Back expand mode shapes from TAM DOF to expanded DOF
ST_EXP=backexp(ST,TAM)
BACKEXP takes the supplied imat_shp or imat_fn ST and substructure TAM and generates an expanded set of mode shapes or functions. ST_EXP is an imat_shp or imat_fn containing the expanded shapes or functions. For imat_shps, the expanded shape coefficients will be in the local coordinate system(s) of the nodes. To transform these to global coordinates, use imat_shp/xform. For imat_fns, for each reference coordinate the functions must all be the same type must have the same abscissa values.
The input substructure, TAM, must have at least the fields .aset, .oset, and .constraint. Both ASET and OSET fields are imat_ctrace, and the back expansion matrix defined in TAM.constraint must have dimensions [oset aset].
By default, the back-expanded shapes will contain bothOSETand ASET DOF, as well as other test measured DOF. If you pass in the string 'noaugment', the back-expanded shapes will only contain the OSET and extra DOF.
While BACKEXP has a specific use for modal test data, it can be used as a generalized utility to multiply shapes or functions by a matrix. For each abscissa value in the functions, or each shape, BACKEXP performs the following matrix multiplication:
EXP = CONSTRAINT * ST
where CONSTRAINT is TAM.constraint, and is of size [nset aset], where nset = oset for 'noaugment', and nset = oset+aset by default. Prior to performing the multiplication, it will adjust the sign of the coefficients based on the directions in the coordinate traces. Note that any coefficients not in OSET or ASET will pass through to the expanded result as well.
If you have substructure matrices from NASTRAN, use MAT2SUBST to convert the matrices into the TAM substructure format.
>> st_exp=backexp(st,TAM);
imat_shp/xform, readnas, mat2subst