hm and optistruct and lit review

8/9/2019 HM and OptiStruct and Lit Review

http://slidepdf.com/reader/full/hm-and-optistruct-and-lit-review 1/19



In addition to shaving weight composite materials allow bicycles to haveimproved elastic properties. $ased on how you manufacture composites youcan customi"e how much they bend and how much they resist bending2these properties are called compliance and sti*ness respectively and are

opposites of each other. $ecause energy is most e5ciently transferredthrough sti* members a torsionally sti* bottom bracket and head tube aredesirable. although it may not be noticeable if a frame has a tendency totwist from side to side with each pedal stroke the rider will expendunnecessary energy. In addition to conserving energy lateral sti*ness alsoprovides better handling. Improved in(plane vertical compliance means thatthe bicycle can 6ex up and down a little in order to absorb sudden shocksand vibrations for the road ultimately resulting in a more comfortable andstable ride.

Composite Materials

7everal materials can be combined in di*erent con#gurations to createcomposite materials which can be given enhanced properties than thosefound in each one of the composing materials individually. 7uch is the casewith carbon #ber which is made by bounding a series of long thin #bers of carbon with epoxy to create a lamina. $y themselves epoxy and carbon arerather weak materials but by strategically combining them they can begiven properties that surpass those of common metals.

'hen manufacturing composites using unidirectional #ber composites eachlamina can be arranged with a di*erent orientation. The overall #ber layup

can therefore be tailored to optimi"e the behavior of the structure itcomposes.

&sing )yper'orks I #nd optimal the #ber orientation and layer thickness tobetter respond to the loading conditions.

Force Analysis

The frame of the bicycle is the main structure designed to support the mainexternal loads. A pedaling force from the rider is transmitted through a chainmechanism and is made to rotate a rear wheel thus propelling the bicycle

and rider forward. 8oing a simpli#ed analysis of the transmission of powerthe bicycle experiences it can be seen that forces come from the rider at #vekey locations9 two at the handlebar one on each pedal and one on thesaddle. As the rider shifts position . A rider may alternate between sitting andstanding positions e*ectively shifting his weight between the front and readof the bicycle as well as vary the application of forces from side to side.8uring intense pedaling a left pedal stroke is couple with a downward andupward force on the left and right end of the handlebar respectively.



An often overlooked point noted by : %aestrelli in ;< is that due to thestandard placement of the chain on the right side of the bicycle causes thatthe loading conditions associated to the push of the right and left pedal areasymmetric.

There is a contact point at the location where each wheel meets the ground.At each of these contact points the play of forces aboard the bicycle iscountered by a normal force and a traction force perpendicular to thedirection of travel of the wheel. The balance of forces and its relationship tothe geometry of the bicycle determines the direction of travel or whether thebicycle is able to stay up or go around turns.

Structural Analysis

It is important to overstate the importance of structural analysis of the frame

when designing a bicycle. The strength and sti*ness of a bicycle can bepredicted and modi#ed by coupling the theoretical understanding of mechanics of composites and structures with the use of computer modelingtechniques such as Finite Element Analysis.



Motivations

8esign lighter bikes that can be ridden faster and for longer.

-ptimi"e performance minimi"e weight.

Flexing of rear triangle to absorb shock.



Hypermesh

The bicycle frame model was designed on 7olid'orks based on the general

dimensions of a =ocky %ountan $li""ard bicycle.

Each tube that composes the frame was considered as an individual section.



$ottom bracket concentrated loading from rider>s weight as well as a

moment



Material

The material used for this simmulation is A703?41@( carbonn #ber and its

properties are as follows9

AS!"#$%&'

tB1.114

[email protected]

[email protected]@e

C@B1.?

[email protected]

GTB??1e?

G,B(1e?

HTB.4e?

H,B(?4e?

7B0e?



8e6ection analysis



Optimization

Finite Element 7tructural -ptimi"ation methods are ways of applyingtraditional optimi"ation algorithms to structural design problems using FiniteElement Analysis. ,ompared to standard mathematical techniques these

methods have the advantage of being able to analy"eotherwise cumbersome numerical problems and of providing a visualrepresentation of the optimal results. ;%arco ,ava""uti<

,ommon optimi"ation methods in mechanical engineering

• Topology optimi"ation

• Topometry optimi"ation

• Topography optimi"ation

• 7i"e optimi"ation

• 7hape optimi"ation

As with the numerical methods necessary elements used for structuraloptimi"ation are9

• 8esign space meshJ

•

Cariables thickness angle massKJ

• -ptimi"ation constraints measurement sti*ness displacement

stress strain failure hill etcJJ

• -b!ective functionmin3max3minmax3maxminJ %inimi"e mass

maximi"e vertical compliance maximi"e lateral sti*ness etc

• -ptimi"ation Algorithm gradient based mmaJ

• In the case of topology topometry topography@8 or shell elementsJ

and si"e optimi"ation the element density can vary between 1 voidJand presentJ



Optimization

-b!ective9 %inimi"e Colume massJ of chain stay

,onstraint9 8isplacement

:ower boundB.0

&pper [email protected]

Cariables9 thk thk@ thk? thk0

The layers are symmetric about the middle axis. This results in there being

0 di*erent ply orientations ? of which have a corresponding match about themid(plane. This allows for the use of only 0 design variables which simpli#es

calculations.



Optimization results

Through the -pti7truct %odule the ob!ective function was minimi"ed

throughout 4 iterations. The volume of the chain stay can be seen to go

from around .? to 1.@ cmL?.

It can be seen that in iteration 0 and the maximum constraint ondisplacement was violated. The thickness was reduced too much which

caused the displacement to go over the constrain limit.



The following image shows the #nal thickness of each set of layers. The

results show that the mid plane should be the thickest layer.



Conclusion

The analysis shows results that are numerically o* to those that would apply

to a real life model but give insight to how much e*ect each variable has in

the behavior of the frame. There is more work and learning to be done inorder to improve the modeling and optimi"ation.

In the future a large part of the frame will be created using simpli#ed hollow

pipe structures directly on )yper%esh to avoid the meshing complications

that #le importing brought along.



(iterature )evie*

An early use of Finite Element %ethods for bicycle design was done byMaterson and :ondry in / ;< who represented a tubular frame structure

using eulerian beam elements and measured their respective de6ectionvon %ises stress and strain energy under various loading conditions. Theirrudimentary study laid down important grounndwork and proved theusefulness of FE% techniques in the design of bicycle frames. Their #ndingsshowed that energy dissipation in the vertical direction could be increasedwith minimal negative e*ect on hill climbing when pedaling out of the saddleand that the down tube was the greatest ebsorber of train energy.

In //0 :essard et al also modeled tubular frames using beam elements andcompared the analysis of several frame designs to experimentalmeasurements focusing on maximi"ing the vertical compliance and lateral

sti*ness. )e emphasi"ed that in the classical tubular diamond shape framestructure problems arose at the !unction between tubes.. In his study :essardstudied and identi#ed the boundary conditions that a frame would encounterduring realistic riding conditions and narrowed them down to threegenerali"ed loading cases9 braking front impact and stand up peadling. )eused arbitrary loads and comments that the choice of load to apply isarbitrary since he was only studying displacement and the tests are donewithin the elastic limit of the material.

)e suggests that composite bicycle frames should be composed of amonocoque structure in which loads are supported through a low mass skin

of a large surface area therefore improving sti*ness characteristics. $ecausethe ideal racing frame should e*ectively transfer human energyt hat therider puts into the pedals and handlebar with minimal losses due to theframe. )e suggests a torsionally sti* bottom bracket and head tube asenergy is most e*ectively transfered through sti* members. )e adds that theframe should allow for in(plane vertical compliance to dissipate road surfaceforces. :essard comments that there is room for study of the relationshipbetween quanti#able frame sti*ness characteristics and qualitativedescription of the experience of the rider.

8erek ,ovill used parametric #nite element analysis of bicycle framegeometries to study the vertical compliance and lateral sti*nesscharacteristics of @ existing bicycle frames. )is results showed that smallerframes behave most favourably in terms of vertical compliance and lateralsti*ness and that a shorter top tube length and larger head tube angleresult in a laterally sti*er frame. )e suggests that there is further room fordevelopment of the study regarding a more detailed tube geometry the useof alternative materials and analysis of of other structural characteristics.



Maolo $alisedra used the FE% software )yper%esh to study four di*erentbicycle fork designs and used eight di*erent quasi(isotrpoic laminatesgenerated using the )yper:aminate module. )e notes that the virtual modelrepresents an ideal component and neglects possible defects that may

occurr during the manufacturing process such as porosity wavyness or plydrops. The results were used to validate the use of a manufactured framewhich was subsequently used for races through a total distance of around411 km. The fork was later submitted to lateral static load tests and showedno signi#cant redution in sti*ness.

Noting the incorrect assumptions that can be made about the location of stresses on a bicycle during real riding conditions professional cyclingcompany ,ervelo created an instrumented +strain gage+ bike out#tted withsensors and +ridden hard+. They accounted for di*erent situations and ridingstyles in their tests and concluded that bending and torsion loads were

distributed di*erently than previously believed. $eing a private companythese results were not released to the public.

,ervelo+s analysis showed that a large .@ inch axle increased the sti*ness of the bottom bracket and allowed the seat tube and down tube to be lighter aswell at a lower weight. They cite that they use carbon3epoxy prepreg of diferent moduli supplied by Ntwport Adhesives and ,omposites and NipponDraphite Fiber ,orp.J in di*erent areas of the frame to tailor the mechanicalproperties of each section and use a #berglass scrim in the places where thecarbon layup comes in contact with metal components.

,ervelo manufactures the frame+s top tube head tube down tube seat tubeand bottom bracket as a monocoque shell and chain stay and seat staymolded as separate pieces2 using in6atable latex bladders to achieve anaccurate #ber architecture and a consistent all thickness.

Giang introduces in @1 the principles of biomechanics and ergonomicknowledge noting that feature parameters of the rider are often not includedin the frame design. )e de#nes the relative position between the saddle thehandlebar and the central axis as the bicycle+s threepivot and uses it as amain parameter in order to improve rider confort. The optimi"ation goal of

his methods is to keep the rider comfortable by maintaining the backmuscles in a relaxation state and minimi"ing leg fatigue.

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