Search results for " Integra"

The McShane, PU and Henstock integrals of Banach valued functions

2002

Some relationships between the vector valued Henstock and McShane integrals are investigated. An integral for vector valued functions, defined by means of partitions of the unity (the PU-integral) is studied. In particular it is shown that a vector valued function is McShane integrable if and only if it is both Pettis and PU-integrable. Convergence theorems for the Henstock variational and the PU integrals are stated. The families of multipliers for the Henstock and the Henstock variational integrals of vector valued functions are characterized.

A Survey on how to Cross-Reference Web Information Sources

2015

International audience; The goal of giving information a well-defined meaning is currently shared by different research communities. Once information has a well-defined meaning, it can be searched and retrieved more effectively. Therefore, this paper is a survey about the methods that compare different textual information sources in order to determine whether they address a similar information or not. The improvement of the studied methods will eventually lead to increase the efficiency of documentary research. In order to achieve this goal, the first category of methods focuses on semantic measure definitions. A second category of methods focuses on paraphrase identification techniques, an…

Non-linear Systems Under Poisson White Noise Handled by Path Integral Solution

2008

An extension of the path integral to non-linear systems driven by a Poissonian white noise process is presented. It is shown that at the limit when the time increment becomes infinitesimal the Kolmogorov— Feller equation is fully restored. Applications to linear and non-linear systems with different distribution of the Dirac's deltas occurrences are performed and results are compared with analytical solutions (when available) and Monte Carlo simulation.

CVBEM solution for De Saint-Venant orthotropic beams under coupled bending and torsion

2014

The aim of this paper is to provide a solution for the coupled flexure–torsion De Saint Venant problem for orthotropic beams taking full advantage of the complex variable boundary element method (CVBEM) properly extended using a complex potential function whose real and imaginary parts are related to the shear stress components, the orthotropic ratio and the Poisson coefficients. The proposed method returns the complete stress field and the unitary twist rotation of the cross section at once by performing only line integrals. Numerical applications have been reported to show the validity and the efficiency of the proposed modified CVBEM to handle shear stress problems in the presence of ort…

Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals

2012

Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.

On the translation of the three fundamental problems of elastic equilibrium of anisotropic bodies into systems of Fredholm first kind integral equati…

1972

CVBEM application to a novel potential function providing stress field and twist rotation at once

2013

AbstractIn this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performin…

Path integral solution handled by Fast Gauss Transform

2009

Abstract The path integral solution method is an effective tool for evaluating the response of non-linear systems under Normal White Noise, in terms of probability density function (PDF). In this paper it has been observed that, using short-time Gaussian approximation, the PDF at a given time instant is the Gauss Transform of the PDF at an earlier close time instant. Taking full advantage of the so-called Fast Gauss Transform a new integration method is proposed. In order to overcome some unsatisfactory trends of the classical Fast Gauss Transform, a new version termed as Symmetric Fast Gauss Transform is also proposed. Moreover, extensions to the two Fast Gauss Transform to MDOF systems ar…

Path Integral Method for Nonlinear Systems Under Levy White Noise

2017

In this paper, the probabilistic response of nonlinear systems driven by alpha-stable Lévy white noises is considered. The path integral solution is adopted for determining the evolution of the probability density function of nonlinear oscillators. Specifically, based on the properties of alpha-stable random variables and processes, the path integral solution is extended to deal with Lévy white noises input with any value of the stability index alpha. It is shown that at the limit when the time increments tend to zero, the Einstein–Smoluchowsky equation, governing the evolution of the response probability density function, is fully restored. Application to linear and nonlinear systems under…

Direct stiffness matrices of BEs in the Galerkin BEM formulation

2001

Abstract In the analysis of an elastic two-dimensional solid body by means of the Symmetric Galerkin Boundary Element Method (SGBEM), difficulties arise in the computation of some terms of the solving system coefficients. In fact these coefficients are expressed as double integrals with singularities of order 1/ r 2 , r being the distance between the field and source points. In order to compute these coefficients a strategy based on Schwartz's distribution theory is employed. In this paper the direct stiffness matrix related to the generic node of the free boundary are computed in closed form.