a b s t r a c tIn current practice, structural engineers commonly focus on the wind-resistant design by means of static wind loads. In the case of non-Gaussianities, there is room for improvement to properly derive these static loads. First, this paper extends in a non-Gaussian context the concept of the load-response correlation (LRC) method establishing equivalent static wind loads (ESWLs). This is done by a proper recourse to the new concept of conditional expected static wind load and a proposed bicubic model for the joint and conditional distribution functions. Second, this paper investigates the envelope reconstruction problem targeting the efficient reconstruction of the envelope values of a set of non-Gaussian structural responses by means of principal static wind loads (PSWLs). They have been introduced in a Gaussian context and are obtained by a singular value decomposition of ESWLs. This paper addresses the extension of PSWLs to non-Gaussian structural responses, as well. The developments apply to structures with a linear behavior and subjected to an aerodynamic pressure field exhibiting mildly to strongly nonGaussian features. In this context, the well-known load-response correlation and conditional sampling methods are used for comparisons. This study is undertaken for quasi-static analysis of structures and is illustrated on a low-rise building.
In current practice, wind structural design is often carried out using the concept of equivalent static wind loads. The main characteristic of such loadings is to reproduce, with static analyses, the same extreme structural responses as those resulting from a formal buffeting analysis. This paper proposes a method for the computation of equivalent static wind loads for structures with slight non-proportional damping in a modal framework. Because of the smallness of the out-of diagonal terms, this method is based on recent developments related to asymptotic expansion of the modal transfer matrix of such structures. As a main benefit, the static loading is described as a perturbation of the equivalent loading that would be obtained for the uncoupled system. The main contribution of this paper is to formalize the expression of the correction terms resulting from the non-proportionality of damping. The method is presented with a detailed illustrative example.
Probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function ψ (pdf). The time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient Fokker-Planck-Kolmogorov equation (FPK). The FPK equation is a conservation equation of a hypothetical or abstract fluid, which models the transport of probability. This paper presents a generalized formalism for the resolution of the transient FPK equation using the well-known mesh-free Lagrangian method, Smoothed Particle Hydrodynamics (SPH).Numerical implementation shows notable advantages of this method in an unbounded state space: (i) the conservation of total probability in the state space is explicitly written, (ii) no artifact is required to manage far-field boundary conditions , (iii) the positivity of the pdf is ensured and (iv) the extension to higher dimensions is straightforward.Furthermore, thanks to the moving particles, this method is adapted for a large kind of initial conditions, even slightly dispersed distributions. The FPK equation is solved without any a priori knowledge of the stationary distribution; just a precise representation of the initial distribution is required.
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