The formulation of the CQUAD4 and CTRIA3 elements are based on the Mindlin-Reissner shell theory. These elements do not provide direct elastic stiffness for the rotational degrees-of-freedom which are normal to the surface of the element.
Consequently, for example, if a grid point is attached only to CQUAD4 elements only, all the elements are in the same plane, then the rotational degrees of freedom about the surface normal have zero stiffness. This zero stiffness results in a singular stiffness matrix, which prevents NX Nastran from solving the model.
To avoid this problem, you can:
• Constrain the rotational degree-of-freedom either manually with an SPC entry (either in field 8 of the GRID entry or an SPC entry) or automatically with the AUTOSPC parameter.
If using the SPC method, ensure that you do not constrain any components that have stiffness attached.
• Apply an artificial stiffness term to the degrees of freedom using PARAM K6ROT. Remember when using this parameter that the stiffness being included for the rotational degree of freedom is not a true stiffness and should not be used as such. For example, if you want to connect a CBAR element to the CQUAD4 element, you shouldn’t rely on the K6ROT stiffness to transfer the bending moment at the end of the CBAR into the plate.
See Also
• “Single-Point Constraints” in the in the NX Nastran User’s Guide.
• “Automatically Applying Single-Point Constraints” in the NX Nastran User’s Guide.
• “K6ROT” in the NX Nastran Quick Reference Guide.
CQUAD4
CQUAD4 is NX Nastran’s most commonly used element for modeling plates, shells, and membranes. The CQUAD4 is a quadrilateral flat plate connecting four grid points. It can
represent in-plane, bending, and transverse shear behavior, depending upon data provided on the PSHELL property entry.
You should use the CQUAD4 element when the surfaces you are meshing are reasonably flat and the geometry is nearly rectangular. For these conditions, the quadrilateral elements eliminate the modeling bias associated with the use of triangular elements, and the quadrilaterals give more accurate results for the same mesh size. If the surfaces are highly warped, curved, or swept, you should use triangular elements.
Under extreme conditions, quadrilateral elements will give results that are considerably less accurate than triangular elements for the same mesh size. Quadrilateral elements should be kept as nearly square as possible, because their accuracy tends to deteriorate as their aspect ratio increases.
CQUAD4 Element Coordinate System
The element coordinate systems for the CQUAD4 is shown inFigure 4-6. The orientation of the element coordinate system is determined by the order of the connectivity for the grid points.
The element z-axis, often referred to as the positive normal, is determined using the right-hand rule. Therefore, if you change the order of the grid points connectivity, the direction of this positive normal might also reverse.
This rule is important to remember when you’re applying pressure loads or viewing the element forces or stresses. Often, element stress contours appear to be strange when they’re displayed by a post-processor because the normals of the adjacent elements may be inconsistent. Remember that NX Nastran always outputs components of forces, moments, and element stresses in the element coordinate system.
• The element’s x-axis bisects the angle 2a. The positive direction is from G1 to G2.
• The element’s y-axis is perpendicular to the element x-axis and lies in the plane defined by G1, G2, G3, and G4. The positive direction is from G1 to G4.
• The element’s z-axis is normal to the x-y plane of the element. The positive z direction is defined by applying the right-hand rule to the ordering sequence of G1 through G4.
Figure 4-6. CQUAD4 Element Geometry and Coordinate Systems
Figure 4-6also shows that each element has an element coordinate system and a material coordinate system that may be the same or different. Using a material coordinate system different from the element coordinate system is useful when the material properties are orthotropic or anisotropic.
CQUAD4 Format
The format of the CQUAD4 entry is as follows:
1 2 3 4 5 6 7 8 9 10
CQUAD4 EID PID G1 G2 G3 G4 THETA or
MCID ZOFFS
T1 T2 T3 T4
Field Contents
EID Element identification number.
PID Property identification number of a PSHELL or PCOMP entry.
Gi Grid point identification numbers of connection points.
THETA Material property orientation angle in degrees.
MCID Material coordinate system identification number.
ZOFFS Offset from the surface of grid points to the element reference plane.
Ti Membrane thickness of element at grid points G1 through G4.
Grid points G1 through G4 must be ordered consecutively around the perimeter of the element.
THETA and MCID are not required for homogenous, isotropic materials. ZOFFS is used when offsetting the element from its connection point. The continuation entry is optional. If you don’t supply values for T1 to T4, the software sets them equal to the value of T (plate thickness) you define on the PSHELL entry. Finally, all interior angles of the CQUAD4 element must be less than 180°.
See Also
• “CQUAD4” in the NX Nastran Quick Reference Guide.
CTRIA3
The CTRIA3 element is a triangular plate connecting three grid points. The CTRIA3 is most commonly used for mesh transitions and filling in irregular boundaries. The element may exhibit excessive stiffness, particularly for membrane strain. Thus, as a matter of good modeling practice, you should locate CTRIA3 elements away from areas of interest whenever possible. In other respects, the CTRIA3 is analogous to the CQUAD4. Triangular elements should be kept as nearly equilateral as possible as their accuracy tends to deteriorate when the element’s shape becomes obtuse and the ratio of the longest to the shortest side increases.
CTRIA3 Element Coordinate System
CTRIA3 element forces and stresses are output in the element coordinate system. The element coordinate system is established as follows:
• The element x-axis lies in the direction from G1 to G2.
• The element y-axis is perpendicular to the element x-axis, and the positive x-y quadrant contains G3.
• The element z-axis is normal to the plane of the element. The positive z direction is established by applying the right-hand rule to the ordering sequence of G1 through G3.
NX Nastran calculates forces and moments at the element centroid. It calculates stresses at distances Z1 and Z2 from the element reference plane. You specify Z1 and Z2 on the PSHELL entry).
Figure 4-7. CTRIA3 Element Geometry and Element Coordinate System CTRIA3 Format
The format of the CTRIA3 element entry is as follows:
1 2 3 4 5 6 7 8 9 10
CTRIA3 EID PID G1 G2 G3 THETA or
MCID ZOFFS
T1 T2 T3
Field Contents
EID Element identification number. (Integer > 0)
PID Property identification number of a PSHELL or PCOMP entry.(Integer > 0;
Default is EID)
Gi Grid point identification numbers of connection points. (Integers > 0, all unique)
THETA Material property orientation angle in degrees. (Real; Default = 0.0)
MCID Material coordinate system identification number. The x-axis of the material coordinate system is determined by projecting the x-axis of the MCID
coordinate system (defined by the CORDij entry or zero for the basic coordinate system) onto the surface of the element. (Integer ≥ 0; if blank, then THETA = 0.0 is assumed)
ZOFFS Offset from the surface of grid points to the element reference plane. (Real) Ti Membrane thickness of element at grid points G1, G2, and G3. (Real ≥ 0.0
or blank, not all zero)
If you don’t supply values for Ti, then the software sets the element corner thicknesses T1 through T3 equal to the value of T on the PSHELL entry.
See Also
• “CTRIA3” in the NX Nastran Quick Reference Guide.