Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics
Tài liệu tham khảo
Sanz-Serna, 1994
Stuart, 1996, Dynamical systems and numerical analysis
Hairer, 2002, Geometric numerical integration, 10.1007/978-3-662-05018-7_2
Leimkuhler, 2004, Simulating Hamiltonian dynamics
Channell, 1996, An introduction to symplectic integrators, 10, 45
Maeda, 1980, Canonical structure and symmetries for discrete dynamics, Math. Japon., 25, 405
Marsden, 2001, Discrete mechanics and variational integrators, Acta Numer., 10, 357, 10.1017/S096249290100006X
Lall, 2006, Discrete variational Hamiltonian mechanics, J. Phys. A, 39, 5509, 10.1088/0305-4470/39/19/S11
Labudde, 1976, Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion — I. Motion of a single particle, Numer. Math., 25, 323, 10.1007/BF01396331
Labudde, 1976, Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion — II. Motion of a system of particles, Numer. Math., 25, 323, 10.1007/BF01396331
Lewis, 1996, Conserving algorithms for the N-dimensional rigid body, Fields Inst. Commun., 10, 121
Simo, 1992, Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics, Comput. Meth. Appl. Mech., 100, 63, 10.1016/0045-7825(92)90115-Z
Simo, 1992, The discrete energy–momentum method. Conserving algorithms for nonlinear elastodynamics, Z. Angew. Math. Phys., 43, 757, 10.1007/BF00913408
Gonzalez, 2000, Exact energy–momentum conserving algorithms for general models in nonlinear elasticity, Comput. Meth. Appl. Mech., 190, 1763, 10.1016/S0045-7825(00)00189-4
Lewis, 1996, Conserving algorithms for the N-dimensional rigid body, 121
Simo, 1991, Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum, Int. J. Numer. Meth. Engrg., 31, 19, 10.1002/nme.1620310103
Simo, 1995, Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms, Int. J. Numer. Meth. Engrg., 38, 1431, 10.1002/nme.1620380903
Simo, 1994, A new energy and momentum conserving algorithm for the non-linear dynamics of shells, Int. J. Numer. Meth. Engrg., 37, 2527, 10.1002/nme.1620371503
Romero, 2002, An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics, Int. J. Numer. Meth. Engrg., 54, 1683, 10.1002/nme.486
Betsch, 2007, Energy-momentum conserving integration of multibody dynamics, Multibody Syst. Dyn., 17, 243, 10.1007/s11044-007-9043-9
Armero, 1998, Formulation and analysis of conserving algorithms for frictionless dynamic contact/impact problems, Comput. Meth. Appl. Meth., 158, 269, 10.1016/S0045-7825(97)00256-9
Wendlandt, 1997, Mechanical integrators derived from a discrete variational principle, Physica D, 106, 223, 10.1016/S0167-2789(97)00051-1
Kane, 2000, Variational integrators and the newmark algorithm for conservative and dissipative mechanical systems, Int. J. Numer. Meth. Engrg., 49, 1295, 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W
Lew, 2003, Asynchronous variational integrators, Arch. Ration. Mech. Anal., 167, 85, 10.1007/s00205-002-0212-y
Lew, 2004, Variational time integrators, Int. J. Numer. Meth. Engrg., 60, 153, 10.1002/nme.958
Meng, 2002, Energy consistent algorithms for dynamic finite deformation plasticity, Comput. Meth. Appl. Mech., 191, 1639, 10.1016/S0045-7825(01)00349-8
Armero, 2007, Volume-preserving energy-momentum schemes for isochoric multiplicative plasticity, Comput. Meth. Appl. Mech., 196, 4130, 10.1016/j.cma.2007.04.002
Grmela, 1997, Dynamics and thermodynamics of complex fluids I. Development of a general formalism, Phys. Rev. E, 56, 6620, 10.1103/PhysRevE.56.6620
Öttinger, 1998, Relativistic and nonrelativistic description of fluids with anisotropic heat conduction, Phys. A, 254, 433, 10.1016/S0378-4371(98)00045-4
Jongschaap, 2004, The mathematical representation of driven thermodynamic systems, J. Non-Newton. Fluid Mech., 120, 3, 10.1016/j.jnnfm.2003.11.008
Kröger, 2004, Beyond-equilibrium molecular dynamics of a rarefied gas subjected to shear flow, J. Non-Newton. Fluid Mech., 120, 175, 10.1016/j.jnnfm.2003.11.010
Öttinger, 2005
Öttinger, 2006, Nonequilibrium thermodynamics for open systems, Phys. Rev. E, 73, 036126, 10.1103/PhysRevE.73.036126
Öttinger, 2008, Role of nonequilibrium entropy in Einstein's theory of gravitation, Phys. A, 387, 4560, 10.1016/j.physa.2008.03.015
Gonzalez, 1996, Time integration and discrete Hamiltonian systems, J. Nonlinear Sci., 6, 449, 10.1007/BF02440162
Romero, 2009, Thermodynamically consistent time stepping algorithms for nonlinear thermomechanical systems, Int. J. Num. Meth. Engrg., 79, 706, 10.1002/nme.2588
Hughes, 1976, Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics, Comput. Struct., 6, 313, 10.1016/0045-7949(76)90007-9
Belytschko, 1975, On the uncondtional stability of an implicit algorithm for nonlinear structural dynamics, J. Appl. Mech., 42, 865, 10.1115/1.3423721
Gonzalez, 1996, On the stability of symplectic and energy-momentum algorithms for non-linear Hamiltonian systems with symmetry, Comput. Meth. Appl. Mech., 134, 197, 10.1016/0045-7825(96)01009-2
Kulh, 1999, Energy conserving and decaying algorithms in non-linear structural dynamics, Int. J. Num. Meth. Engrg., 45, 569, 10.1002/(SICI)1097-0207(19990620)45:5<569::AID-NME595>3.0.CO;2-A
Armero, 2001, On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low order methods for two model problems and nonlinear elastodynamics, Comput. Meth. Appl. Mech., 190, 2603, 10.1016/S0045-7825(00)00256-5
Armero, 2001, On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second order methods, Comput. Meth. Appl. Mech., 190, 6783, 10.1016/S0045-7825(01)00233-X
Hughes, 1986, A new finite element formulation for computational fluid mechanics: I. Symmetric forms of the compressible Euler and Navier–Stokes equations and the second law of thermodynamics, Comput. Meth. Appl. Mech., 54, 223, 10.1016/0045-7825(86)90127-1
Carlson, 1972, Linear thermoelasticity, VIa/2, 297
Day, 1985, Heat conduction within linear thermoelasticity, 10.1007/978-1-4613-9555-3
Šilhavý, 1997, The mechanics and thermodynamics of continuous media
Holzapfel, 2000
Salençon, 2001
Miehe, 1995, Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Comput. Meth. Appl. Mech., 120, 243, 10.1016/0045-7825(94)00057-T
Armero, 1996, Long-term dissipativity of time-stepping algorithms for an abstract evolution equation with applications to the incompressible MHD and Navier–Stokes equations, Comput. Meth. Appl. Mech., 131, 41, 10.1016/0045-7825(95)00931-0
Armero, 1992, A new unconditionally stable fractional step method for nonlinear coupled thermomechanical problems, Int. J. Num. Meth. Engrg., 35, 737, 10.1002/nme.1620350408
Nicholson, 2008, Finite element analysis
Gross, 2010, Energy-momentum consistent finite element discretization of dynamic finite viscoelasticity, Int. J. Numer. Meth. Engrg., 81, 1341, 10.1002/nme.2729
O. Gonzalez. Design and anlysis of conserving integrators for nonlinear Hamiltonian systems with symmetry. PhD thesis, Stanford University, Department of Mechanical Engineering, 1996.
Simo, 1992, Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation, Comput. Meth. Appl. Mech., 98, 41, 10.1016/0045-7825(92)90170-O