1,721,162 research outputs found
Approximate solution of the Fokker-Planck-Kolmogorov equation
No full textThe aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions in order to obtain improved estimates of the response PDF are discussed in detail. Finally, a simple and very effective iterative solution procedure is proposed. © 2002 Published by Elsevier Science Ltd
Long-range interactions in 1D heterogeneous solids with uncertainty
Full text linkIn this paper, the authors aim to analyze the response of a one-dimensional non-local elastic solid with uncertain Young's modulus. The non-local effects are represented as long-range central body forces between non-adjacent volume elements. Following a non-probabilistic approach, the fluctuating elastic modulus of the material is modeled as an interval field. The analysis is conducted resorting to a novel formulation that confines the overestimation effect involved in interval models. Approximate closed-form expressions are derived for the bounds of the interval displacement fiel
A new displacement-based framework for non-local Timoshenko beams
Full text linkIn this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed non-local beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature
A sofi,a fogalma Arisztotelész két művében és magában a Szeptuagintában
No full textA sofi,a fogalma címben megadott keretek között történő elemzésének eredménye a következő: Arisztotelésznél a sofi,a összetett és lenyűgöző tudomány. Az evpisth,mh a tudományos ismeret vagy szaktudás, világosan megkülönböztethető más tudásformáktól, mint például a fro,nhsij, a gyakorlati okosság vagy ítélőképesség; a su,nesij, a megismerés, amely az érzékelés révén vezet problémák megoldásához; a dia,noia, az értelmes gondolkodás; a te,cnh, a kézügyesség, technikai jártasság és a nou/j, az ész, intellektus, intelligencia. A sofi,a önmagában is hasznos, használható, de a nou/j és evpisth,mh kombinációjaként bontakozik ki igazán a gyakorlatban, amikor képessé teszi a bölcset (sofo,j) arra, hogy bizonyítékokkal legyen meggyőző erejű (avpo,deixij). Arisztotelésznél a sofi,a nem feltétlen isteni eredetű, míg a Szeptuagintában az a sofi,a, amely a bölcset igazán bölccsé teszi, egyértelműen az Úrhoz kötődik
Dynamic analysis of prestressed cables with uncertain pretension
No full textThis paper deals with finite element dynamic analysis of prestressed cables with uncertain pretension subjected to deterministic excitations. The theoretical model addressed for cable modeling is a two-dimensional finite-strain beam theory, which allows us to eliminate any restriction on the magnitude of displacements and rotations. The dynamic problem is formulated by referring the motion to the inertial frame, which leads to a simple uncoupled quadratic form for the kinetic energy. The effect of the externally applied stochastic pretension is approximately described by means of an uncertain 'axial' component of stress resultant, which is assumed constant along the cable in its dead load configuration. The so-called improved perturbation approach is employed to solve this stochastic problem, obtaining two coupled systems of nonlinear deterministic ordinary differential equations, governing the mean value and deviation of response. An efficient and accurate iterative procedure is proposed to obtain the solution of these equations. In order to investigate the influence of random pretension on structural response, few numerical applications are presented and results are discussed
Interval serviceability assessment of footbridges
No full textThis paper studies serviceability assessment of footbridges through a non-deterministic approach. The parameters defining pedestrian-induced loading and the structural dynamic properties are characterized through possible ranges of variation. Starting from analytical expressions for the spectral moments of the structural response, the improved interval analysis is applied together with an optimization strategy that allows us to obtain the bounds of the standard deviation of the footbridge acceleration and of the mean value and cumulative distribution function of its maximum value. Based on this approach, a possible interval of variation of the structural response is evaluated, rather than a single deterministic value. Thus, an interval level of comfort can be defined
Monte Carlo simulation for the response analysis of long-span suspended Cables under wind loads
No full textServiceability Assessment of Footbridges Via Improved Interval Analysis
No full textThis paper studies the propagation of uncertainties on serviceability assessment of footbridges in unrestricted traffic condition based on a nondeterministic approach. Multipedestrian loading is modeled as a stationary Gaussian random process through the equivalent spectral model which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the improved interval analysis, is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level
Nonstationary response envelope probability densities of nonlinear oscillators
No full textThe nonstationary random response of a class of lightly damped nonlinear oscillators subjected to Gaussian white noise is considered. An approximate analytical method for determining the response envelope statistics is presented. Within the framework of stochastic averaging, the procedure relies on the Markovian modeling of the response envelope process through the definition of an equivalent linear system with response-dependent parameters. An approximate solution of the associated Fokker-Planck equation is derived by resorting to a Galerkin scheme. Specifically, the nonstationary probability density function of the response envelope is expressed as the sum of a time-dependent Rayleigh distribution and of a series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. These functions are the eigen-functions of the boundary-value problem associated with the Fokker-Planck equation governing the evolution of the probability density function of the response envelope of a linear oscillator. The selected basis functions possess some notable properties that yield substantial computational advantages. Applications to the Van der Pol and Duffing oscillators are presented. Appropriate comparisons to the data obtained by digital simulation show that the method, being nonperturbative in nature, yields reliable results even for large values of the nonlinearity parameter. Copyright © 2007 by ASME
One-dimensional heterogeneous solids with uncertain elastic modulus in presence of long-range interactions: Interval versus stochastic analysis
Full text linkThe analysis of one-dimensional non-local elastic solids with uncertain Young's modulus is addressed. Non-local effects are represented as long-range central body forces between non-adjacent volume elements. For comparison purpose, the fluctuating elastic modulus of the material is modeled following both a probabilistic and a non-probabilistic approach. To this aim, a novel definition of the interval field concept, able to limit the overestimation affecting ordinary interval analysis, is introduced. Approximate closed-form expressions are derived for the bounds of the interval displacement field as well as for the mean-value and variance of the stochastic respons
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