Download - MD Nastran Elements 4

TWO-DIMENSIONAL ELEMENTS

1Copyright© 2010 MSC.Software CorporationCopy For Politecnico of Milano


● Two-Dimensional Elements Overview


TWO-DIMENSIONAL ELEMENTS (Cont.)

● A plate is a structural element with one small dimension and two large dimensions.● A thin plate is one in which the thickness is much less than the next

larger dimension (roughly 1/15)● For linear analysis, MD Nastran plate elements assume classical

engineering assumptions of thin plate behavior:


engineering assumptions of thin plate behavior:● The deflection of the midsurface is small compared with the thickness● The midsurface remains unstrained (neutral) during bending. (This

applies to lateral loads, not in-plane loads.)● The normal to the midsurface remains normal to the midsurface during

bending


● Plate and shell elements (except CQUADR and CTRIAR) have no stiffness in the normal rotational (drilling) degrees of freedom.● CQUADR and CTRIAR plate elements have stiffness in the drilling

degrees of freedom.


No stiffness in the drilling degrees of freedom or no rotational stiffness in the direction normal to the plate


● Commonly used parameters for plate and shell elements● For V2001

● PARAM, K6ROT, 0. is the default for all linear solution sequences● PARAM, K6ROT, 100. is the default in nonlinear solution sequences● PARAM, SNORM, 20., is the default

● For V2004 and later


● PARAM, K6ROT, 100. is the default for all solution sequences● PARAM, SNORM, 20., is the default

THE QUAD4 ELEMENT

● The QUAD4 element is the most commonly used plate element

● It is a 4-noded flat plate element● It is capable of resisting both, in-plane and out-of-plane

loads● It is capable of modeling either plane strain or plane

stress


stress● It has terms in its stiffness matrix to account for

transverse shear flexibility and also for membrane-bending coupling

● In-plane penalty bending stiffness term is added with a default PARAM,K6ROT,100. (see section 5 for further details)

● PARAM,SNORM,20. is a default as well (see section 5)

The QUAD4 Element (Cont.)


The QUAD4 Element (Cont.)

● Element force output includes:● Fx,Fy Membrane force per unit length● Fxy Membrane shear force per unit length● Mx,My Bending moments per unit length● Mxy Twisting moment per unit length

● Vx,Vy Transverse shear forces per unit length


● Element Stress output includes:● Stress components: σx, σy, τxy, (at center - optionally at corners)

● The sign convention for these terms is shown in the next slides

SIGN CONVENTION OF FORCE OUTPUT FOR

THE QUAD4 ELEMENT


SIGN CONVENTION OF STRESS OUTPUT FOR

THE QUAD4 ELEMENT (Cont.)


1 2 3 4 5 6 7 8 9 10

CQUAD4 EID PID GRID1 GRID2 GRID3 GRID4 THETA or MCID

ZOFFS

CQUAD4 1 1 1 2 23 22

TFLAG T1 T2 T3 T4


● Element connectivity is defined on the NASTRAN CQUAD4 entry, looking at Element 1 in our rib:


CQUAD4 1 1 1 2 23 22CQUAD4 2 1 2 3 24 23CQUAD4 3 1 3 4 25 24CQUAD4 4 1 4 5 26 25CQUAD4 5 1 5 6 27 26

.bdf file extract


Field Contents

EID Element identification number (integer>0)

PID Identification number of a PSHELL or PCOMP property entry

G1,G2,G3,G4 Grid point identification numbers of connection points. (All interior angles of this element must be less than 180°.)

Theta Material property orientation specification. If real or blank, specifies material property orientation angle in degrees. If integer, material x-


material property orientation angle in degrees. If integer, material x-axis orientation is along projection onto the plane of the x-axis of the specified coordinate system.

T1,T2, T3,T4 The continuation entry is optional. If supplied, it describes the membrane thickness of the element at grid points G1 through G4 (real ≤ 0., not all zero). If not supplied, then T1 through T4 is set equal to the value of T on the PSHELL data entry.

ZOFFS Offset from the surface defined by the grid points to the element reference plane in the element coordinate system.

QUAD4 ELEMENT COORDINATE SYSTEM

● The element coordinate system● Is defined based on the order and location of the connecting points● Defines positive sense of normal pressures applied to the element● Used to define layers of a composite material● Used to interpret the element output forces and stresses (element


● Used to interpret the element output forces and stresses (element output is in the element coordinate system by default for these elements)

● See illustration on following slide


(Cont.)



(Cont.)

● Element x-axis bisects the angle 2α. Positive direction is from G1 towards G2.

● Element y-axis is perpendicular to the element x-axis and lies in the plane defined by G1, G2, G3, and G4. Positive


lies in the plane defined by G1, G2, G3, and G4. Positive direction is from G1 towards G4.

● Element z-axis is normal to the x-y plane of the element. Positive sense is defined by the right-hand rule and the ordering of the connected grids.

QUAD4 ELEMENT PROPERTIES

● Are defined using either a PSHELL, PCOMP (composite), PCOMPG (composite) or PLPLANE (nonlinear) entry.

12I/T3


QUAD4 ELEMENT PROPERTIES (Cont.)Field ContentsPID Property identification numberMID1 Material identification number for

membrane behavior (integer > 0 orblank)

T Plate or membrane thicknessMID2 Material identification number for

bending behavior (integer > 0 or blank,


bending behavior (integer > 0 or blank, MID2 = -1 represents plane strain) NOTE: THE DEFAULT FOR MID2 IS NOT TO INCLUDE THE BENDING STIFFNESS. FOR MOST MODELS, MID2 SHOULD NOT BE BLANK

12I/T3 Normalized bending inertia per unit length (real or blank, default = 1.0). The default value is correct for solid, homogeneous plates.

QUAD4 ELEMENT PROPERTIES (Cont.)Field ContentsMID3 Material identification number for

transverse shear behavior (integer > 0 or blank)

TS/T Transverse shear thickness divided bymembrane thickness (default = .833333).The default value is correct for solid,homogeneous plates.


homogeneous plates.

NSM Nonstructural mass per unit area (real)

Z1,Z2 Stress recovery distances for bending (real, default Z1 = -1/2 thickness,

Z2 = +1/2 thickness)

MID4 Material identification number to definecoupling between membrane and bending deformation

QUAD4 ELEMENT PROPERTIES (Cont.)

● The QUAD4 element can have in-plane, bending, andtransverse shear behavior. The element mechanicalbehavior is specified by the presence or absence of amaterial ID number in the appropriate field(s) on thePSHELL entry.


● To model a membrane plate, use only MID1


● To model a plate with bending stiffness only, use only MID2

● For bending with transverse shear flexibility, use MID2 and


● For bending with transverse shear flexibility, use MID2 andMID3

● Note: Mass is not calculated if MID1 is blank.


● Use MID3 to include an extra shear term in the element stiffness calculations (i.e. includes transverse shear flexibility).



● For a solid homogeneous plate, MID1, MID2, and MID3 should reference the same material ID

● MID4: The MID4 field (bending and membrane deformation coupling) should be defined only


deformation coupling) should be defined only if the element’s cross section is unsymmetric. Default is blank = symmetric cross section.

● For more information on MID4, see the MSC Nastran Common Questions and Answers.


● In summary, the results of leaving an MID field blank are:

● MID1 No membrane or coupling stiffness or Mass● MID2 No bending, coupling, or transverse shear

stiffness● MID3 No transverse shear flexibility


● MID3 No transverse shear flexibility● MID4 No bending-membrane coupling

QUAD4 EXAMPLE


QUAD4 EXAMPLE (Cont.)


Notice that the inNotice that the in--plane rotation is constrained for the plane rotation is constrained for the model positioned in the xmodel positioned in the x--y plane.y plane.


DISP = ALL � displacement for all Grid Points


QUAD4 EXAMPLE (Cont.)Force = All � element forces at the center only (default)


QUAD4 EXAMPLE (Cont.)Stress = ALL � element stress at center only (default)


σσσσHVM = [(3.024E6)2 – (3.024E6)(2.268E5) + (2.268E5)2] ½ = 2.917E6

-

STRESS(BILIN) = ALL � element stress at center plus extrapolated at the 4 nodal positions



STRAIN(BILIN,FIBER) = ALL � element strain at the fiber distances at center plus extrapolated at the 4 nodal positions

QUAD4 ALTERNATE PROPERTY DEFINITION

● The PCOMP property entry may be used when the element is acomposite consisting of layers of unidirectional fibers. The informationon the PCOMP entry includes the thickness, orientation, and materialidentification of each layer. This information is used within MD Nastranto compute the entries of a PSHELL entry, which should not besimultaneously entered by the user for the same element(s). Speciallayer-by-layer output is provided when the PCOMP option is used.


layer-by-layer output is provided when the PCOMP option is used.Putting the Nastran prtpcomp=1 system cell at the top of the .dat filealong with “echo=sort” will print the equivalent PSHELL and MAT2entries.

● See MSC Nastran Reference Manual for detailed information about simulating composite materials with MD Nastran.

QUADR/TRIAR ELEMENT● In 2004, a new QUADR/TRIAR element was added● Similar to the old QUADR/TRIAR element, it has

stiffness in the drilling degree of freedom● Drilling loads are transferred correctly

● The new QUADR/TRIAR element ● Contains differential stiffness matrix (can be used in

SOL105)


SOL105)● Supports layered composite● Couples the membrane and bending stiffness● Yields correct results for curved shell models● Supports heat transfer

QUADR/TRIAR ELEMENT (Cont.)● Offset is allowed (shell normal should be turned off,

otherwise you will get incorrect results) PARAM,SNORM,0.0 must be specified.

● Rotational mass is implemented for the drilling DOF (param,coupmass,1)

● Supports SOL 200● Supports consistent load application—including edge loads

(PLOAD4)


(PLOAD4)● Unlike the old QUADR, the new QUADR contains all the

capabilities of the QUAD4.

● QUADR/TRIAR have been extended to support nonlinear analysis as of MD Nastran R2

CQUAD4 1 1 1 2 23 22


● A snap shot of the NASTRAN input file for this problem, showing how the connectivity entry, the property entry, and the material entry are linked together:


$ Referenced Material Records$ Material Record : aluminum$ Description of Material : Date: 09-Oct-00 Time: 11:49:27MAT1 1 1.+7 .33

………

$ Elements and Element Properties for region : rib_webPSHELL 1 1 .063 1 1

ANALYSIS OF COMPOSITE MATERIALS

● The following slides provide a brief introduction to the analysis of composite materials.

● Please attend the NAS113 Analysis of Composite Materials with MD Nastran course for a more comprehensive treatment of composite analysis.


PLY DEFINITION

● Typically a ply is a flat group of fibers imbedded in a matrix.● The matrix is usually an isotropic material that holds the

fibers together.● In a ply called a tape, the fibers are unidirectional.● In a ply called a cloth, the fibers are woven at 0 and 90

degree directions.


degree directions.

TAPE PLIES

● Fiber:● Unidirectional in tape● Direction is the 1 axis of the

ply coordinate system

● Matrix:● Glue that holds fibers


● Glue that holds fibers together

● Matrix direction is the 2 axis● 90 degrees to the 1 axis

● Material properties are: ● 2D orthotropic material in

Patran ● MAT8 in Nastran

MAT8 BULK DATA ENTRY

● Defines the ply orthotropic properties.● Elastic properties are E1, E2, NU12, G12, G1Z, G2Z.● Allowables are Xt, Xc, Yt, Yc, S. ● Use STRN=1.0 if allowables are in units of strain.● F12 is for the Tsai-Wu failure theorem.● Thermal coefficients of expansion are A1 and A2. ● The MAT8 TREF reference temperature is not used since it is overridden by the PCOMP TREF.● Density is RHO. ● The MAT8 GE structural damping is not used since it is overridden by the PCOMP GE.

● The example below is typical for a graphite/epoxy tape.


● The example below is typical for a graphite/epoxy tape.

1 2 3 4 5 6 7 8 9 10

MAT8 MID E1 E2 NU12 G12 G1Z G2Z RHO

MAT8 1 20.+6 2.+6 0.35 1.0+6 1.0+6 1.0+6 1.3-4

A1 A2 TREF Xt Xc Yt Yc S

-2.3-7 4.5-6 1.3+5 1.2+5 1.1 +4 1.2+4 1.25+4

.bdf file extract

GE F12 STRN

mat8, 1, 20.+6, 2.+6, 0.35, 1.0+6, 1.0+6, 1.0+6, 1.3-4,++, -2.3-7, 4.5-6,, 1.3+5, 1.2+5, 1.1+4, 1.2+4, 1.25+4

Materials: Create/ 2d Orthotropic/ Manual Input.

Material Name

PATRAN 2D ORTHOTROPIC


Material NameInput Properties

Linear ElasticApply

Input PropertiesFailureApply

Note : Linear Elastic and Failure properties must be input separately with an Apply between and

after.

COMPOSITE MATERIAL

● Stack of plies● Each ply has a different direction, material,

and thickness● Composite properties are calculated in the

material coordinate system (Xm, Ym, Zm)


● Zm is the same as the element Z axis (Ze)● Right hand rule of grid ordering,

G1,G2,G3,G4

● Xm is in the direction of the 0 degree ply● Positive angles are defined by right hand

rule around Zm

PCOMP BULK DATA ENTRY

● Defines the composite layup.1 2 3 4 5 6 7 8 9 10

PCOMP PID Z0 NSM SB FT TREF GE LAM

PCOMP 1 5000.0 HILL 0.0

MID1 T1 THETA1 SOUT1 MID2 T2 THETA2 SOUT2

1 0.0054 0.0 YES 1 0.0054 45.0 YES

MID3 T3 THETA3 SOUT3 etc.


1 0.0054 90.0

● Z0 is composite offset. ● Use default = -(composite thickness)/2

● NSM is nonstructural mass● SB is allowable interlaminar shear stress

● Put as Bonding Shear Stress in Patran 2D Orthotropic Material

● Required for failure indices

● FT is the ply failure theorem● Required for failure indices

● TREF is reference temperature● Overrides TREFs on ply MAT8s

● GE is element damping● Overrides GE on ply MAT8s

● LAM is layup options● MIDi is ply material ID

● MAT8 ID

● Ti is ply thickness● THETAi is ply angle● SOUTi is data recovery option

PCOMP BULK DATA ENTRY (cont.)

● The example composite below is an 8 ply layup, symmetric about it’s centerline, with an equal number of plies in each of the 0, +45, 90 degree directions.

.bdf file extract


PCOMP, 1,,, 5000., HILL, 1, .0054, 0., YES, 1, .0054, 45., YES, 1, .0054, -45., YES, 1, .0054, 90., YES, 1, .0054, 90., YES, 1, .0054, -45., YES, 1, .0054, 45., YES, 1, .0054, 0., YES

Properties : Composite / Laminate.

To create a ply, click on a ply material in Existing Materials. Repeat for each of the plies

PATRAN COMPOSITE


Repeat for each of the plies

Enter Thickness for all layers: 0.0054 in the box under Input Data <return>

Click on first cell in Orientation column

Enter Orientations: 0 45 -45 90 90 -45 45 0 in the box under Input Data.

Apply

CQUAD4 BULK DATA ENTRY

● Defines the composite plate.● Material coordinate system can be

defined one of two ways:● MCID – (integer) - ID of a user defined

coordinate system who’s X-axis is projected onto the element to define the element’s material coordinate system’s X-axis. This along with the Z-axis of the element coordinate system defines the material coordinate system.

● THETA – (real) - an angle between the

CQUAD4, 1, 1, 1, 2, 5, 4, 99


● THETA – (real) - an angle between the G1G2 vector of the element and the X-axis of the material coordinate system. The positive sense of this angle is the right hand rule direction around the element’s Z-axis.

1 2 3 4 5 6 7 8 9 10

CQUAD4 EID PID G1 G2 G3 G4 THETA or MCID ZOFFS

CQUAD4 1 1 1 2 3 4 99

CQUAD4, 1, 1, 1, 2, 5, 4, 25.0

PATRAN COMPOSITE PROPERTIES

Properties : 2D Properties / Shell

Property Set Name

Option: Laminate


Input Properties

Click on Mat Prop Name Icon to select the material

Click on coord. sys. for projection to material coord. sys.

OK

Select elements

Apply

PATRAN MATERIAL COORD. Z-AXIS

Meshing : FEM Actions / Verify

Draw Normal Vectors


Draw Normal Vectors

Apply

PATRAN MATERIAL COORD. X-AXIS

Properties: Property Actions / Show Property.


Material Orientation

Apply

NASTRAN INPUT FILE

● The single ply per line format on PCOMP continuation fields allows easier cutting and pasting of plies

GRID 1 0. 0. 0.GRID 2 0. .5 0.GRID 3 0. 1. 0.GRID 4 .5 0. 0.GRID 5 .5 .5 0.GRID 6 .5 1. 0.GRID 7 1. 0. 0.GRID 8 1. .5 0.

SOL 101CENDTITLE = Composite Workshop Chapter 2 - Sample Composite Input

SPC = 1LOAD = 1DISP = ALLSTRESS =ALL

$

.dat file extract


GRID 8 1. .5 0.GRID 9 1. 1. 0.$ SPC1,1,1235,1SPC1,1,135,2,3$ FORCE 1 3 500. 0. 1. 0.FORCE 1 6 500. 0. 1. 0.FORCE 1 6 500. 0. 1. 0.FORCE 1 9 500. 0. 1. 0.FORCE 1 7 250. 1. 0. 0.FORCE 1 8 250. 1. 0. 0.FORCE 1 8 250. 1. 0. 0.FORCE 1 9 250. 1. 0. 0.FORCE 1 7 250. 0. 1. 0.FORCE 1 8 250. 0. 1. 0.FORCE 1 8 250. 0. 1. 0.FORCE 1 9 250. 0. 1. 0.$ CORD2R, 99,, 0., 0., 0., 0., 0., 1., 0., 1., 0.ENDDATA

$BEGIN BULKPARAM, POST, -1$ PCOMP, 1,,, 5000., HILL, 1, .0054, 0., YES, 1, .0054, 45., YES, 1, .0054, -45., YES, 1, .0054, 90., YES, 1, .0054, 90., YES, 1, .0054, -45., YES, 1, .0054, 45., YES, 1, .0054, 0., YESMAT8, 1, 2.+7, 2.+6, .35, 1.+6, 1.+6, 1.+6,,,,130000., 120000., 11000., 12000., 12500.$ CQUAD4 1 1 1 2 5 4 99CQUAD4 2 1 2 3 6 5 99CQUAD4 3 1 4 5 8 7 99CQUAD4 4 1 5 6 9 8 99$

● Printed in the f06 file if STRESS=ALL or STRAIN=ALL Case Control Commands are used.

S T R E S S E S I N L A Y E R E D C O M P O S I T E E L E M E N T S ( Q U A D 4 )ELEMENT PLY STRESSES IN FIBER AND MATRIX DIRECTIONS INTER-LAMINAR STRESSES PRINCIPAL STRESSES (ZERO SHEAR) MAXID ID NORMAL-1 NORMAL-2 SHEAR-12 SHEAR XZ-MAT SHEAR YZ-MAT ANGLE MAJOR MINOR SHEAR

0 1 1 2.55820E+05 2.81603E+04 2.73019E+04 0.0 0.0 6.74 2.59049E+05 2.49319E+04 1.17058E+050 1 2 4.96222E+05 1.19674E+04 -2.69492E+03 0.0 0.0 -0.32 4.96237E+05 1.19524E+04 2.42142E+050 1 3 -3.72387E+04 4.79000E+04 2.69492E+03 0.0 0.0 88.19 4.79852E+04 -3.73239E+04 4.26546E+040 1 4 2.03163E+05 3.17071E+04 -2.73019E+04 0.0 0.0 -8.83 2.07406E+05 2.74647E+04 8.99705E+040 1 5 2.03163E+05 3.17071E+04 -2.73019E+04 0.0 0.0 -8.83 2.07406E+05 2.74647E+04 8.99705E+040 1 6 -3.72387E+04 4.79000E+04 2.69492E+03 0.0 0.0 88.19 4.79852E+04 -3.73239E+04 4.26546E+040 1 7 4.96222E+05 1.19674E+04 -2.69492E+03 0.0 0.0 -0.32 4.96237E+05 1.19524E+04 2.42142E+05

NASTRAN PLY STRESS OUTPUT


0 1 7 4.96222E+05 1.19674E+04 -2.69492E+03 0.0 0.0 -0.32 4.96237E+05 1.19524E+04 2.42142E+050 1 8 2.55820E+05 2.81603E+04 2.73019E+04 0.0 0.0 6.74 2.59049E+05 2.49319E+04 1.17058E+050 2 1 2.20297E+05 -1.59550E+04 9.95088E+03 0.0 0.0 2.41 2.20715E+05 -1.63734E+04 1.18544E+050 2 2 9.15727E+04 -7.28449E+03 -2.31267E+04 0.0 0.0 -12.54 9.67154E+04 -1.24272E+04 5.45713E+040 2 3 -1.02861E+05 5.81209E+03 2.31267E+04 0.0 0.0 78.47 1.05290E+04 -1.07578E+05 5.90535E+040 2 4 -2.31585E+05 1.44826E+04 -9.95088E+03 0.0 0.0 -87.69 1.48844E+04 -2.31987E+05 1.23436E+050 2 5 -2.31585E+05 1.44826E+04 -9.95088E+03 0.0 0.0 -87.69 1.48844E+04 -2.31987E+05 1.23436E+050 2 6 -1.02861E+05 5.81209E+03 2.31267E+04 0.0 0.0 78.47 1.05290E+04 -1.07578E+05 5.90535E+040 2 7 9.15727E+04 -7.28449E+03 -2.31267E+04 0.0 0.0 -12.54 9.67154E+04 -1.24272E+04 5.45713E+040 2 8 2.20297E+05 -1.59550E+04 9.95088E+03 0.0 0.0 2.41 2.20715E+05 -1.63734E+04 1.18544E+050 3 1 -5.90459E+04 1.03837E+04 8.14704E+03 0.0 0.0 83.40 1.13269E+04 -5.99891E+04 3.56580E+040 3 2 1.11984E+05 -1.13646E+03 9.35916E+03 0.0 0.0 4.70 1.12753E+05 -1.90558E+03 5.73294E+040 3 3 -4.72039E+04 9.58604E+03 -9.35916E+03 0.0 0.0 -80.88 1.10887E+04 -4.87066E+04 2.98976E+040 3 4 1.23826E+05 -1.93411E+03 -8.14704E+03 0.0 0.0 -3.69 1.24352E+05 -2.45970E+03 6.34056E+040 3 5 1.23826E+05 -1.93411E+03 -8.14704E+03 0.0 0.0 -3.69 1.24352E+05 -2.45970E+03 6.34056E+040 3 6 -4.72039E+04 9.58604E+03 -9.35916E+03 0.0 0.0 -80.88 1.10887E+04 -4.87066E+04 2.98976E+040 3 7 1.11984E+05 -1.13646E+03 9.35916E+03 0.0 0.0 4.70 1.12753E+05 -1.90558E+03 5.73294E+040 3 8 -5.90459E+04 1.03837E+04 8.14704E+03 0.0 0.0 83.40 1.13269E+04 -5.99891E+04 3.56580E+040 4 1 8.79761E+04 9.55942E+01 1.42040E+04 0.0 0.0 8.96 9.02149E+04 -2.14316E+03 4.61790E+04

.f06 file extract

PATRAN PLY OUTPUT REQUEST

Analysis: Analyze / Entire Model

Translation Parameters / OP2


Subcases / Create

Output Requests / Advanced / Element Stress

Ply Stresses

OK

Apply

PATRAN PLY STRESS RESULTS


Download - MD Nastran Elements 4

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