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SUBROUTINE SHSTTS (TAB,UAB,VAB)
C
C TO CREATE STRESS TENSOR TRANSFORMATION MATRICES FROM AN ORTHOGONAL
C TRANSFORMATION FOR SHELL ELEMENTS.
C
C INPUT :
C TAB - ORTHOGONAL INPLANE ROTATION TRANSFORMATION
C OUTPUT:
C UAB - TENSOR TRANSFORMATION FOR NORMAL AND INPLANE SHEAR
C COMPONENTS
C VAB - TENSOR TRANSFORMATION FOR OUT-OF-PLANE SHEAR
C
C USAGE:
C THE INPUT IS ASSUMED TO BE ROW-LOADED.
C OUTPUTS ARE CREATED ROW-LOADED.
C DEFINING:
C [S] AS A 2-D STRESS VECTOR;
C [E] AS A 2-D STRAIN VECTOR;
C [Q] AS A 2-D SHEAR FORCE VECTOR;
C [G] AS A 2-D STRESS/FORCE-STRAIN RELATION; AND
C [ALPHA] AS A VECTOR OF THERMAL EXPANSION COEFFICIENTS,
C
C THEN THE FOLLOWING RELATIONSHIPS ARE TRUE:
C
C T T
C [S] = [UAB] [S] [G] = [UAB] [G] [UAB]
C A B A B
C
C T
C [Q] = [VAB] [Q]
C A B
C
C IF [TBA] IS INPUT, THE OUTPUT WILL BE:
C
C -1 -1 T
C [UAB] = [UBA], AND [VAB] = [VAB] = [VBA]
C
C WHICH MAY BE USED IN THE FOLLOWING:
C
C [E] = [UBA] [E] [ALPHA] = [UBA] [ALPHA]
C A B A B
C
C [Q] = [VBA][Q]
C A B
C
C
REAL TAB(9),UAB(9),VAB(4)
C
UAB(1) = TAB(1)*TAB(1)
UAB(2) = TAB(4)*TAB(4)
UAB(3) = TAB(1)*TAB(4)
UAB(4) = TAB(2)*TAB(2)
UAB(5) = TAB(5)*TAB(5)
UAB(6) = TAB(2)*TAB(5)
UAB(7) = TAB(1)*TAB(2)*2.0
UAB(8) = TAB(4)*TAB(5)*2.0
UAB(9) = TAB(1)*TAB(5) + TAB(2)*TAB(4)
C
VAB(1) = TAB(5)*TAB(9)
VAB(2) = TAB(2)*TAB(9)
VAB(3) = TAB(4)*TAB(9)
VAB(4) = TAB(1)*TAB(9)
C
RETURN
END
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