Numerical stabilization of the Stokes problem in vorticity–velocity–pressure formulation

We work on a vorticity, velocity and pressure formulation of the bidimensional Stokes problem for incompressible fluids. In previous papers, the authors have developed a natural implementation of this scheme. We have then observed that, in case of unstructured meshes with Dirichlet boundary conditions on the velocity, the convergence is not optimal. In this paper, we propose to add ‘‘bubble’’ velocity functions with compact support along the boundary to improve convergence. We then prove a convergence theorem and illustrate by numerical results better behaviour of the scheme in general cases

Vibro-impact of a plate on rigid obstacles: existence theorem, convergence of a scheme and numerical simulations

The purpose of this paper is to describe a fully discrete approximation and its convergence to the continuum dynamical impact problem for the fourth-order Kirchhoff–Love plate model with nonpenetration Signorini contact condition. We extend to the case of plates the theoretical results of weak convergence due to Y. Dumont and L. Paoli, which was stated for Euler–Bernouilli beams. In particular, this provides an existence result for the solution of this problem. Finally, we discuss the numerical results we obtain

Adaptive mesh refinements for thin shells whose middle surface is not exactly known

A strategy concerning mesh refinements for thin shells computation is presented. The geometry of the shell is given only by the reduced information consisting in nodes and normals on its middle surface corresponding to a coarse mesh. The new point is that the mesh refinements are defined from several criteria, including the transverse shear forces which do not appear in the mechanical energy of the applied shell formulation. Another important point is to be able to construct the unknown middle surface at each step of the refinement. For this, an interpolation method by edges, coupled with a triangle bisection algorithm, is applied. This strategy is illustrated on various geometries and mechanical problems

A coupled parametric and nonparametric approach for modal analysis of a satellite

This study takes place in the context of dynamical prediction for satellite structures. Aims of such studies are to survey the dynamical response of satellite equipment and components, to check that requirements are correct and to give prediction of vibration levels, which are inputs for the experimental test validation according to the launcher specification. This prediction is done by modal analysis performed on a numerical model built by finite element method. Uncertainties on equipment and components properties lead to random frequency response function (FRF). This paper aims at understanding how modal approach can be adapted to probabilistic framework in order to calculate cumulative density function or, at least, some quantiles of a FRF. Starting point of deterministic modal analysis is the study of a single degree of freedom (DOF) system. C. Heinkelé analytically expresses the probability density function (PDF) of the FRF of an oscillator with a random natural pulsation following a uniform law. We have generalized this work to random natural pulsation following a law of finite variance. Then, the expression of a FRF between two DOF of the structure is a linear function of random oscillators FRF and DOF components of random eigenvectors. Assuming that random eigenvectors are close to their means, we have access to the characteristic function of the random FRF between two DOF as a multi-dimensional integral with respect to the joint PDF of the oscillators FRF. This paper mainly focuses on two major points which are calculation of oscillators joint PDF and inversion of characteristic functions. The first one is tackled by copulas theory. Dependence structure of random eigenvalues are identified and modeled by a copula. Then we apply results on copulas transformations to obtain joint PDF of oscillators FRF. Classical results concern monotonic transformations but we extended these ones to non-monotonic cases. Concerning inversion of characteristic function, several methods are studied to numerically compute the Gil-Pelaez formula. This approach allows to access some FRF quantiles by numerical integration which error can be controlled. Moreover, an interesting point is the flexibility in the identification of the random eigenvalues PDF. This is especially interesting in order to couple parametric identification with nonparametric one, when only few dispersion informations are given for equipments, housed in the satellite primary structure

A new adaptive response surface method for reliability analysis

Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed

Coupling Harmonic Functions-Finite Elements for Solving the Stream Function-Vorticity Stokes Problem

We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity form. The classical finite element method of degree one usually used does not allow the vorticity on the boundary of the domain to be computed satisfactorily when the meshes are unstructured and does not converge optimally. To better approach the vorticity along the boundary, we propose that harmonic functions obtained by integral representation be used. Numerical results are very satisfactory, and we prove that this new numerical scheme leads to an optimal convergence rate of order 1 for the natural norm of the vorticity and, under higher regularity assumptions, from 3/2 to 2 for the quadratic norm of the vorticity

A localization and updating strategy of large finite element models in structural dynamics

The purpose of this paper is to evaluate the application of the error of constitutive law method to the updating of large FE models of space structures using FRF experimental results. First, we briefly recall the theoretical basis of this method in modal and frequency approaches. Then, the notion of visibility is introduced to improve the modelling of localization error and the quality of modal updating, for low frequencies. Finally we propose a global strategy and discuss the results we obtained on satellite JASON2

Model-Based Adaptation of Software Communicating via FIFO Buffers

Software Adaptation is a non-intrusive solution for composing black-box components or services (peers) whose individual functionality is as required for the new system, but that present interface mismatch, which leads to deadlock or other undesirable behaviour when combined. Adaptation techniques aim at automatically generating new components called adapters. All the interactions among peers pass through the adapter, which acts as an orchestrator and makes the involved peers work correctly together by compensating for mismatch. Most of the existing solutions in this field assume that peers interact synchronously using rendezvous communication. However, many application areas rely on asynchronous communication models where peers interact exchanging messages via buffers. Generating adapters in this context becomes a difficult problem because peers may exhibit cyclic behaviour, and their composition often results in infinite systems. In this paper, we present a method for automatically generating adapters in asynchronous environments where peers interact using FIFO buffers.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Joint Subcarrier and Power Allocation in NOMA: Optimal and Approximate Algorithms

Non-orthogonal multiple access (NOMA) is a promising technology to increase the spectral efficiency and enable massive connectivity in 5G and future wireless networks. In contrast to orthogonal schemes, such as OFDMA, NOMA multiplexes several users on the same frequency and time resource. Joint subcarrier and power allocation problems (JSPA) in NOMA are NP-hard to solve in general. In this family of problems, we consider the weighted sum-rate (WSR) objective function as it can achieve various tradeoffs between sum-rate performance and user fairness. Because of JSPA's intractability, a common approach in the literature is to solve separately the power control and subcarrier allocation (also known as user selection) problems, therefore achieving sub-optimal result. In this work, we first improve the computational complexity of existing single-carrier power control and user selection schemes. These improved procedures are then used as basic building blocks to design new algorithms, namely Opt-JSPA, $\varepsilon$-JSPA and Grad-JSPA. Opt-JSPA computes an optimal solution with lower complexity than current optimal schemes in the literature. It can be used as a benchmark for optimal WSR performance in simulations. However, its pseudo-polynomial time complexity remains impractical for real-world systems with low latency requirements. To further reduce the complexity, we propose a fully polynomial-time approximation scheme called $\varepsilon$-JSPA. Since, no approximation has been studied in the literature, $\varepsilon$-JSPA stands out by allowing to control a tight trade-off between performance guarantee and complexity. Finally, Grad-JSPA is a heuristic based on gradient descent. Numerical results show that it achieves near-optimal WSR with much lower complexity than existing optimal methods

Simulation of dynamic delamination and mode I energy dissipation

Delamination initiation and propagation of aeronautic composites is an active field of research. In this paper we present a methodology for critical energy release rate correlation of numerical simulation and experimental data. Experiments of mode I critical energy release rate were carried out at quasi static and pseudo dynamic loading rates. Cohesive finite elements are used to predict the propagation of delamination in a carbon fiber and epoxy resin composite material. A bilinear material model is implemented via user defined cohesive material subroutine in LS-DYNA. The influence of mode I energy release rate in mixed mode loading, due to a low velocity impact, is also investigate