Finite Element Analysis for the Buckling Load of Corrugated Tubes

The buckling behavior of the geometry subjected to static loading (compression) is presented. The columns under consideration were made with corrugation perpendicular to the line of action which coincides exactly with the unstrained axis of the column. Four different arrangements of tubes have been considered for all the conditions taken into consideration. The thickness of the tubes, the number of corrugation, and diameter of the tubes, pitch and depth of the tubes have been varied accordingly. Analysis of the prepared tubes was performed using ANSYS 17.0. A linear buckling analysis was performed to calculate the critical load of the corrugated tubes. The effect of buckling and maximum critical load of the FEM models are discussed

Finite element approximation of the FENE-P model

International audienceWe extend our analysis on the Oldroyd-B model in Barrett and Boyaval [1] to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $D ⊂ R d , d = 2 or 3$, subject to no flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conforma-tion tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a) the velocity field is approximated by continuous piecewise quadratics ($d = 2$) or a reduced version, where the tangential component on each simplicial edge ($d = 2$) or face ($d = 3$) is linear. In case (b) the velocity field is approximated by continuous piecewise quadratics or the mini-element. We show that both of these types of schemes, based on the backward Euler type time discretiza-tion, satisfy a free energy bound, which involves the logarithm of both the conformation tensor and a linear function of its trace, without any constraint on the time step. Furthermore, for our approximation (b) in the presence of an additional dissipative term in the stress equation, the so-called FENE-P model with stress diffusion, we show (subsequence) convergence in the case $d = 2$, as the spatial and temporal discretization parameters tend to zero, towards global-in-time weak solutions of this FENE-P system. Hence, we prove existence of global-in-time weak solutions to the FENE-P model with stress diffusion in two spatial dimensions

Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors

This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor $L^2$ approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering

On the estimation of the persistence exponent for a fractionally integrated brownian motion by numerical simulations

For a fractionally integrated Brownian motion (FIBM) of order alpha is an element of (0, 1], X-alpha(t), we investigate the decaying rate of P(tau(alpha)(S) > t) as t -> +infinity, where tau(alpha)(S) = inf{t > 0 : X-alpha(t) >= S} is the first-passage time (FPT) of X-alpha(t) through the barrier S > 0. Precisely, we study the so-called persistent exponent theta = theta(alpha) of the FPT tail, such that P(tau(alpha)(S) > t) = t(-theta+o(1)), as t -> +infinity, and by means of numerical simulation of long enough trajectories of the process X-alpha(t), we are able to estimate theta(alpha) and to show that it is a non-increasing function of alpha is an element of (0, 1], with 1/4 <= theta(alpha) <= 1/2. In particular, we are able to validate numerically a new conjecture about the analytical expression of the function theta = theta(alpha), for alpha is an element of (0, 1]. Such a numerical validation is carried out in two ways: in the first one, we estimate theta(alpha), by using the simulated FPT density, obtained for any alpha is an element of (0, 1]; in the second one, we estimate the persistent exponent by directly calculating P(max(0)<= s <= tX(alpha)(s) < 1). Both ways confirm our conclusions within the limit of numerical approximation. Finally, we investigate the self-similarity property of X-alpha(t) and we find the upper bound of its covariance function