First- and second-order sensitivities of beams with respect to cross-sectional cracks

This paper deals with a variational formulation for the sensitivity problem of beam systems in the context of deformable solids with cracks. Natural frequencies are defined as state variables involved in the energy functional of the system, while the cracks length and position are treated as system parameters. The hierarchical equation system is formed and solved for the first and second derivatives of the natural frequency functions with respect to the cracks length and position. An analytical procedure for calculations of the second-order sensitivities of natural frequencies is proposed for the non-symmetrical equation system operator. Numerical algorithms are worked out and implemented computationally. Analytical and numerical aspects of the problem are discussed in detail through a number of illustrative results.The support of this work by the State Committee for Scientific Research (KBN) under Grant No. 4-050-0148/17-98-00 is gratefully acknowledged.     

Analysis of Newton’s Method to Compute Travelling Waves in Discrete Media

We present a variant of Newton’s method for computing travelling wave solutions to scalar bistable lattice differential equations. We prove that the method converges to a solution, obtain existence and uniqueness of solutions to such equations with a small second order term and study the limiting behaviour of such solutions as this second order term tends to zero. The robustness of the algorithm will be discussed using numerical examples. These results will also be used to illustrate phenomena like propagation failure, which are encountered when studying lattice differential equations. We finish by discussing the broad application range of the method and illustrate that higher dimensional systems exhibit richer behaviour than their scalar counterparts.     

The modified Casson＇s equation and its application to pipe flows of shear-thickening fluid

A few additional data from our previous experiments were plotted to emphasize the shear-thickening behavior of deoxy sickle erythrocyte (SS) suspension. A constitutive equation (named as FX equation) was developed and applied to a cylindrical pipe flow of a shear-thickening fluid. A blunt velocity profile and its volume flow rate were calculated. The flow was non-viscous (potential) in the central part of the pipe (i.e. the central core or the central plug-flow), and became more and more viscous towards the wall of the pipe after a specific radial distance, which was determined by a critical shear rate of (named as Fungs shear rate). Furthermore, combining the FX equation with the original Cassons equation, the author obtained a modified Cassons equation by introducing .The English text was polished by Yunming Chen.     

Ductile fracture criteria for simulating shear by node separation method

This study is concerned with the mechanics of ductile fracture in bulk metal forming processes by a finite-element analysis and experiments. Developed is a computer program using conventional finite-element method such that the behavior of crack propagation after ductile fracture can be analyzed. The phenomenon of a material separating into two pieces upon shearing and tensile tests has been simulated using the developed computer program. Special attention is focused on the effect of various ductile fracture criteria on crack initiation and propagation during shearing and tensile tests.     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Une méthode inverse d'ordre un pour les problèmes de complétion de données

An iterative resolution method for inverse Cauchy problems is presented. The successive iterations satisfy the equilibrium equations exactly. Numerical simulations prove the accuracy of the method and its ability to solve Cauchy problems when the domain boundary is not regular. To cite this article: A. Cimetière et al., C. R. Mecanique 333 (2005).