Computational Methods in Stochastic Dynamics: Volume 2 by Anas Batou, Christian Soize (auth.), Manolis Papadrakakis,

By Anas Batou, Christian Soize (auth.), Manolis Papadrakakis, George Stefanou, Vissarion Papadopoulos (eds.)

The substantial impact of inherent uncertainties on structural habit has led the engineering group to acknowledge the significance of a stochastic method of structural difficulties. concerns relating to uncertainty quantification and its impact at the reliability of the computational versions are consistently gaining in value. particularly, the issues of dynamic reaction research and reliability evaluation of buildings with doubtful approach and excitation parameters were the topic of continuing study during the last 20 years because of the expanding availability of strong computing assets and know-how.

This publication is a persist with up of a prior ebook with an analogous topic (ISBN 978-90-481-9986-0) and specializes in complicated computational equipment and software program instruments that could hugely help in tackling advanced difficulties in stochastic dynamic/seismic research and layout of constructions. the chosen chapters are authored through the most energetic students of their respective components and characterize probably the most contemporary advancements during this field.

The booklet includes 21 chapters which are grouped into numerous thematic issues together with dynamic research of stochastic platforms, reliability-based layout, structural keep an eye on and health and wellbeing tracking, version updating, procedure id, wave propagation in random media, seismic fragility research and harm assessment.

This edited ebook is essentially meant for researchers and post-graduate scholars who're conversant in the basics and want to review or to increase the state-of-the-art on a selected subject within the box of computational stochastic structural dynamics. however, working towards engineers may gain advantage to boot from it as so much code provisions are likely to include probabilistic options within the research and layout of buildings.

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1) have become standard in the literature. Excellent references, for example [2, 3, 10, 20] are available on this topic. In Eq. 11), A0 (ω) ∈ Cn×n and Ai (ω) ∈ Cn×n ; i = 1, 2, . . , M are symmetric matrices which are deterministic in nature, u(ω, θ ) ∈ Cn is the solution vector and f0 ∈ Cn in the input vector. We assume that the eigenvalues of the generalized eigenvalue problem with the deterministic mass (M0 ) and stiffness matrices K0 are distinct. The number of terms M in Eq. 11) can be selected based on the accuracy desired for the representation of the underlying random field.

11) in an efficient manner and is the main topic of this paper. We propose a solution technique for Eq. 11) when ξi (θ ) are in general non-Gaussian and correlated random variables. 11) is a key step in the stochastic finite element analysis. As a result, several methods have been proposed. These methods include, first- and second-order perturbation methods [14, 18], Neumann expansion method [1, 36], Galerkin approach [11], linear algebra based methods [6, 7, 17] and simulation methods [26]. More recently efficient collocation methods have been proposed [8, 19].

8b) are in close agreement with the corresponding MCS estimates. In all cases examined the maximum error in the computed Var[u(t)], observed at the peak values of the variance, is less than 25%, while in all other time steps this error is less than 3–4%. In the case of ε[u(t)], the predictions of Eq. 8b) are almost identical to the ones obtained with MCS, with an error of less than 3% in all cases. From Figs. 7(a)–(c), it can be observed that in all cases, the mean response time 24 V. Papadopoulos and O.

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