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TWO-DIMENSIONAL ELEMENTS

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

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Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

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TWO-DIMENSIONAL ELEMENTS Two-Dimensional Elements Overview

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

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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: 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

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

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TWO-DIMENSIONAL ELEMENTS (Cont.) 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

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TWO-DIMENSIONAL ELEMENTS 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

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

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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 It has terms in its stiffness matrix to account for transverse shear flexibility and also for membranebending 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)7

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

The QUAD4 Element (Cont.)

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The QUAD4 Element (Cont.) Element force output includes: Fx,Fy Fxy Mx,My Mxy Vx,Vy

Membrane force per unit length Membrane shear force per unit length Bending moments per unit length Twisting moment per unit length Transverse shear forces per unit length

Element Stress output includes: Stress components: x, y, xy, (at center - optionally at corners)

The sign convention for these terms is shown in the next

slidesCopyright 2010 MSC.Software Corporation Copy For Politecnico of Milano 9

SIGN CONVENTION OF FORCE OUTPUT FOR THE QUAD4 ELEMENT

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SIGN CONVENTION OF STRESS OUTPUT FOR THE QUAD4 ELEMENT (Cont.)

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TWO-DIMENSIONAL ELEMENTS (Cont.) Element connectivity is defined on the NASTRAN CQUAD4

entry, looking at Element 1 in our rib:1 CQUAD4 CQUAD4 2 EID 1 3 PID 1 TFLAG 4 GRID1 1 T1 5 GRID2 2 T2 6 GRID3 23 T3 7 GRID4 22 T4 8 THETA or MCID 9 ZOFFS 10

.bdf file extractCQUAD4 CQUAD4 CQUAD4 CQUAD4 CQUAD4 1 2 3 4 5 1 1 1 1 1 1 2 3 4 5 2 3 4 5 6 23 24 25 26 27 22 23 24 25 26

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TWO-DIMENSIONAL ELEMENTS (Cont.)Field EID PID G1,G2,G3,G4 Theta Contents Element identification number (integer>0) Identification number of a PSHELL or PCOMP property entry Grid point identification numbers of connection points. (All interior angles of this element must be less than 180.) Material property orientation specification. If real or blank, specifies material property orientation angle in degrees. If integer, material xaxis orientation is along projection onto the plane of the x-axis of the specified coordinate system. 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. Offset from the surface defined by the grid points to the element reference plane in the element coordinate system.

T1,T2, T3,T4

ZOFFS

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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

output is in the element coordinate system by default for these elements)

See illustration on following slide

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QUAD4 ELEMENT COORDINATE SYSTEM (Cont.)

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QUAD4 ELEMENT COORDINATE SYSTEM (Cont.) Element x-axis bisects the angle 2. 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 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.Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano 16

QUAD4 ELEMENT PROPERTIES Are defined using either a PSHELL, PCOMP (composite),

PCOMPG (composite) or PLPLANE (nonlinear) entry.12I/T3

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QUAD4 ELEMENT PROPERTIES (Cont.)Field PID MID1 T MID2 Contents Property identification number Material identification number for membrane behavior (integer > 0 or blank) Plate or membrane thickness Material identification number for 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.18

Copyright 2010 MSC.Software Corporation Copy For Politecnico of Milano

QUAD4 ELEMENT PROPERTIES (Cont.)Field MID3 TS/T ContentsMaterial identification number for transverse shear behavior (integer > 0 or blank) Transverse shear thickness divided by membrane thickness (default = .833333). The default value is correct for solid, homogeneous plates. Nonstructural mass per unit area (real) Stress recovery distances for bending (real, default Z1 = -1/2 thickness, Z2 = +1/2 thickness) Material identification number to define coupling between membrane and bending deformation19

NSM Z1,Z2 MID4

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QUAD4 ELEMENT PROPERTIES (Cont.) The QUAD4 element can have in-plane, bending, and

transverse shear behavior. The element mechanical behavior is specified by the presence or absence of a material ID number in the appropriate field(s) on the PSHELL entry. To model a membrane plate, use only MID1

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QUAD4 ELEMENT PROPERTIES (Cont.) To model a plate with bending stiffness only, use only MID2

For bending with transverse shear flexibility, use MID2 and

MID3

Note: Mass is not calculated if MID1 is blank.

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QUAD4 ELEMENT PROPERTIES (Cont.) Use MID3 to include an extra shear term in the element

stiffness calculations (i.e. includes transverse shear flexibility).

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QUAD4 ELEMENT PROPERTIES (Cont.) 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 if the elements cross section is unsymmetric. Default is blank = symmetric cross section. For more information on MID4, see the MSC Nastran Common Questions and Answers.

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QUAD4 ELEMENT PROPERTIES (Cont.) In summary, the results of leaving an MID field blank are: MID1 MID2 MID3 MID4

No membrane or coupling stiffness or Mass No bending, coupling, or transverse shear stiffness No transverse shear flexibility No bending-membrane coupling

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QUAD4 EXAMPLE

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QUAD4 EXAMPLE (Cont.)

Notice that the in-plane rotation is constrained for the inmodel positioned in the x-y plane. xCopyright 2010 MSC.Software Corpora

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