Download E-books Discrete Mechanics (Iste) PDF

By Jean-Paul Caltagirone

This publication provides the basic ideas of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics linked to the actual modeling.  the improvement and the complementarity of sciences bring about evaluation this present day the outdated suggestions that have been the root for the improvement of continuum mechanics. The differential geometry is used to check the conservation legislation of mechanics. for example, this formalism calls for a unique situation of vector and scalar amounts in house. The equations of Discrete Mechanics shape a process of equations the place the Helmholtz-Hodge decomposition performs a massive position.

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1. 6. Conservation of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 four 6 eight 10 12 17 19 20 22 25 26 29 30 C HAPTER 2. M OMENTUM C ONSERVATION . . . . . . . . . 33 2. 1. Classification of forces . . . . . . . . . . . . . . . . . . . 33 vi Discrete Mechanics 2. 2. 3 basic experiments . . . . . . . . . . 2. 2. 1. Equilibrium in a tumbler of water . . . . . . . . 2. 2. 2. Couette flow . . . . . . . . . . . . . . . . . . 2. 2. three. Poiseuille flow . . . . . . . . . . . . . . . . . 2. three. Postulates . . . . . . . . . . . . . . . . . . . . . . 2. four. Modeling of the strain forces . . . . . . . . . . 2. five. Modeling of the viscous forces . . . . . . . . . . 2. five. 1. Modeling of the viscous results of quantity . 2. five. 2. Modeling of the viscous floor results . . . 2. five. three. pressure country . . . . . . . . . . . . . . . . . . . 2. 6. Objectivity . . . . . . . . . . . . . . . . . . . . . 2. 7. Discrete movement stability equation . . . . . . . . . 2. 7. 1. basic legislations of dynamics . . . . . . . . 2. 7. 2. Eulerian step . . . . . . . . . . . . . . . . . . 2. 7. three. Mechanical equilibrium . . . . . . . . . . . . 2. eight. formula when it comes to density and temperature 2. nine. Similitude parameters . . . . . . . . . . . . . . . 2. nine. 1. effect at the floor of a liquid . . . . . . . 2. 10. Hypercompressible media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 35 forty four forty seven fifty one fifty two fifty seven fifty seven fifty nine sixty two sixty four sixty seven sixty seven seventy three seventy four seventy eight eighty one eighty five 88 C HAPTER three. C ONSERVATION OF H devour F LUX AND E NERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety one three. 1. advent . . . . . . . . . . . . . . . . . . . three. 2. Conservation of flux . . . . . . . . . . . . . . three. three. Conservation of power . . . . . . . . . . . . three. three. 1. Conservation of overall power . . . . . . . three. three. 2. Conservation of kinetic strength . . . . . . three. three. three. Conservation of the interior power . . . three. four. Discrete equations for the flux and the strength three. five. an easy heat-conduction challenge . . . . . . three. five. 1. Case of anisotropic fabrics . . . . . . . C HAPTER four. P ROPERTIES OF D ISCRETE E QUATIONS . . . one zero five . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ninety one ninety two ninety five ninety five ninety seven ninety eight ninety nine a hundred 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . four. 1. A approach of equations and potentials four. 2. Physics represented . . . . . . . . . . four. 2. 1. Poiseuille flow and potentials . . four. 2. 2. Celerity and greatest speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a hundred and five 107 a hundred and ten 112 Contents vii four. 2. three. feedback approximately turbulence . . . . . . . . . . . . . . . four. three. Boundary stipulations . . . . . . . . . . . . . . . . . . . . four. three. 1. touch floor . . . . . . . . . . . . . . . . . . . . . four. three. 2. Shockwaves . . . . . . . . . . . . . . . . . . . . . . . four. three. three. area stipulations . . . . . . . . . . . . . . . . . . . . four. three. four. Slip situation . . . . . . . . . . . . . . . . . . . . . . four. three. five. Capillary results . . . . . . . . . . . . . . . . . . . . four. three. 6. Thermal boundary stipulations . . . . . . . . . . . . . four. four. Penalization of the potentials . . . . . . . . . . . . . . . four. five. Continua and discrete mediums . . . . . . . . . . . . . . four. five. 1. alterations with the Navier–Stokes equation . . . . four. five. 2. Dissipation . . . . . . . . . . . . . . . . . . . . . . . four. five. three. Case of rigidifying motions . . . . . . . . . . . . . . four. five. four. An instance of the dissipation of strength . . . . . . . four. 6. Hodge–Helmholtz decomposition . . . . . . . . . . . . four. 7. Approximations . . . . . . . . . . . . . . . . . . . . . . . four. 7. 1. Bernoulli’s legislation . . . . . . . . . . . . . . . . . . . . . four. 7. 2. Irrotational flow . . . . . . . . . . . . . . . . . . . . four. 7. three. Inviscid fluid . . . . . . . . . . . . . . . . . . . . . . four. 7. four. Incompressible flow . . . . . . . . . . . . . . . . . . four. eight. Gravitational waves . . . . . . . . . . . . . . . . . . . . four. nine. Linear visco-elasticity .

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