Thin Shell Coordinate Systems

Thin shell coordinate systems

Global Cartesian and element local.

By default thin shell results are written in the following coordinate systems:

• Tensor components such as stress and strain are written in the global system
• Force and moment resultants are written in the element local system
• Other results, eg effective plastic strain, thickness, etc have no intrinsic coordinate system.

It is possible to write tensor results in other systems by using special flags on some material cards. If you do this be aware that there is no flag in the results database to indicate the coordinate sytem used, so D3PLOT will not "know about" this and will assume that these results are in the global system.

Effect of INN flag on *CONTROL_ACCURACY card on local coordinate system axes

By default element local axes in Ansys LS-DYNA align their local X' axis with the vector N1N2. However if the element is poorly shaped, or becomes heavily deformed during the analysis, this can degrade the accuracy of the stress calculation as the original stress directions become misaligned with the updated axes, so an improved calculation method is provided via flag INN on *CONTROL_ACCURACY , although this costs more cpu time. The diagram below shows how the local axis system ceases to be so dependent on the N1N2 vector.

The INN value is reported in the d3plot (.ptf) database file for versions of Ansys LS-DYNA from approximately 2012 onwards (exact version not known at time of writing). If it is present and set to a non-default value D3PLOT will adjust its local axis calculation for shell elements to use the correct axis system. This will affect the following:

• Calculation of cut-section forces through shell elements, which use the shell force and moment resultants
• Conversion of tensor-based results from global to local axes ("Local" frame of reference)
• Conversion of tensor-based results into composite ply local axes.
• Display of local element triads.

The local element axes, [X',Y',Z'] , are calculated as follows.

Default case: INN = 0 or 1 on *CONTROL_ACCURACY

If we adopt the notation that the vector from node 1 to node 2 is N1N2 :

X'	=	N1N2 approximately: the final X' vector recomputed below.
Z'	=	N1N3 x N2N4	(Where x is a vector cross-product)
Y'	=	Z' x X'
X'	=	Y' x Z' This final transformation is required to correct for any warping

Some components are written in the global Cartesian system, and D3Plot can transform these results to the local element system if required with the FRAME_OF_REFERENCE options. Examples are the stress and strain tensor values.

Other components are written in the element local system. Examples are the force and moment resultants.

Invariant case: INN = +/-2 or +/-4 on *CONTROL_ACCURACY

A more complex vector calculation is performed to obtain more natural coordinates, as shown in the image above.

We will revisit this topic in Summary of coordinate systems and default locations of thin shell results .