Principal Stress Values From Stress Tensor - Excel Labs LAMBDA Function

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Principal Stress Values From Stress Tensor - Excel Labs LAMBDA Function 图片 1

PrincipalStressLambdaFunction

/**
* Returns Principal Stress Values from Tensor (Sx,Sy,Sz,Sxy,Syz,Sxz)
* - Tensor is a row range of values
* - Direct solution of the cubic polynomial
**/
PRINCIPALSTRESS=LAMBDA( StressTensor,
LET(
SX, INDEX(StressTensor,,1),
SY, INDEX(StressTensor,,2),
SZ, INDEX(StressTensor,,3),
SXY, INDEX(StressTensor,,4),
SYZ, INDEX(StressTensor,,5),
SXZ, INDEX(StressTensor,,6),
B, 2*(SX+SY+SZ),
C, 6*(SX*SY+SY*SZ+SX*SZ-SXY^2-SYZ^2-SXZ^2),
D, 108*(SX*SY*SZ-SX*SYZ^2-SY*SXZ^2-SZ*SXY^2+2*SXY*SYZ*SXZ),
P, B^2-2*C, // P >= 0
Q, B*(P-C)+D,
V, ABS(C^2*(3*P-2*C)-D*(2*Q-D)),
T, IF( OR(P=0,Q+V=0), 0, ATAN2(Q, SQRT(V))/3 ),
R, SQRT(ABS(P)),
X, R*COS(T),
Y, R*SIN(T)*SQRT(3),
HSTACK(B+2*X, B-X+Y, B-X-Y)/6
)
);
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