Compliance formula

I havecome accross two versions of the compliance formula

• C= 0.5*uTf (Used in optistruct)

• C= uTf (Used in the 99 line matlab code for SIMP)

The difference between the two being the 0.5. My questions are:

1. Which is the correct formula to use?
2. What is the significance of the 0.5?

By definition, the compliance is :

C = 1/2 \int \epsilon * \sigma * \epsilon dv which corresponds to your first equation C = 1/2 u^T * K * u 

It's a strain energy (that's why we have 1/2) that measures the displacement of the structure under the defined BC. 

Which is the correct formula to use?

In general, you have to use the correct formula (see my first comment). But for the optimization, it's the same ...

In other words, the minimization problems MIN C(x) = U^T * K * U or MIN MIN C(x) = 1/2* U^T * K * U has the same solution X_s

Cheers,