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Beams: Composite Materials and Open Cross Sections

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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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