Accounting for coherence in wind forces in finite element models

The behaviour of civil engineering structures subjected to wind forces is generally approached
by means of finite element models. These numerical models are necessary since the shape of the structure as well as the representation of the applied forces are difficult to handle in closed forms.
In stochastic dynamic analyses, the coherence of the applied forces – in this context coming from the wind flow – is represented by the off-diagonal terms in the power spectral density matrix. This matrix is obtained by assembling elementary matrices, each of them corresponding to a stochastically loaded finite element.
Even though the unique rigorous approach is not so complicated, simplified formulations are generally used to set up these elementary matrices. These simplifications result in a bad estimation of the high frequency content of the applied forces. Comparing these approached power spectral density’s to the actual ones enables to determine numerical admittance functions which allow correcting the bad estimation of the forces. This paper presents several finite element formulations for the estimation of the applied forces and derives the corresponding expressions of the numerical admittance functions.