06359cam a2200781 i 4500 ocn878668144 OCoLC 20171030133328.0 m o d cr ||||||||||| 140428s2014 si ob 001 0 eng 2014016885 9781118567289 (ePub) 1118567285 (ePub) 9781118567227 (Adobe PDF) 1118567226 (Adobe PDF) 9781118567210 (electronic bk.) 1118567218 (electronic bk.) 111856720X (cloth) 9781118567203 (cloth) 9781306979764 (MyiLibrary) 1306979765 (MyiLibrary) 9781118567203 (cloth) CHBIS 010442047 CHVBK 334092353 DEBSZ 431727732 NZ1 15906880 DEBSZ 475027361 DEBBG BV043396729 (OCoLC)878668144 (OCoLC)884646610 (OCoLC)889305901 (OCoLC)961577277 (OCoLC)962610705 DLC eng rda pn DLC YDX YDXCP DG1 IDEBK N$T CDX COO RECBK E7B EBLCP DEBSZ OCLCQ DEBBG pcc MAIN TA357.5.G47 SCI 041000 bisacsh SCI 096000 bisacsh 531/.163 23 Matuttis, Hans-Georg, author. Understanding the discrete element method : simulation of non-spherical particles for granular and multi-body systems / Hans-Georg Matuttis, the University of Electro-Communications, Japan, Jian Chen, Riken Advanced Institute for Computational Science, Japan. [electronic resource] Singapore : Wiley, 2014. 1 online resource. text txt rdacontent computer n rdamedia online resource nc rdacarrier Includes bibliographical references and index. UNDERSTANDING THE DISCRETE ELEMENT METHOD SIMULATION OF NON-SPHERICAL PARTICLES FOR GRANULARAND MULTI-BODY SYSTEMS; Copright; Contents; Exercises; About the Authors; Preface; Acknowledgements; List of Abbreviations; 1 Mechanics; 1.1 Degrees of freedom; 1.1.1 Particle mechanics and constraints; 1.1.2 From point particles to rigid bodies; 1.1.3 More context and terminology; 1.2 Dynamics of rectilinear degrees of freedom; 1.3 Dynamics of angular degrees of freedom; 1.3.1 Rotation in two dimensions; 1.3.2 Moment of inertia; 1.3.3 From two to three dimensions. 1.3.4 Rotation matrix in three dimensions1.3.5 Three-dimensional moments of inertia; 1.3.6 Space-fixed and body-fixed coordinate systems andequations of motion; 1.3.7 Problems with Euler angles; 1.3.8 Rotations represented using complex numbers; 1.3.9 Quaternions; 1.3.10 Derivation of quaternion dynamics; 1.4 The phase space; 1.4.1 Qualitative discussion of the time dependence of linear oscillations; 1.4.2 Resonance; 1.4.3 The flow in phase space; 1.5 Nonlinearities; 1.5.1 Harmonic balance; 1.5.2 Resonance in nonlinear systems; 1.5.3 Higher harmonics and frequency mixing. 1.5.4 The van der Pol oscillator1.6 From higher harmonics to chaos; 1.6.1 The bifurcation cascade; 1.6.2 The nonlinear frictional oscillator and Poincar ́e maps; 1.6.3 The route to chaos; 1.6.4 Boundary conditions and many-particle systems; 1.7 Stability and conservationlaws; 1.7.1 Stability in statics; 1.7.2 Stability in dynamics; 1.7.3 Stable axes of rotation around the principal axis; 1.7.4 Noether's theorem and conservation laws; 1.8 Further reading; Exercises; References; 2Numerical Integration of OrdinaryDifferential Equations; 2.1 Fundamentals of numerical analysis. 2.1.1 Floating point numbers2.1.2 Big-O notation; 2.1.3 Relative and absolute error; 2.1.4 Truncation error; 2.1.5 Local and global error; 2.1.6 Stability; 2.1.7 Stable integrators for unstable problems; 2.2 Numerical analysis for ordinary differential equations; 2.2.1 Variable notation and transformation of the order of adifferential equation; 2.2.2 Differences in the simulation of atoms and molecules, as compared to macroscopic particles; 2.2.3 Truncation error for solutions of ordinary differential equations; 2.2.4 Fundamental approaches; 2.2.5 Explicit Euler method. 2.2.6 Implicit Euler method2.3 Runge-Kutta methods; 2.3.1 Adaptive step-size control; 2.3.2 Dense output and event location; 2.3.3 Partitioned Runge-Kutta methods; 2.4 Symplectic methods; 2.4.1 The classical Verlet method; 2.4.2 Velocity-Verlet methods; 2.4.3 Higher-order velocity-Verlet methods; 2.4.4 Pseudo-symplectic methods; 2.4.5 Order, accuracy and energy conservation; 2.4.6 Backward error analysis; 2.4.7 Case study: the harmonic oscillator with andwithout viscous damping; 2.5 Stiff problems; 2.5.1 Evaluating computational costs; 2.5.2 Stiff solutions and error as noise. Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particlesProvides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulationHighlights the numerical tricks and pitfalls that are usually only realized after years o. Print version record and CIP data provided by publisher. Granular flow. Discrete element method. Multibody systems. Mechanics, Applied Computer simulation. Discrete element method. Granular flow. Mechanics, Applied Computer simulation. Multibody systems. SCIENCE Mechanics General. bisacsh SCIENCE Mechanics Solids. bisacsh Electronic books. Chen, J. F. (Jian-Fei), 1963- author. Print version: Matuttis, Hans-Georg, author. Understanding the discrete element method. Hoboken, NJ : John Wiley & Sons Inc., 2014 9781118567203 (DLC) 2014005447 http://onlinelibrary.wiley.com/book/10.1002/9781118567210 Wiley Online Library ddc BK 207409 207409