PROJECT #1: DESIGN FOR DEFLECTION ME-42ProfessorChiesaandProfessorLeisk

ShreyanshAgarwal,EvanSlack,DylanWagmanNovember5,2019

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EXECUTIVE SUMMARY

This paper is our analysis of the Phase II part of Project 1, for our Tufts University ME-42 class.

The purpose of this paper is to convey our design process and our analysis of the testing

performed.

The estimated vertical deflection for our conservative structure, at the load, as computed using

Castigliano’s method was 0.277 inches downward, in the direction of the force. The numerical

result of our SolidWorks FEA simulation, for the same conservative structure, predicted a total

deflection of 0.200 inches and a vertical deflection of 0.181 inches downward, in the direction of

the force. This discrepancy is likely due to the discrepancy between the simulation conditions.

This is further analyzed in the Castigliano’s method section of the report. The test results for this

structure indicated a deflection of about 0.15 inches and a spring constant, 31.018 lbf/inch.

For the efficient structure, the numerical result of our SolidWorks FEA simulation predicted a

deflection of 0.200 inches downwards. The actual test results indicated a deflection of about

0.142 inches with a spring constant of 34.221 lbf/inch.

This discrepancies between our predicted and actual results are likely due to a number of factors

including, actual thickness, actual Young’s modulus, and mis-interpreting the SolidWorks

deflection plots. These will be analyzed in this report.

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Table of Contents

EXECUTIVE SUMMARY..................................................................................................................................1

INTRODUCTION.................................................................................................................................................3

APPROACH............................................................................................................................................................4

I) SOLIDWORKS SIMULATION..........................................................................................................................6CONSERVATIVE STRUCTURE................................................................................................................................6EFFICIENT STRUCTURE.........................................................................................................................................9II) CASTIGLIANO’S METHOD FOR CONSERVATIVE STRUCTURE...........................................................11

TEST RESULTS.................................................................................................................................................13

DISCUSSION.......................................................................................................................................................15

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INTRODUCTION

The overall goal of this project was to utilize different methods for computing deflection to

design an acrylic structure. This structure should experience elastic, linear deflection to the

specified amount with a given load. Maximum deflection at the load was calculated with the

strain energy method (Castigliano’s Theorem) as well as with SolidWorks’ Simulation Finite

Element Analysis. Both a weight independent, conservative, and a weight dependent, efficient,

acrylic structure were designed. The designed structures were then laser cut and tested on an

Instron testing device. The estimated deflection was then compared to the actual deflection. The

acrylic used in this experiment had Young’s modulus, E, of 379,000 psi and a yield strength of

6,527 psi.

Specifically the project phase II goal was for both structures to deflect 0.2 inches with an applied

force of 5 lbs. These designs had to conform to a given design space and loading areas (Figure

1). The goal of the efficient structure was to hit the same deflection as the conservative under the

same loading conditions, however with the weight of the structure, hence the amount of material

used, to be minimal.

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APPROACH

FIGURE 1: Design Space, loading located at uppermost circle

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FIGURE 2: Conservative Structure Drawing and Dimensions

FIGURE 3: Efficent Structure Drawing and Dimensions

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ANALYSIS

I) SolidWorks Simulation

Conservative Structure

FIGURE 4: Conservative structure, deflection at load, predicted thickness 0.23 inches

FIGURE 5: Conservative structure, vertical deflection at load, predicted thickness 0.23 inches

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FIGURE 6: Conservative structure, vertical deflection at load, actual thickness 0.237 inches

FIGURE 7: Conservative structure, stress analysis, actual thickness 0.237 inches

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FIGURE 8: Conservative structure, mesh analysis

FIGURE 9: Conservative structure, aspect ratio of mesh analysis

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Efficient Structure

FIGURE 10: Efficient structure, deflection at load, predicted thickness 0.23 inches

FIGURE 11: Efficient structure, vertical deflection at load, actual thickness 0.237 inches

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FIGURE 12: Efficient structure, stress analysis, actual thickness 0.237 inches

FIGURE 13: Efficient structure, mesh analysis

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FIGURE 14: Efficient structure, aspect ratio of mesh analysis

II) Castigliano’s Method for Conservative Structure

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Finite Element Method Comparison:

FEM for vertical deflection with a predicted thickness of 0.23 inches was: 0.181 inches

downward

Castigliano’s method vertical deflection with the same thickness was: 0.277 inches downward

Difference between the values: 42%

This discrepancy is likely due to the discrepancy between the simulation conditions. For

instance, the loading conditions in the FEA simulation accounted for a fixed hinge and roller

reactions, whereas the Castigliano’s approach idealized both reactions as rollers. This is due to

the lack of force in the x-direction in the simplified model. Additionally, the simplified

Castigliano model does not account for the holes in the structure, and the exact locations of the

loading and restriction conditions.

Although the numbers were off, Castigliano’s method was only about 0.1 inches different from

the FEA analysis, deemed as the more correct model. This indicated that our approach was on

the right track, and no glaring discrepancy was present.

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TEST RESULTS

IMAGE 1: Conservative structure, max load IMAGE 2: Conservative structure, after loading

IMAGE 3: Efficeint structure, max load IMAGE 4: Conservative structure, after loading

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The data in both graphs above (Figure 15 and 16) enforce the goal of our design, to enable linear

elastic performance. This can be seen by the linear slope of the lines of best fit and in the images

(Image 1-4) above. These images show that even after the max load is applied, the structures

return to their original shape. Although the data behaves linearly, there is a discrepancy between

our performance and the target performance. Both graphs indicate a similar deviation from the

target slope of 25 lbf/inch and -0.2-inch y-intercept. This indicates that both models likely

experienced the same experimental and systematic error. These errors could be due to the

structures’ variation in thickness from the predicted thickness, experimental environmental

conditions, and a systematic design error. Looking at the shape of the data for the conservative

structure (Figure 15), a stick-slip pattern can be noticed. This is potentially due to excessive

friction at the hinge support (free to rotate) as during test performance the structure was observed

moving with a jerk in regular intervals.

FIGURE 16: Efficient structure, Instron machine loading test results

FIGURE 15: Conservative structure, Instron machine loading test results

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DISCUSSION

Our results differed from our initial FEA predictions due to a number of likely factors. First of

all, we were probing for total deflection instead of just vertical deflection at the load. After the

results were recorded and this common mistake was discussed in class, we went back and re-ran

the simulation. We changed the thickness to a more accurate value for our structures (.237in and

.238in for conservative and efficient models respectively) and changed the deflection definition

to show the vertical deflection. This new simulation predicted values that were much closer to

the observed deflections. The actual deflection of our conservative structure was approximately

0.154 inches while our final FEA predicted 0.175 inches. The actual deflection of our efficient

structure was 0.140 inches while our FEA predicted 0.147 inches. In both cases the actual

structures deflected less than their respective predictions. There are multiple possible reasons for

these discrepancies.

Firstly, the actual young’s modulus of the acrylic used might be slightly higher than the value

used in our calculations and simulations. We were working with a value of 379,000 psi for the

Young’s modulus, but it is likely that the actual young’s modulus was closer to 400,000 -

410,000 psi.

Secondly, previously induced thermal strain was not accounted for and could have contributed to

the difference in results. Right before performing the test, when the efficient structure was put

under the strain viewer, quite a few locations, especially in the efficient structure, appeared red.

This can partially be seen in Image 4. This could be due to the thermal strain that was induced on

the structure by the laser cutter and could be the reason behind the discrepancies seen between

the FEA deflection and the final test deflection for the efficient structure.

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Another reason for the discrepancies could be the friction present at the roller support. Although

not accounted for in the FEA analysis, a stick-slip behavior was observed while conducting the

test and could certainly be a prominent factor contributing to the difference in results. Further,

the roller support was modelled to be present on only part of the cross section of the hole on the

right side. However, during the test, a circular rod was inserted into the hole, thus providing

support to the entire cross section of hole. This could be a factor behind the discrepancies

between the FEA model and the test.

When modelling our efficient structure, we aimed to hit the 0.2-inch deflection while reducing

the overall weight of the structure. This was achieved by removing material from the inner

portion of the structure. The trade-off of removing material is that the same amount of force is

applied over a smaller amount of material, therefore the overall stress will increase. We had to

inspect the FEA stress study to ensure that no single area of the structure had a stress greater than

the yield stress of acrylic (6,527 psi). Areas of concern that showed high stresses had their cross-

sectional areas increased to alleviate stress. Overall, no single area was close to having a stress

greater than the yield stress, so we were confident that the structure would not break. Our

calculations proved correct as neither model broke during testing.