How can I calculate the quantity known as "epsilon," which is described as the ratio of the work done by the residual load vector and the work done by externally applied forces? It is calculated as

dP = Ku-P
epsilon = (uT*dP)/(uT*P)

This can be done using APDL Math in ANSYS v13 with the following APDL:

*SMAT,k,D,IMPORT,FULL,file.full,STIFF ! stiffness, BCS ordering
*VEC ,p,D,IMPORT,FULL,file.full,RHS ! RHS vector, BCS ordering
*VEC ,nod2bcs,D,IMPORT,FULL,file.full,NOD2BCS ! mapping vector

*VEC ,int_u,D,IMPORT,RST,file.rst,1,1 ! DOF vector, internal ordering
*MULT,nod2bcs,,int_u,,u ! convert to BCS ordering

! dP = Ku-P
! ep = (uT*dP)/(uT*P)


scalar_uTdP = uTdP(1)
scalar_uTP = uTP(1)

epsilon = scalar_uTdP/scalar_uTP

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