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Composite materials have found increasing applications in many applications and slender structures like rotor blades or high-aspect-ratio wings may be modeled in one-dimension as a 1-D beam provided the complex cross sectional properties (ultimately represented as a 2-D finite element mesh) can be captured properly. Here, a new way for composite beam analysis is introduced. The Variational Asymptotic Method (VAM) computes the properties of a beam’s arbitrary cross section containing composite materials. VAM, the mathematical basis of VABS, splits a general 3-D nonlinear elasticity problem for a beam-like structure into a two-dimensional (2-D) linear cross-sectional analysis and a 1-D nonlinear beam analysis. For details on VAM, refer to Yu, W., Volovoi, V., Hodges, D. and Hong, X. “Validation of the Variational Asymptotic Beam Sectional Analysis (VABS)”, AIAA Journal, Vol. 40, No. 10, 2002 (available at http://www.ae.gatech.edu/people/dhodges/papers/AIAAJ2002.pdf). VAM’s key benefit lies in the ability to model a beam made of composite material with only 1-D elements, namely CBEAM3.

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Chapter 33: Beams: Composite Materials and Open Cross Sections
33
Beams: Composite Materialsand Open Cross Sections
Summary - Composite Beam 517
Introduction 518
Solution Requirements 518
FEM Solution 519
Modeling Tips 520
Input File(s) 521
Summary - VKI and VAM Beam Formulations 522
Introduction 523
Solution Requirements 523
FEM Solution 524
Input File(s) 525
517
CHAPTER 33
Beams: Composite Materials and Open Cross Sections
Summary - Composite Beam
TitleChapter 33: Composite BeamGeometryMaterial propertiesãLinear elastic orthotropic material using
MAT8
ãAssumptions: E33 = 0.8E22; 13= 23= 12ãTheta on
PCOMP
/
PCOMPG
specifies the angle between X-axis of material coordinateand X-axis of element coordinate.Analysis typeLinear static analysisBoundary conditionsCantilever configurationApplied loadsBendingElement typeCBEAM3FE resultsãConverted
PBEAM3
from
PBMSECT
ãStress recovery - screened based on max failure indexã
bdf
file for FE mesh of cross section shown here
FyFz
X, XeY, YeZ, Ze
Straight Cantilever Beam with load (Fy or Fz) applied at Free-EndElement coordinate (Xe, Ye, Ze) coincides with Basic Coordinate (X,Y,Z)
ZYX
MD Demonstration ProblemsCHAPTER 33
518
Introduction
Composite materials have found increasing applications in many applications and slender structures like rotor bladesor high-aspect-ratio wings may be modeled in one-dimension as a 1-D beam provided the complex cross sectionalproperties (ultimately represented as a 2-D finite element mesh) can be captured properly. Here, a new way forcomposite beam analysis is introduced. The Variational Asymptotic Method (VAM) computes the properties of abeam’s arbitrary cross section containing composite materials. VAM, the mathematical basis of VABS, splits a general3-D nonlinear elasticity problem for a beam-like structure into a two-dimensional (2-D) linear cross-sectional analysisand a 1-D nonlinear beam analysis. For details on VAM, refer to Yu, W., Volovoi, V., Hodges, D. and Hong, X.“Validation of the Variational Asymptotic Beam Sectional Analysis (VABS)”,
AIAA Journal
, Vol.
40
, No. 10, 2002(available athttp://www.ae.gatech.edu/people/dhodges/papers/AIAAJ2002.pdf ). VAM’s key benefit lies in the abilityto model a beam made of composite material with only 1-D elements, namely CBEAM3.
Solution Requirements
In general, the solution requires the layup of composite material and the description of this general or arbitrary crosssection.
PCOMP
entries are used to provide the composite layup and
PBMSECT
entry is utilized to describe the profileof cross section and the link to the composite layup via
PCOMP
. An example is shown as follows:The theta field on
PCOMP
is utilized to specify the angle between the X-axis of the material coordinate and the X-axisof the element coordinate. A cutout of the FEM mesh at the intersect of
OUTP=101
and
BRP=103
illustrates the plylayup shown inFigure33-1.
$$ Composite casePBMSECT 32 1 OP 0.015OUTP=101,C=101,brp=103,c(1)=[201,pt=(15,34)]pcomp 101 -0.1 5000. hill 0.0501 0.05 0.0 501 0.05 90.0501 0.05 -45.0 501 0.05 45.0501 0.05 0.0pcomp 201 5000. tsai 0.0 SYM501 0.05 -45.0 501 0.05 45.0501 0.05 0.0$MAT15013.6.3mat8,501,2.0e7,2.0e6,.35,1.0e6,1.0e6,1.0e6,0.0,++,0.0,0.0,0.0,2.3e5,1.95e5, 13000., 32000., 12000.
519
CHAPTER 33
Beams: Composite Materials and Open Cross Sections
Figure33-1 Intersection of Ply Layups 101 and 201
FEM Solution
The converted
PBEAM3
for
PBMSECT
,32 is as follows:Note that the
MID
field of above
PBEAM3
has value of 0 which is a flag for using the Timoshenko 6 x 6 matrix storedfrom the seventh line of
PBEAM3
. Timoshenko 6 x 6 matrix includes cross sectional and material properties. Thecross-sectional shape and the FE mesh is shown inFigure33-2. The coordinate shown in the figure matches withelement coordinate.
*** USER INFORMATION MESSAGE 4379 (IFP9B)THE USER SUPPLIED PBMSECT BULK DATA ENTRIES ARE REPLACED BY THE FOLLOWING PBEAM3 ENTRIES.CONVERSION METHOD FOR PBARL/PBEAML - .PBEAM33204.7202E+008.3059E+012.9578E+01-1.5664E+013.2316E+010.0000E+001.8014E+014.2136E+001.7100E+01-2.7858E+003.8881E+00-3.5404E+004.7202E+002.6994E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+000.0000E+001.2253E+08-2.1160E+058.1193E+04-2.4761E+06-3.7193E+067.9049E+06-2.1160E+052.1792E+06-1.7859E+061.9780E+075,4643E+05-3.5845E+058.1193E+04-1.7859E+062.7228E+071.7190E+072.9835E+042.1407E+06-2.4761E+061.9780E+071.7190E+072.2332E+085.8182E+06-1.2186E+06-3.7193E+065.4643E+052.9835E+045.8182E+062.1349E+09-4.0706E+088.9040E+06-3.5845E+052.1407E+06-1.2186E+06-4.0706E+087.5602E+08
ZYX-45,PCOMP 201-4545, 45,0,0,
045-45900045-45900PCOMP101PCOMP101

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