Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Stochastic seismic analysis of multidegree of freedom systems
1984
Abstract A unconditionally stable step-by-step procedure is proposed to evaluate the mean square response of a linear system with several degrees of freedom, subjected to earthquake ground motion. A non-stationary modulated random process, obtained as the product of a deterministic time envelope function and a stationary noise, is used to simulate earthquake acceleration. The accuracy of the procedure and its extension to nonlinear systems are discussed. Numerical examples are given for a hysteretic system, a duffing oscillator and a linear system with several degrees of freedom.
Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration
2002
Abstract The problem of calculating the response of a distributed parameter system excited by a moving oscillator with random mass, velocity and acceleration is investigated. The system response is a stochastic process although its characteristics are assumed to be deterministic. In this paper, the distributed parameter system is assumed as a beam with Bernoulli–Euler type analytical behaviour. By adopting the Galerkin's method, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained. The statistical characteristics of the deflection of the beam are computed by using an improved perturbation approach with respect t…
The Mean-Field Limit for Solid Particles in a Navier-Stokes Flow
2008
We propose a mathematical derivation of Brinkman's force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Omega subset of R-3 for the velocity field u of an incompressible fluid with kinematic viscosity v and density 1. Brinkman's force consists of a source term 6 pi rvj where j is the current density of the particles, and of a friction term 6 pi vpu where rho is the number density of particles. These additional terms in the motion equation for the fluid are obtained from the Stokes or steady Navier-Stokes equations set in Omega minus the disjoint union of N balls of radius epsilo…
Set-valued and fuzzy stochastic differential equations driven by semimartingales
2013
Abstract In the paper we present set-valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties. Then we study the existence of solutions to set-valued and fuzzy-set-valued stochastic differential equations driven by semimartingales. The stability of solutions is also established.
Set-valued stochastic integral equations driven by martingales
2012
Abstract We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.
The Itô Integral
2014
The Ito integral allows us to integrate stochastic processes with respect to the increments of a Brownian motion or a somewhat more general stochastic process. We develop the Ito integral first for Brownian motion and then for generalized diffusion processes (so called Ito processes). In the third section, we derive the celebrated Ito formula. This is the chain rule for the Ito integral that enables us to do explicit calculations with the Ito integral. In the fourth section, we use the Ito formula to obtain a stochastic solution of the classical Dirichlet problem. This in turn is used in the fifth section in order to show that like symmetric simple random walk, Brownian motion is recurrent …
Fuzzy Stochastic Integral Equations Driven by Martingales
2011
Exploiting the properties of set-valued stochastic trajectory integrals we consider a notion of fuzzy stochastic Lebesgue–Stieltjes trajectory integral and a notion of fuzzy stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of fuzzy stochastic integral equations. We investigate the existence and uniqueness of solution to such the equations.
Boundary Integral Formulation for Composite Laminates in Torsion
1997
The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem's analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characte…
Influence of data input in the evaluation of Stress Intensity Factors from Thermoelastic Stress Analysis
2021
Abstract Thermoelastic Stress Analysis (TSA) is applied to evaluate the Stress Intensity Factor (SIF), T-stress and J-Integral in a Single-Edge-Notched-Tension sample undergoing fatigue cycling. The Williams’ series stress formulation and a least-square fitting (LSF) procedure are used to obtain the SIF and the T-stress. The evaluation is carried out with the aim to investigate the influence of the input data in the system of equations solved with the LSF, and in particular: the number of coefficients used in the Williams’ series and the choice and position of the fitted experimental data points. Three algorithms for the determination of the crack tip position are also evaluated: a coarse g…
An Approximate Technique for Dynamic Elastic-Plastic Analysis
1994
The possibility of obtaining an approximate sufficiently reliable response for elasticplastic discretized structures subjected to dynamic load (kinematical and/or mechanical), with alow computational effort, has been considered. A suitable technique to this effect comes from the form of the dynamic influence matrix of imposed plastic strains on self-stresses, which is shaped by adding up a sparse time-dependent matrix and a block diagonal time-independent matrix (which is the sum of two block diagonal matrices). Several cases of practical interest have been studied, among these cases a special one where all the degrees-of-freedom are dynamic. The technique is compared to other approximate t…