An Efficient Evaluation of Structural Safety applying Perturbation Techniques

The application of probabilistic techniques on structural safety evaluation has suffered a great expansion in the last years. However, one of the main problems in the introduction of these techniques is the long computational time consuming required, particularly when simulation methods as Monte-Carlo method are used, even when sampling reduction techniques are adopted [

2

]. In this paper is presented an efficient structural reliability method that couples perturbation techniques with the finite element method [

1

]. This method allows, in one only structural analysis, to evaluate the mean value and the standard deviation of the structural response, by defining previously the probability distribution of problem basic random variables. Consequently a much faster analysis is performed, when compared with the most frequent used methods based on reliability techniques. Considering a structural system, with n structural elements, submitted to a load defined by F· Φ = F·[Φ

1

, Φ

2

, ..., Φ

n

]; where F is the load intensity and [Φ

1

, Φ

2

, ..., Φ

n

] is the load distribution vector along the structure. According to the finite element method, the system equilibrium is defined by the following equation: K(

u

)·U = F·Φ; where K(

u

) is the tangent stiffness matrix of the structure, defined as a function of the nodal displacements U and F·Φ is the nodal forces vector (it includes dead loads, live loads, wind, etc.). By applying perturbation techniques to this equation it is possible to quantify the mean structural response and its dispersion, in terms of displacements or forces. Finally comparative examples between the results obtained with this technique and other probabilistic methods are presented, allowing to appraise the potentialities of the proposed method.