05595nam 2200733 450 991013249800332120200520144314.01-118-56728-51-118-56722-61-118-56721-8(CKB)3580000000001264(EBL)1745057(SSID)ssj0001222361(PQKBManifestationID)11654047(PQKBTitleCode)TC0001222361(PQKBWorkID)11201017(PQKB)10704171(OCoLC)889305901(MiAaPQ)EBC1745057(DLC) 2014016885(Au-PeEL)EBL1745057(CaPaEBR)ebr10901875(CaONFJC)MIL629227(OCoLC)884646610(PPN)251305139(EXLCZ)99358000000000126420140814h20142014 uy 0engur|n|---|||||txtccrUnderstanding the discrete element method simulation of non-spherical particles for granular and multi-body systems /Hans-Georg Matuttis, Jian ChenSingapore :Wiley,2014.©20141 online resource (480 p.)Description based upon print version of record.1-118-56720-X Includes bibliographical references at the end of each chapters 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 dimensions1.3.4 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 mixing1.5.4 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 analysis2.1.1 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 method2.2.6 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 noise2.5.3 Order reduction 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 oGranular flowDiscrete element methodMultibody systemsMechanics, AppliedComputer simulationGranular flow.Discrete element method.Multibody systems.Mechanics, AppliedComputer simulation.531/.163Matuttis Hans-Georg873827Chen J. F(Jian-Fei),1963-MiAaPQMiAaPQMiAaPQBOOK9910132498003321Understanding the discrete element method1950877UNINA