CLT Writeup

7/21/2019 CLT Writeup

http://slidepdf.com/reader/full/clt-writeup 1/5



(n engineering) an important material $idel* used in modern &abrication is composite laminates+

, laminate o& this -ind consists o& se.eral la*ers o& di&&erent &ibrous materials held together b*

some adhesi.e) each o& $hich has a single directionalit*+ !enerall*) neighboring plies .ar* in

the direction o& materials) in order to increase the strength o& the o.erall composite+ "ach pl* is

generall* /uite thin) allo$ing &or the properties o& the composite material to be &inel* controlled+

Modern engineering demands) such as sti&&ness) strength) and coe&&icient o& thermal epansion

can there&ore o&ten be met to a greater etent than $ith other materials+

Figure 1: Composite laminate materials consist of layers of fibers in sheets of resin, bound

together with layers of adhesive. Varying the direction of the fibers in each layer increases the

strength of the composite material.1

1 Public domain image: http:upload+$i-imedia+org$i-ipediacommons11Composite3d+png

2 public domain image http:en+$i-ipedia+org$i-iFile:'oeing38&irst3&light+jpg



Composite laminates are $idel* used in modern industr*: &or eample) a 'oeing 8 is

constructed o& up to 506 composite laminates 7Figure 2+ ,n understanding o& the beha.ior o& a

$ide .ariet* o& laminates) and the abilit* to model .er* speci&ic composites) is necessar* to

ensure that materials used in industr* meet per&ormance and sa&et* re/uirements+

Figure 2: A oeing !"! is constructed of up to #$% composite materials2

Since the main utilit* o& composite laminates in.ol.es achie.ing particular ph*sical properties) it

is important that the potential &ailure points o& these materials be determined+ Particularl*) $e

are interested in modeling the $a*s in $hich the material bends 7distortion) ho$ the load a&&ects

each pl* 7stress conditions) and $here and ho$ the material might brea- 7&ailure conditions+

nli-e homogeneous materials) $hich are relati.el* eas* to model) composite materials re/uire a

more comple approach+ 9he input re/uired to calculate these stresses and strains is comple)

and the modeling must be done in three dimensions 7Figure +



Figure &: Composite laminates must be modeled in &' to calculate stress and strain ()a*en from

the attached reference document, +A ummary of Classical -amination )heory/.

First) the appropriate &orces must be input: the .ertical and hori#ontal stress &orces) shear &orces)

and moment 7t$isting &orces+ ,dditionall*) the material properties are re/uired &or each pl*:

thermal epansion) moisture epansion) elasticit*) and the angle o& the &iber in each la*er+

Finall*) the en.ironmental conditionsambient temperature and moisturesmust be included in

the model+ 9he calculations necessar* to deri.e the a&orementioned output properties in.ol.e

calculating products o& ;; matrices) and i& done b* hand) re/uire se.eral hours to compute+

9here&ore) a computeri#ed method &or per&orming these calculations and producing the desired

output is a &ar more attracti.e option+

9he Sage<based modeling program uses the =interact &eature to re/uest user input &or material

properties) en.ironmental conditions) and &orces &or the material to be anal*#ed+ (t then

calculates a reduced sti&&ness matri &or each component t*pe in the laminate speci&ied)

trans&orms these matrices) and uses them to calculate the ,'> matri+ 9he ,'> matri is the

central component o& the calculation) because it de&ines the relationship bet$een the loads and



strains in the laminate+ For each component t*pe in the laminate) a corresponding ,'> matri is

deri.ed) assembled) and in.erted+ 9he thermal and moisture epansion coe&&icients &or each pl*

are then calculated and combined $ith the trans&ormed reduced sti&&ness matrices to determine

the thermal and moisture resultants+ ,t this point) the program has all the in&ormation it needs to

deri.e the midplane stresses and strains) as a product o& the ,'> matrices and the

thermalmoisture resultants+ Finall*) the indi.idual pl* strains are calculated &rom the midplane

stress and strain results) and the pl* stresses are deri.ed &rom the product o& the reduced sti&&ness

matri and the di&&erence bet$een the strain and the thermalmoisture components+ 7For &urther

re&erence) see the attached document) ?, Summar* o& Classical Lamination 9heor*@+

9he output results are displa*ed in a tet table) $ith each /uantit* clearl* annotated+ (& the

material &ails at an* point) a message is displa*ed indicating the particular pl* that brea-s+ From

this) an* desired composite laminate material could be anal*#ed to /uic-l* obtain an* o& the

listed outputs+ 9he program is capable o& handling e.en large input .alues) i+e) etremel* high

&orces+ Future $or- on the program might in.ol.e adding graphical displa*s) such as bar charts)

to sho$ the relati.e stress and strain on each pl* in the composite in /uestion+

Documents

CLT Writeup