Copyright

by

Bennett Alan Ford

2011

The Report Committee for Bennett Alan Ford Certifies that this is the approved version of the following report:

Structural Optimization for a Photovoltaic Vehicle

APPROVED BY

SUPERVISING COMMITTEE:

James T. O’Connor

John D. Borcherding

Supervisor:

Structural Optimization for a Photovoltaic Vehicle

by

Bennett Alan Ford, B.S.

Report

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science in Engineering

The University of Texas at Austin

May 2011

Dedication

This report is dedicated to my wife, Lauren, who has sustained me since the day we met.

v

Acknowledgements

I would like to thank James O’Connor, John Borcherding, and Steve Nelson for

their service as educators and mentors at The University of Texas. I would also like to

thank Ramon Carrasquillo, Make McDermott, and Mark Begert for their roles in

facilitating my education and career. Most importantly, I want to thank my family for

their constant support.

vi

Abstract

Structural Optimization for a Photovoltaic Vehicle

Bennett Alan Ford, M.S.E.

The University of Texas at Austin, 2011

Supervisor: James T. O’Connor

Photovoltaic vehicles are designed to harness solar energy and use it for self-propulsion.

In order to collect sufficient energy to propel a passenger, a relatively large photovoltaic

array is required. Controlling the loads imparted by the array and the body that supports

it, while protecting the passenger and minimizing vehicle weight, presents a unique set of

design challenges. Weight considerations and geometric constraints often lead system

designers toward unconventional structural solutions. This report details analytical and

experimental processes aimed at proving the concept of integrating aluminum space-

frame elements with composite panels. Finite element analysis is used to simulate load

conditions, and results are compared with empirical test data.

vii

Table of Contents

Background ..............................................................................................................1

Chassis Design Development ..................................................................................2

Roll Cage Design Development...............................................................................7

Validation of Simulation Software ..........................................................................9

Chassis Simulation Results ....................................................................................14

Roll Cage Simulation Results ................................................................................19

Buckling Simulation ..............................................................................................25

Physical Model Fabrication ...................................................................................27

Test Gage Placement..............................................................................................29

Load Testing ..........................................................................................................32

Comparison of Simulation and Experimental Results ...........................................37

Conclusion and Further Research ..........................................................................39

Appendix A Nomenclature ...................................................................................40

Appendix B Shop Drawings .................................................................................41

Appendix C CosmosWorks Load Cases ...............................................................44

References ..............................................................................................................45

Vita ... .....................................................................................................................46

viii

List of Tables

Table 1: Theoretical and FEA Results for Stress & Displacement…………….….13

Table 2: Simulation Results……………………………………………………….14

Table 3: Roll Cage Properties……………………………………….…………….19

Table 4: Maximum Stress and Deformation………………………...…………….19

Table 5: Test Strain Readings vs. Simulation Predictions…………..…………….38

ix

List of Figures

Figure 1: Initial Chassis Design……………………………………………...…..….5

Figure 2: Design Concepts with Load Interfaces……………………………...….…5

Figure 3: Adhesive Dispensing Gun…………………………………………………6

Figure 4: Load Conditions……………………………………………………..…….7

Figure 5: Roll Cage Iterations……………………………………………………….8

Figure 6: Validation Test Tube…………………………………………………...….9

Figure 7: Von Mises Visualization………………………………...……………….10

Figure 8: Front Impact Simulation Results…………………..…………………….15

Figure 9: Side Impact Simulation Results………………………………………….15

Figure 10: Stress vs. Location……………………………………………………….16

Figure 11: Displacement vs. Location (front)……………………….………………17

Figure 12: Displacement vs. Location (side)…………………………………...……18

Figure 13: CosmosWorks Stress Visualizations……………………………….…….20

Figure 14: Displacement Visualizations……………………………………….…….21

Figure 15: Distance Along Low Arc vs. Stress………………………………..…….22

Figure 16: Distance Along High Arc vs. Displacement……………………….…….23

Figure 17: Distance Along Low Arc vs. Displacement……………………..……….24

Figure 18: Buckling Test Results for Chassis Test………………………………….25

Figure 19: Buckling Loads and Restraints………………………….……………….26

Figure 20: Pipe Bender………………………………………………………...…….27

Figure 21: Pipe Bending Setup………………………………….......……………….28

Figure 22: TIG Welding Process…………………………………………………….28

Figure 23: Strain Gauge……………………………………………………...……....29

Figure 24: Sanding Process………………………………………………………….29

Figure 25: Cleansing Process…………………………………………….………….30

Figure 26: Aligning a Gage………………………………………………………….30

Figure 27: Attachment of the Gage………………………………………………….31

Figure 28: Strain Gage Setting…………………………………………...………….31

x

Figure 29: Compressing Testing Setup……………………………………..……….32

Figure 30: Data Acquisition Setup…………………………………………….…….33

Figure 31: Strain Gage Placement……………………………………………..…….33

Figure 32: Roll Cage at Moment of Failure…………………………………………34

Figure 33: Load and Displacement vs. Time…………………………...……………35

Figure 34: Gage Strain vs. Time………………………………………………….….35

Figure 35: Load and Displacement vs. Time…………………………...……………37

Figure 36: Strain vs. Time during Compression Testing……………………………38

Figure 37: Final Chassis and Roll Cage Design……………………….…………….39

1

Background Photovoltaic (PV) vehicle design, while not directly aimed at producing automobiles with

immediate commercial potential, is a breeding ground for engineering innovation. The

extraordinary challenge of building a reliable transportation device, powered only by the

sun, encourages innovation in material sciences. The primary goals of PV vehicle chassis

design are to provide safety for the passenger, reduce vehicle weight, maintain structural

integrity under service loads, and provide mounting locations for system hardware.

The scope of this report is the design and testing of a structural system consisting of a

chassis and a roll cage, which act together to carry the design loads of a PV vehicle.

Testing standards given by the American Solar Challenge Regulations (regulations) were

chosen to model the stress and deflection experienced when a PV vehicle chassis is

subjected to collision forces.

A composite honeycomb sandwich panel was selected as a primary structural material

due to its ease of assembly, extremely high specific strength, and simple geometry. Thin-

wall aluminum tube was selected as a roll cage material due to its strength, ductility, and

suitability for space frame construction. Chassis and roll cage designs were iterated

multiple times, with improvements integrated based on the results of finite element

analysis (FEA).

Roll cage testing, conducted by applying normal compressive loading, was performed

using a compression tester provided by the Texas Engineering Experiment Station

(TEES). In order to simulate finite element analysis loading conditions and restraints, a

steel test jig was fabricated to orient the roll cage properly with respect to the testing

machine. A custom fabricated horizontal load-spreader beam was used to apply a

compressive load across the roll hoops. Final test set-up included the strategic placement

of strain gages.

2

Chassis Design Development

Basic geometric parameters were provided by the Solar Motorsports Team (SMT), a

collegiate PV vehicle design group. SMT also specified that the chassis architecture must

include two parallel wheels in the front of the chassis and one wheel in the rear. Vehicle

dynamic considerations dictated that a front tire braking system must be utilized. In order

to ensure proper braking, 60-70% of the total car weight must be statically transferred to

the driving surface through the front tires. To verify this weight distribution, the center of

gravity of all components with considerable weight must be calculated. These

calculations are made based on geometry-specific equations. One such equation used for

the batteries, which have a cubic shape, is given in the following Equation 1 (Barber 46):

〉〈=−−−

kjiinLincg ,,)(*5.0)(3

Where L is the length of a side (1)

Overall chassis weight has significant impact on vehicle dynamics. Newton’s laws of

motion state that force is a product of mass and acceleration given in Equation 2.

(2)

Therefore, lighter materials are desired to allow for rapid vehicle acceleration.

Two classes of materials are generally used for resisting chassis loads: composites and

metals. Fiber reinforced composites tend to have very high specific strengths, but their

properties are typically orthotropic [1] and they tend to be brittle. Metals generally have

isotropic properties and are typically much stronger than composites, but also tend to

have lower specific strengths. Additionally, fabrication techniques for metals are

generally easier to control and test than for composites.

)sec**

(

)sec

()()(

2

2

f

mc

m

f

lbinlb

g

inalbmlbF

∗=

3

Several equations are instrumental in evaluating material stress. For example, normal

stress can be found using Equation 3:

(3)

When analyzing stress failure modes, Von Mises Stress theory is suitable and can be

performed through finite element analysis [2]. The theory states the following in

Equation 4.

2 2 2 2 2 23 3 3E xx yy zz xx yy yy zz zz xx xy yz zxσ σ σ σ σ σ σ σ σ σ σ σ σ= + + − − − + + + (4)

Where σxx, σyy, σzz are planar stress values and σxy, σxz, and σyz are shear values

The Von Mises stress is compared to the yield and tensile strength of the material to

determine whether failure will occur. Deflection of the chassis is also a safety concern in

chassis design. Elastic deflection can be computed by first using Hooke’s Law, shown in

Equation 5, to calculate the strain [2]:

(5)

Once the strain is found, the deflection is calculated through Equation 6, the definition of

strain [2]:

(6)

)()(

)( 2inAlbF

psi f=σ

)()( psiEpsi =ε

σ

)()(

inLinL∆

=ε

4

Both stress and deflection can be estimated by modeling the chassis in three dimensions,

placing appropriate loading conditions, and simulating it using finite element analysis

software.

CosmosWorks is a simulation tool bundled with SolidWorks, a 3D computer drafting

software package. When a simulation is run using CosmosWorks, a factor of safety is

indicated with respect to the type of simulation (stress, displacement, strain, etc). Only a

fraction of the ultimate load capacity of a structural member should be utilized when the

allowable load is applied. The remainder of the load-carrying capacity of the member is

kept in reserve to assure safety. The ratio of the ultimate load to the allowable load is

used to define the factor of safety. The equation for the factor of safety is given in

Equation 7.

(7)

An alternate expression to satisfy the definition of factor of safety is shown in Equation 8.

)(

)(.psitressAllowableS

psiressUltimateStSF = (8)

The initial chassis design is shown in Figure 1. The stress results calculated in Cosmos

Works were used to generate plots in Microsoft Excel.

)()(

..f

f

lboadAllowableLlbadUltimateLo

SF =

5

Figure 1: Initial Chassis Design

Figure 2: Design Concepts with Load Interfaces

6

Figure 2 shows all of the chassis designs analyzed. Design geometry for the chassis was

largely dependent upon fabrication techniques. The construction of the chassis requires

that the honeycomb composite panels be glued together at all joints. For this process a

two-part epoxy, 3M Plexus™, was chosen . Plexus™ epoxy has a tensile strength of

approximately 22 Mpa and lap shear strength of 22 Mpa. In a 23°C ambient environment

the glue has a 4-6 minute working time and achieves 75% strength in 15 minutes. The

glue is dispensed from the hand-held gun shown in Figure 3. The glue is applied between

all joints and also used as a filleting compound along perpendicular joints.

Figure 3: Adhesive Dispensing Gun

7

Roll Cage Design Development

Geometry for the roll cage was partially driven by the geometry of the chassis. The

design also needed to take into account the size of the driver, the height limitations given

by the body assembly, and the specifications given by the regulations. The SMT required

that the roll cage and chassis be large enough to fit a person 74 inches tall with a 36”

waist.

Beginning with the three-dimensional SolidWorks model of the preliminary chassis

design, designs were tested and modified based on FEA simulations. Various load cases,

were simulated for each design. Figure 4 shows the loading conditions that the roll cage

must withstand to comply with the regulations.

Figure 4: Load Conditions

8

Figure 5: Roll Cage Iterations

The second and third design iterations focused on reducing the weight of the roll cage.

With the back and front planes of the roll cage fixed in size by regulations constraints, the

primary methods available for doing so were to reduce wall thicknesses and optimize

brace geometries.

9

Validation of Simulation Software

In order to check the accuracy of the simulation software with respect to tubular roll

cages, a solid model of a simple Aluminum 6061 pipe was generated in SolidWorks.

Figure 6: Validation Test Tube

The tube was constrained at one end while a normal applied load of 1238 lbf was applied

to the opposite face. The tube was assigned material properties such as the modulus of

elasticity, Poisson’s ratio, yield strength, and tensile strength. A solid mesh was

incorporated into the model with a node element size that was smaller than the pipe

thickness to ensure that the entire model was meshed. The simulation was run and Von

Mises Stress and displacement values were recorded.

In order to directly compare theoretical results to the FEA values, exact model

dimensions and material specs were incorporated into the theoretical equations. To enable

calculation of both Von Mises and displacement, several factors were first computed then

embedded into their respective governing equations. First, the cross-sectional area of the

pipe was found from Equation 9.

10

(9)

Where A = cross sectional area, d0 = outer diameter, di= inner diameter

Von Mises stress can be found from Equation 10.

2 2 2 2 2 23 3 3E xx yy zz xx yy yy zz zz xx xy yz zxσ σ σ σ σ σ σ σ σ σ σ σ σ= + + − − − + + + (10)

The formula above can also be rewritten as shown in Equation 11.

( )2 2 2 * * *E L circ rad L circ rad circ L radσ σ σ σ σ σ σ σ σ σ= + + − + + (11)

Where Lσ = longitudinal stress, circσ = circumferential stress, radσ = radial stress

Visually, this concept can be seen as:

Figure 7: Von Mises Visualization

σ 1 IS LONGITUDINAL STRESS σ 2 IS CIRCUMFERENTIAL STRESS σ 3 IS RADIAL STRESS "a" IS OUTSIDE RADIUS OF SECTION

"b" IS INSIDE RADIUS OF SECTION

"L" IS LENGTH OF SECTION

"r" IS RADIUS AT SELECTED SECTION

( ))()(4

)( 22222 indindinA io −=π

11

Longitudinal stress:

(12)

Asect = section area (in2); F = applied mechanical load (lbf)

Circumferential stress on internal diameter element:

(13)

Pi = internal pressure (psi); Ro = outer radius (in), Ri = inner radius (in)

Circumferential stress on outer diameter element:

(14)

Radial stress on internal diameter element:

(15)

Radial stress on external diameter element:

(16)

tL A

F

sec

=σ

22

22

22

22 )(

io

oext

io

ioicirc RR

RPRRRRP

ID −∗

−−+

=σ

22

22

22

22 )(

io

ioext

io

iicirc RR

RRPRRRP

OD −+

−−∗

=σ

irad PID −=σ

extrad POD −=σ

12

Displacement equations were adopted from Zienkiewics’ The Finite Element Method.

Equations 17 through 19 allow for calculation of the generated outside and internal

diameters as well as the new section length once loading conditions are applied. These

equations are illustrated below:

Outside Diameter under load:

22 2 2 2

2 2 2 2( )i o i ext o o i

o oo i o i

P R R P R R RD RE R R E R R

υ⎡ ⎤⎛ ⎞∗ ∗ ∗ +

= + − −⎢ ⎥⎜ ⎟− −⎝ ⎠⎣ ⎦ (17)

E = modulus of elasticity (psi), υ = Poisson’s ratio (dimensionless)

Inside Diameter under load:

(18)

Section length under load:

( ) ( ) tt

io

otext

io

ititt AE

lFRRE

RlPRRE

RlPlL

sec

sec22

22sec

22

22sec

secsec ∗∗

+−

∗∗∗+

−∗∗∗

−=εε

(19)

All calculations presented in this section were embedded into a Microsoft Excel

spreadsheet. Final stress and displacement values from the FEA and theoretical

computations are presented and compared (in terms of percent difference) in the

following table:

( )2

22

22

22

22

⎥⎦

⎤⎢⎣

⎡

−∗∗

−⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+∗

+=io

ioext

io

ioiiii RRE

RRPRRRR

ERPRD ε

13

Table 1: Theoretical and FEA Results for Stress & Displacement

VON MISES STRESS (PSI)

OVERALL DISPLACEMENT (IN)

FINITE ELEMENT 3720 8.1770E-03 ANALYSIS

THEORY 3699 8.1101E-03

PERCENT DIFFERENCE 0.54 0.818

Clearly the theoretical and simulation values display good agreement. This result

suggests that the FEA protocol used in the validation test is suitable for roll cage

simulation.

14

Chassis Simulation Results

The stresses and deflections for all four designs in the five regulation-driven loading tests

are presented in Table 2. Safety factors are also displayed in the table.

Table 2: Simulation Results

DESIGN CASE

Von MisesMAX

STRESS (psi)

MAXDEFLECTION

(inches)

Safety factor for

plasticdeformation

Safety factor for

failureSMT original 3 g bump 3744 0.05401 3.07 3.60

5 g front 2803 0.5426 4.10 4.81(First Design) 5 g rear 19610 1.044 0.59 0.69

5 g side 7500 1.733 1.53 1.803g angular 7845 1.669 1.47 1.72

Triangle Design 3 g bump 3702 0.0527 3.11 3.645 g front 2943 0.4846 3.91 4.58

(Second Design) 5 g rear 6896 0.2032 1.67 1.965 g side 3100 0.4014 3.71 4.35

3g angular 8793 1.625 1.31 1.53Beam Support Design 3 g bump 3711 0.05448 3.10 3.63

5 g front 2496 0.2928 4.61 5.40(Third Design) 5 g rear 3090 0.1898 3.72 4.37

5 g side 2253 0.0833 5.10 5.993g angular 8747 1.576 1.31 1.54

Fillets Focused Design 3 g bump 3720 0.05582 3.09 3.635 g front 1845 0.295 6.23 7.31

(Fourth Design) 5 g rear 4449 0.1817 2.58 3.035 g side 1675 0.079 6.87 8.05

3g angular 8743 1.607 1.32 1.54

CosmosWorks visually displays the results by color-coding areas where the differing

levels of stress and deflection are experienced. Figures 8 and 9 show these results for the

front and side CosmosWorks simulations.

15

Figure 8: Front Impact Simulation Results

Figure 9: Side Impact Simulation Results

Several graphs were produced to display directional stress and deflection behavior of the

designs for the various simulations. Figure 10 displays the stress behavior experienced

16

during the front impact test while Figures 11 and 12 compare displacement for the front

and side tests, respectively.

Figure 10: Stress vs. Location

Figure 10 compares the stress values experienced laterally across the front panel during

the front impact test. These results show that the minimum stress occurred along the front

corners of the chassis where the sides connected to the front.

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30

Stre

ss (p

si)

Displacement along Z-axis (in)

Original DesignTriangle DesignBeam DesignFinal Design

17

Figure 11: Displacement vs. Location (front)

Figure 11 compares the displacement values experienced laterally across the front panel

during the front impact test. The beam design experienced the lowest total vertical

displacement with the final design demonstrated the second smallest displacement.

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0 5 10 15 20 25

Verti

cal D

ispl

acem

ent (

in)

Distance along Z-axis (in)

Original Design

Triangle Design

Beam Design

Final Design

18

Figure 12: Displacement vs. Location (side)

Figure 12 shows the deflection experienced across the side of the chassis. The deflection

of the final design is significantly reduced by linking the chassis sidewalls.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 10 20 30 40 50 60 70

Disp

lace

men

t (in

)

Distance Along X-Axis (in)

Original Design

Triangle Design

Beam Design

Final Design

19

Roll Cage Simulation Results

Table 3 indicates the mass properties of the roll cage assembly iterations.

Table 3: Roll Cage Properties

Design Volume (in3) Total Length (in) Total Length (ft) Mass (lbm)

Original Design 105.40 316.87 26.41 10.28

Second Design 105.14 316.09 26.34 10.26

Final Design 106.65 320.62 26.72 10.40

A load of 1500 lb force, which is 3 times the expected weight of the vehicle, was applied

over the top plane of the car which gave a direct force to the high and low roll hoop arcs.

Table 4: Maximum Stress and Deformation

DESIGN CASEVon Mises

MAX STRESS

MAXDEFLECTION

(inches) Safety Factor for

Plastic Deformation

Safety factor for

failure

Original Design 3g 16100 0.5564 0.71 0.84

Second Design 3g 18275 0.07531 0.63 0.74

Final Design 3g 15960 0.04511 0.50 1.13

20

Figure 13: CosmosWorks Stress Visualizations

21

Figure 14: Displacement Visualizations

22

Figure 15: Distance Aong Low Arc vs. Stress

Figure 15 shows that the average and peak stress differences along the lower arc between

each of the designs is small. The final design shows the smallest average of each of the

stress values which was important for choosing among the designs.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

4 9 14 19

Stre

ss (p

si)

Distance Along Lower Arc (in)

Original Design

Second Design

Final Design

23

Figure 16: Distance Along High Arc vs. Displacement

Figure 16 shows the distribution of displacement values experienced at the high arc in

each of the designs. The final design demonstrates the lowest displacement values.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

4 6 8 10 12 14 16 18

Vert

ical

Dis

plac

emen

t Exp

erie

nced

(in)

Distance Along High Arc (in)

Original Design

Second Design

Final Design

24

Figure 17: Distance Along Low Arc vs. Displacement

Figure 17 shows the distribution of displacement values experienced at the low arc in

each of the designs. The final design displays the smallest deflection among the designs.

0

0.01

0.02

0.03

0.04

0.05

0.06

4 9 14

Ver

tica

l Dis

pla

cem

ent

Exp

erie

nce

d (

in)

Distance Along Low Arc (in)

Original Design

Second Design

Final Design

25

Buckling Simulation A section equivalent to the vertical front section of the chassis was utilized for local

buckling analysis, and a total load of three times the total vehicle and passenger weight

(1500 lbf) was placed normal to its top surface. The bottom surface of the piece was

fixed, and buckling analysis was conducted. The resulting deformation visualization,

including the load and restraint, are shown below:

Figure 18: Buckling Test Results for Chassis Test

26

To simulate tube buckling, a test case was set up for the longest tube member on the roll

cage. CosmosWorks produced a load factor of 1.2658. Figure 19 shows the manner in

which the loads and restraints were applied to the pipe.

Figure 19: Buckling Loads and Restraints

27

Physical Model Fabrication

Aluminum (6061 T6) with a side wall thickness of 0.113 in was used for the construction

of the roll cage. A circular saw with a metal cutting blade was used to cut the Aluminum

pipe. A hydraulic pipe bender was used to create the bends in the front and rear hoops of

the roll cage, as shown in Figure 20. A 220V Lincoln Electric square wave TIG welder

was used to weld the individual roll cage components. Pure tungsten electrodes, Argon

gas, and Aluminum 4043 filler rods were the consumables used in the welding process

Figure 20: Pipe Bender

For this particular roll cage design, the front and rear hoops of the roll cage are formed

from bending straight pieces of aluminum.

28

Figure 21: Pipe Bending Setup

The power setting on the welder was AC current mode with a 160 amp maximum power

setting.

Figure 22: TIG welding process

Hydraulic Jack

Roller

29

Test Gage Placement

In order to measure strains during empirical testing, 10 strain gauges were attached to the

roll cage.

Figure 23: Strain Gage

After the gage locations were marked on the tubes, a smooth surface was prepared by

light sanding.

Figure 24: Sanding Process

To cleanse the surface, Methanol was applied swabbed at all gage locations.

30

Figure 25: Cleansing Process

Cellophane tape was used to transfer the gages to the tubes. This process is shown in

Figure 26 and Figure 27.

Figure 26: Aligning a Gage

31

Figure 27: Attachment of the Gage

Finally, the gages are bonded to the tubes using M-Bond AE-10 adhesive. Figure 28

shows the final setting of a strain gage with wires attached.

Figure 28: Strain Gage Setting

32

Load Testing

The testing apparatus for the roll cage can be seen in Figure 29.

Figure 29: Compression Testing Setup

The signal wires were attached to an input device that sends the strain gage readings to

the monitoring computer. Figure 30 shows how the wiring is attached to the input

system.

33

Figure 30: Data Acquisition Setup

Figure 31: Strain Gage Placement

3

4

5 67

8

12

9

34

The compression testing machine was set to advance at one half an inch (1/2 in) per

minute. Figure 32 shows the position of the roll cage in which it was determined that the

cage had failed. The failure occurred in the lower arc of the specimen while the high arc

did not appear to undergo measurable permanent deformation. The higher arc is the more

critical of the two arcs because it protects the driver’s head.

Figure 32: Roll Cage at Moment of Failure

The results of compression test recorded by the data acquisition system displayed the

load and displacement of the compressor in relation to the duration of the experiment

shown in Figure 33. Additional results, shown in Figure 34, give the strain experienced

by the tube members of the roll cage with their respective strain gages attached.

35

Figure 33: Load and Displacement vs. Time

Figure 34: Gage Strain vs. Time

36

The roll cage withstood forces reaching nearly 6000 lbs. about 100 seconds into the test,

after which it began to experience plastic buckling and effective failure. The 6000 lbs.

withstood by the roll cage is well above the 1500 lb. minimum set forth in the

regulations.

37

Comparison of Simulation and Empirical results

Strain gages placed throughout the physical model during the testing allowed observation

of exactly what force magnitude the individual roll cage members experienced. This, in

turn, allows comparison with the FEA simulation Using Figures 35 and 36, it is known

that 1500 lb force was applied 50 seconds into the test.

Figure 35: Load and Displacement vs. Time

50 seconds is when load equals to 1500 lbs

38

Figure 36: Strain vs. Time during Compression Testing

Strain values that intersected with the time of experiment of 50 seconds correlate to a

1500 lb load. These values are listed in Table 5.

Table 5: Test Strain Readings vs. Simulation Predictions Strain Gages Strain - Physical Test Strain - Computer Model Percent Difference

1500 lb 1500 lb1 0.1400% 0.1350% 3.70%2 0.0800% 0.0760% 5.26%3 0.0100% 0.0113% 11.50%4 0.0050% 0.0048% 4.17%5 0.0015% 0.0017% 11.76%6 0.1250% 0.1385% 9.75%7 0.1250% 0.1320% 5.30%8 0.0020% 0.0015% 33.33%9 0.0150% 0.0130% 15.38%

50 seconds is when load equals to 1500 lbs

39

Conclusion and Further Research

Figure 37 illustrates the final chassis and roll cage designs. For tubular and composite

panel elements and assemblies, it has been demonstrated that CosmosWorks can provide

accurate simulations of stress and deflection behavior. However, further research will be

required to validate interface connections between space frames and composite panels

that ensure adequate fatigue life.

Figure 37: Final Chassis and Roll Cage Design

40

Appendices

Appendix A, Nomenclature

2

2

2sec

ina=Acceleration ( )sec

A=Area (in )Section Area (in )

Center of Gravity

Inside Diameter (in)Outside Diameter (in) Modulus of ElasticityForce ( )

Critical Force to cause Buckling

t

g

i

o

f

cr

Ac

ddEF lb

F

==

=

=

==

=

4

m

( )

. . Factor of Safety (dimensionless)Moment Area of Inertia (in )Length (in)

Change in Length (in)Critical Length for Buckling (in)

m=Mass (lb )Internal Pressure (psi)

External Pr

f

c

i

ext

lb

F SIL

LL

PP

=

==

∆ ==

==

xx

yy

xy

essure (psi)Inner Radius (in)Outer Radius (in)

=Stress (psi)Von Mises Stress (psi)Stress in X-Direction (psi)Stress in Y-Direction (psi)

Stress in Z-Direction (psi), , Shea

i

o

E

zz

yz xz

RRσσσσ

σσ σ σ

=

=

===

==

L

circ

rad

r in respective Plane (psi)

Longitudinal Stress (psi)Circumference Stress (psi)Radial Stress (psi)

Strain (dimensionless)Poisson's Ratio (dimensionless)

σσσευ

==

=

==

41

Appendix B, Shop Drawings

42

43

44

Appendix C, CosmosWorks Load Cases

CASE

575 lb TOT.WEIGHTMULT.

FACTORFORCE

lbf

SURFACE AREA FORCE APPLIED

(IN2)PRESSURE

(PSI)3 g bump 3 1725 10.5 164.295 g front 5 2875 183.113 15.705 g rear 5 2875 258.017 11.145 g side 5 2875 89.695 32.05

3g angular 3 1725 N/A N/A3 g bump 3 1725 10.5 164.295 g front 5 2875 182.504 15.755 g rear 5 2875 270.7 10.625 g side 5 2875 89.693 32.05

3g angular 3 1725 N/A N/A

Fillet Focused Study

APPLICABLEDESIGN(S)

Original Study

Triangle studyBeam support study

45

References

1. “American Solar Challenge 2005 Regulations.” November, 2003. http://www.americansolarchallenge.org/event/asc2005/tech/asc2005Nov03.pdf (2 June, 2004) 2. Barber, J.R. Intermediate Mechanics of Materials. Boston: McGraw-Hill, 2001. 3. Callister, William D. Fundamentals of Materials Science and Engineering. 5th ed. New York: John Wiley & Sons, 2001. 4. Zienkiewics, O.C. The Finite Element Method. 3rd ed. London: McGraw-Hill, 1979. 5. Vishay Measurements Group, Inc. Student Manual for Strain Gage Technology USA: TD, 1997

46

Vita

Bennett Alan Ford was born in Dallas Texas. After graduating from Highland

Park High School, he entered Texas A&M University. There he developed an interest in

automotive engineering and photovoltaic energy through involvement in Formula SAE

and Solar Motorsports projects. He graduated with a Bachelor of Science and moved to

Austin, where he began working in the photovoltaic energy industry. Bennett enrolled in

graduate school at the University of Texas in January, 2010.

Email: bennettford@gmail.com

This Report was typed by the author.