Some theoretical aspects in computational analysis of adhesive lap joints

This paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Some numerical results are presented

Asymptotic behavior of Structures made of Plates

The aim of this work is to study the asymptotic behavior of a structure made of plates of thickness $2\delta$ when $\delta\to 0$. This study is carried on within the frame of linear elasticity by using the unfolding method. It is based on several decompositions of the structure displacements and on the passing to the limit in fixed domains. We begin with studying the displacements of a plate. We show that any displacement is the sum of an elementary displacement concerning the normal lines on the middle surface of the plate and a residual displacement linked to these normal lines deformations. An elementary displacement is linear with respect to the variable $x$3. It is written $U(^x)+R(^x)\land x3e3$ where U is a displacement of the mid-surface of the plate. We show a priori estimates and convergence results when $\delta \to 0$. We characterize the limits of the unfolded displacements of a plate as well as the limits of the unfolded of the strained tensor. Then we extend these results to the structures made of plates. We show that any displacement of a structure is the sum of an elementary displacement of each plate and of a residual displacement. The elementary displacements of the structure (e.d.p.s.) coincide with elementary rods displacements in the junctions. Any e.d.p.s. is given by two functions belonging to $H1(S;R3)$ where S is the skeleton of the structure (the plates mid-surfaces set). One of these functions : U is the skeleton displacement. We show that U is the sum of an extensional displacement and of an inextensional one. The first one characterizes the membrane displacements and the second one is a rigid displacement in the direction of the plates and it characterizes the plates flexion. Eventually we pass to the limit as $\delta \to 0$ in the linearized elasticity system, on the one hand we obtain a variational problem that is satisfied by the limit extensional displacement, and on the other hand, a variational problem satisfied by the limit of inextensional displacements

A Modal-Based Partition of Unity Finite Element Method for Elastic Wave Propagation Problems in Layered Media

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] The time-harmonic propagation of elastic waves in layered media is simulated numerically by means of a modal-based Partition of Unity Finite Element Method (PUFEM). Instead of using the standard plane waves or the Bessel solutions of the Helmholtz equation to design the discretization basis, the proposed modal-based PUFEM explicitly uses the tensor-product expressions of the eigenmodes (the so-called Love and interior modes) of a spectral elastic transverse problem, which fulfil the coupling conditions among layers. This modal-based PUFEM approach does not introduce quadrature errors since the coefficients of the discrete matrices are computed in closed-form. A preliminary analysis of the high condition number suffered by the proposed method is also analyzed in terms of the mesh size and the number of eigenmodes involved in the discretization. The numerical methodology is validated through a number of test scenarios, where the reliability of the proposed PUFEM method is discussed by considering different modal basis and source terms. Finally, some indicators are introduced to select a convenient discrete PUFEM basis taking into account the observability of cracks located on a coupling boundary between two adjacent layers.This work has been supported by Xunta de Galicia project “Numerical simulation of high-frequency hydro-acoustic problems in coastal environments - SIMNUMAR” (EM2013/052), co-funded with European Regional Development Funds (ERDF). Moreover, the second and fifth authors have been supported by MICINN projects MTM2014-52876-R, MTM2017-82724-R, PID2019-108584RB-I00, and also by ED431C 2018/33 - M2NICA (Xunta de Galicia & ERDF) and ED431G 2019/01 - CITIC (Xunta de Galicia & ERDF). Additionally, the third author has been supported by Junta de Castilla y León under projects VA024P17 and VA105G18, co-financed by ERDF funds. This work has been funded for open access charge by Universidade da Coruña/CISUGXunta de Galicia; EM2013/052Xunta de Galicia; ED431C 2018/33Xunta de Galicia; ED431G 2019/01Junta de Castilla y León; VA024P17Junta de Castilla y León; VA105G1

A mathematical analysis of a smart-beam which is equipped with piezoelectric actuators

First of all, a brief reminder on piezoelectric effect is given. Then it is applied to a beam equipped with such actuators. The influence of tile shape and location is discussed. A smart beam model is finally presented and analyzed. The controllability is carefully examined in the framework of the H.U.M. method of Lions (1988). Let us also underline that the asymptotic harmonic behaviour of the structure is videly used