NUMERICAL SOLUTION OF A TIME-DEPENDENT SIGNORINI CONTACT PROBLEM

International audienceThe purpose of this work is to study the dynamic frictionless contact problem between an elastic body and a rigid foundation. In order to model the contact we consider Signorini conditions. A numerical algorithm is proposed to approximate the solution; the algorithm involves a contact multi-plier, which is a fixed point of a nonlinear equation solved by using a generalized Newton method. We use one of the Newmark methods for time discretization and a finite element method for space discretization. The convergence of the method is numerically studied, and a simple test problem is used to validate the methodology

Problemas de contacto en elasticidad dinámica con XFEM

En esta memoria se han presentado resultados relativos al análisis, modelado matemático y simulación numérica de diversos problemas de contacto dinámicos. En particular, se consideró un problema dinámico de contacto con sólido rígido sin fricción, y un problema de contacto entre los labios de una grieta en una placa sometida a vibración por ondas de Rayleigh, imponiendo en ambos casos condiciones de Signorini en la frontera de contacto. La simulación numérica se realizó mediante los métodos de elementos finitos clásico y elementos finitos extendidos y se compararon los resultados obtenidos con ambos métodos

Asymptotic Analysis of a Problem for Dynamic Thermoelastic Shells in Normal Damped Response Contact

[Abstract] The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. We then study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.[Resumo] En termoelasticidade, dado un problema de contacto entre una lámina tipo membrana elíptica e un obstáculo, estudamos a existencia de problema bidimensional límite cando o espesor tende a cero. Preséntase un teorema de converxencia para xustificar a bondade da aproximación.This project has received funding from the European Unions Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement Nº 823731 CONMECH and grant MTM2016-78718-P by Ministerio de Economía Industria y Competitividad of Spain with the participation of FEDE

Mathematical and Asymptotic Analysis of Thermoelastic Shells in Normal Damped Response Contact

Financiado para publicación en acceso aberto: Universidade da Coruña/CISUG[Abstract] The purpose of this paper is twofold. We first provide the mathematical analysis of a dynamic contact problem in thermoelasticity, when the contact is governed by a normal damped response function and the constitutive thermoelastic law is given by the Duhamel-Neumann relation. Under suitable hypotheses on data and using a Faedo-Galerkin strategy, we show the existence and uniqueness of solution for this problem. Then, we study the particular case when the deformable body is, in fact, a shell and use asymptotic analysis to study the convergence to a 2D limit problem when the thickness tends to zero.This project has received funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement No 823731 CONMECH and grant MTM2016-78718-P by Ministerio de Economía Industria y Competitividad of Spain with the participation of FEDE

Are Adolescents Engaged in the Problematic Use of Social Networking Sites More Involved in Peer Aggression and Victimization?

The problematic use of social networking sites is becoming a major public health concern. Previous research has found that adolescents who engage in a problematic use of social networking sites are likely to show maladjustment problems. However, little is known about its links with peer aggression and victimization. The main goal of this study was to analyze the relationship between problematic use of online social networking sites, peer aggression ¿overt vs. relational and reactive vs. instrumental¿, and peer victimization ¿overt physical and verbal, and relational¿, taking into account gender and age (in early and mid-adolescence). Participants were selected using randomized cluster sampling considering school and class as clusters. A battery of instruments was applied to 1,952 adolescents¿ secondary students from Spain (Andalusia) (50.4% boys), aged 11 to 16 (M = 14.07, SD = 1.39). Results showed that girls and 14¿16 adolescents were more involved in a problematic use of online social networking sites. Furthermore, adolescents with high problematic use of online social networking sites were more involved in overt¿reactive and instrumental¿and relational¿reactive and instrumental¿aggressive behaviors, and self-reported higher levels of overt¿physical and verbal¿and relational victimization. Even though boys indicated higher levels of all types of victimization, girls with high problematic use of online social networking sites scored the highest on relational victimization. Relating to age, early adolescents (aged 11¿14) with higher problematic use of online social networking sites reported the highest levels of overt verbal and relational victimization. Overall, results suggested the co-occurrence of problematic use of online social networking sites, peer aggression and victimization. In addition, results showed the influence that gender and age had on peer victimization. This study highlights the continuity between offline and online domains with regard to maladjustment problems in adolescence.Departamento de Educación y Psicología SocialVersión del edito

Asymptotic Analysis of Elliptic Membrane Shells in Thermoelastodynamics

In this paper we consider a family of three-dimensional problems in thermoelasticity for elliptic membrane shells and study the asymptotic behaviour of the solution when the thickness tends to zero. We fully characterize with strong convergence results the limit as the unique solution of a two-dimensional problem, where the reference domain is the common middle surface of the family of three-dimensional shells. The problems are dynamic and the constitutive thermoelastic law is given by the Duhamel-Neumann relation.Fil: Cao Rial, M. T.. Universidade da Coruña; EspañaFil: Castiñeira, G.. Universidad de Vigo; EspañaFil: Rodríguez Arós, Á.. Universidade da Coruña; EspañaFil: Roscani, Sabrina Dina. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin