Dynamic frictional contact of a viscoelastic beam
In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The beam is assumed to be situated horizontally and to move, in both horizontal and tangential directions, by the effect of applied forces. The left end of the beam is clamped and the right one is free. Its horizontal displacement is constrained because of the presence of a deformable obstacle, the so-called foundation, which is modelled by a normal compliance contact condition. The effect of the friction is included in the vertical motion of the free end, by using Tresca's law or Coulomb's law. In both cases, the variational formulation leads to a nonlinear variational equation for the horizontal displacement coupled with a nonlinear variational inequality for the vertical displacement. We recall an existence and uniqueness result. Then, by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, a numerical scheme is proposed. Error estimates on the approximative solutions are derived. Numerical results demonstrate the application of the proposed algorithm.
A dynamic viscoelastic contact problem with normal compliance
A dynamic contact problem between a viscoelastic body and a deformable obstacle is numerically considered in this work. The contact is modeled by using the well-known normal compliance contact condition. The variational formulation of this problem is written in terms of the velocity field and it leads to a parabolic nonlinear variational equation. An existence and uniqueness result is stated. Fully discrete approximations are then introduced by using the finite element method to approximate the spatial variable, and a hybrid combination of the implicit and explicit Euler schemes to discretize the time derivatives. An a priori error analysis is recalled. Then, an a posteriori error analysis is provided extending some results already obtained in the study of the heat equation, other parabolic equations and the quasistatic case. Upper and lower bounds are proved. Finally, some two-dimensional numerical simulations are presented to demonstrate the accuracy and the behavior of the error estimators.
Gender Politics and Research: Male and Female Violence in Intimate Relationships
This article reviews a wide range of research reports on male and female violence in intimate relationships and highlights the political nature of domestic violence research. The authors review incidence and prevalence-based research that uses quantitative surveys and illustrate how quantitative, family-focussed researchers tend to ignore the political and social context of domestic violence and the complex issues of gender and power. The authors argue that understanding the complexities of domestic violence requires clear definitions of what constitutes domestic violence and multi-method approaches to research, using a combination of quantitative and qualitative methodologies.