LEADER 05596nam 2200733 450 001 9910821695203321 005 20200520144314.0 010 $a1-118-56728-5 010 $a1-118-56722-6 010 $a1-118-56721-8 035 $a(CKB)3580000000001264 035 $a(EBL)1745057 035 $a(SSID)ssj0001222361 035 $a(PQKBManifestationID)11654047 035 $a(PQKBTitleCode)TC0001222361 035 $a(PQKBWorkID)11201017 035 $a(PQKB)10704171 035 $a(OCoLC)889305901 035 $a(MiAaPQ)EBC1745057 035 $a(DLC) 2014016885 035 $a(Au-PeEL)EBL1745057 035 $a(CaPaEBR)ebr10901875 035 $a(CaONFJC)MIL629227 035 $a(OCoLC)884646610 035 $a(PPN)251305139 035 $a(EXLCZ)993580000000001264 100 $a20140814h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aUnderstanding the discrete element method $esimulation of non-spherical particles for granular and multi-body systems /$fHans-Georg Matuttis, Jian Chen 210 1$aSingapore :$cWiley,$d2014. 210 4$dİ2014 215 $a1 online resource (480 p.) 300 $aDescription based upon print version of record. 311 $a1-118-56720-X 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aUNDERSTANDING 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 327 $a1.3.4 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 327 $a1.5.4 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 327 $a2.1.1 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 327 $a2.2.6 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 327 $a2.5.3 Order reduction 330 $a 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 606 $aGranular flow 606 $aDiscrete element method 606 $aMultibody systems 606 $aMechanics, Applied$xComputer simulation 615 0$aGranular flow. 615 0$aDiscrete element method. 615 0$aMultibody systems. 615 0$aMechanics, Applied$xComputer simulation. 676 $a531/.163 700 $aMatuttis$b Hans-Georg$01607805 702 $aChen$b J. F$g(Jian-Fei),$f1963- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821695203321 996 $aUnderstanding the discrete element method$93934222 997 $aUNINA