Accounting for coherence in wind forces in finite element models

(2005)

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 ... [more ▼]

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. [less ▲]

Generation of spatially correlated wind histories

in Proceedings of the first Internation Conference on Finite Element Methods (2003)

Turbulent wind is a natural and therefore random phenomenon. The analysis of flexible structures subjected to turbulent wind requires, in a finite element approach, the resolution of a system of ... [more ▼]

Turbulent wind is a natural and therefore random phenomenon. The analysis of flexible structures subjected to turbulent wind requires, in a finite element approach, the resolution of a system of stochastic differential equations. It is supposed that the characteristics of the structure are perfectly known; thus the stochastic aspect of the problem comes from the random loading only. As the turbulent wind is most commonly characterized by its frequency content, the resolution of this equation is generally performed in the frequency domain. All governing equations must therefore be linear. If this can be reasonably supposed for the structure, this hypothesis is not mathematically justified for the wind loading. When the non linear behaviour of any part of the structure has to be accounted for, the resolution in the frequency domain is not valid anymore. It is then necessary to compute, with a step-by-step dynamic analysis, the response of the structure to a series of generated wind histories. In a finite element approach, this is for example achieved thanks to Newmark’s or Wilson’s methods. Averaging across the ensemble of the computed time-varying responses allows then to recover statistical results that a stochastic analysis would provide. This analysis method is known as a stochastic Monte Carlo simulation. After having emphasised the need to represent correctly the coherence between wind pressures at different points of the structure, this paper will present a method for generating a set of correlated wind histories that must be used in a finite element analysis. Finally an example of application of the presented method will prove its efficiency. [less ▲]

Analysis of linear structures with non linear dampers

in Proceeding of the Eurodyn Conference 2002 (2002)

This paper provides information about the numerical simulation of the dynamic behaviour of linear structures including non linear dampers, for which the relation between the damping force and the velocity ... [more ▼]

This paper provides information about the numerical simulation of the dynamic behaviour of linear structures including non linear dampers, for which the relation between the damping force and the velocity is described by a power law. A first part of the paper deals with single degree of freedom (SDOF) systems, with a particular emphasis on the resolution of the non linear equation allowing to compute the damping force corresponding to a given velocity. A second part deals with multi degree of freedom (MDOF) systems, and presents a special algorithm to study the behaviour of structures with a very small number of non linear components. [less ▲]