Hole. The figure below shows the cross-section screenshot of the first model. It is understood that the highest moment of inertia is found at the beam’s center. The beam’s most vulnerable spot is in the middle of the hole. Figure V. Cross Section Plate Hole 1 st Model.

Name: Smile Tongkaw Course: ME5221 Task 2. Model Size Shelf In this part of the lab, we create a model size shelf. The drawing of the model is shown below as well as the moment of inertia of the model using Creo’s analysis tool. Figure VI. Drawing of Model-Sized-Shelf Figure VII. Moment of Inertia Task 3. Ribbed Plates Mechanical equivalence: For the beam to be mechanically equivalent, they need the same moment of inertia. Using the deflection equation: δ = PL 3 48 EI

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Name: Smile Tongkaw Course: ME5221 The load, length and the elastic modulus are known values. The task is that we make three shelves that are mechanically equivalent. To do that, the moment of inertia for all the shelves must be equal. We compute the total moment of inertia by adding the moment inertia of the top plate and the moment of inertia of the rib. Hence, I total = I top plate + I rib ×R While R being the number of ribs added to a plate. So, y = hwt + wt 2 + R ( b h 2 2 ) wt + Rbh I total = ( wt 3 12 ) + wt ( y − ( h + t 2 ) ) 2 + R ( ( bh 3 12 ) + bh ( y − h 2 ) 2 ) The first equation is to solve for the centroid of the ribbed plate. Then we use that equation to plug into the second equation that solves for the total moment of inertia. While R is a chosen value, from there we use the equations to solve for variables t, b and h which are the thickness of plate, thickness of the rib, and height correspondingly. The first model of the ribbed plate needs to follow one of the constraint values below: 1.2 mm < t < 1.5 mm 12 mm < h < 18 mm 1.0 mm < b < 1.3 mm The first model variables were: t=4.5 mm, h=13 mm, and R=6 solving for b using MATLAB; b=0.86 mm. which h following at least one of the constraints above.

Name: Smile Tongkaw Course: ME5221 Figure VIII. Model of First Ribbed Plate & Moment of Inertia. Figure IX. Drawings of The First Ribbed Plate and Dimensions . The second model variables were: t=3 mm, h=9mm, R=5 and b=4.87. The figures below show the moment of inertia and the drawing of the plate. Figure X. Model of Second Ribbed Plate & Moment of Inertia.

Name: Smile Tongkaw Course: ME5221 Figure XI. Drawings of The Second Ribbed Plate and Dimensions. The third model’s variables were: t=4mm, h=10mm, and R=8, and b=1.55mm. The figures below show the moment of inertia and the drawing of the plate. Figure XII. Model of Third Ribbed Plate & Moment of Inertia.

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Name: Smile Tongkaw Course: ME5221 Figure XIII. Drawings of The Third Ribbed Plate and Dimensions . Task 4. Optimization In this part of the lab, we constructed a rib-plate with only R=1, which means there is only one rib. The goal is to optimize a design to meet the load and deflection requirements while minimizing the volume. The deflection constraint must be less than 5 mm and the load in the center of the plate is 400 N. Figure XIV. Deflection Analysis Coding

Name: Smile Tongkaw Course: ME5221 Figure XV. Optimization and Graph. Figure XVI Measured Volume. The graph shows the optimization of the volume, and it calculated it to be around 30,000 mm 3 .

Name: Smile Tongkaw Course: ME5221 Figure XVII. Drawing of Model. Note: once we run the optimization, the variables change to the maximum value set in the optimization option.

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