Efficient implementation of an explicit partitioned shear and longitudinal wave propagation algorithm

[1]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[2]  T. Hughes,et al.  Isogeometric collocation for elastostatics and explicit dynamics , 2012 .

[3]  K. Marfurt Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations , 1984 .

[4]  D. Gabriel,et al.  Grid dispersion analysis of plane square biquadratic serendipity finite elements in transient elastodynamics , 2013 .

[5]  K. Bathe,et al.  An explicit time integration scheme for the analysis of wave propagations , 2013 .

[7]  Radek Kolman,et al.  Dispersion of elastic waves in the contact-impact problem of a long cylinder , 2010, J. Comput. Appl. Math..

[8]  M. Okrouhlík,et al.  Complex wavenumber Fourier analysis of the B-spline based finite element method , 2014 .

[9]  K. Bathe,et al.  Performance of an implicit time integration scheme in the analysis of wave propagations , 2013 .

[10]  Michal Beneš,et al.  Asynchronous multi-domain variational integrators for nonlinear hyperelastic solids , 2010 .

[11]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[12]  M. Dokainish,et al.  A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods , 1989 .

[13]  R. D. Krieg Unconditional Stability in Numerical Time Integration Methods , 1973 .

[14]  T. Fung,et al.  Numerical dissipation in time-step integration algorithms for structural dynamic analysis , 2003 .

[15]  S. S. Cho,et al.  A method for multidimensional wave propagation analysis via component‐wise partition of longitudinal and shear waves , 2013 .

[16]  Isaac Fried Bounds on the extremal eigenvalues of the finite element stiffness and mass matrices and their spectral condition number , 1972 .

[17]  John C. Houbolt,et al.  A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft , 1950 .

[18]  C. Felippa,et al.  A Variational Framework for Solution Method Developments in Structural Mechanics , 1998 .

[19]  Shuenn-Yih Chang,et al.  An explicit method with improved stability property , 2009 .

[20]  Julien Diaz,et al.  Multi-level explicit local time-stepping methods for second-order wave equations , 2015 .

[21]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[22]  Gérard Rio,et al.  Comparative study of numerical explicit time integration algorithms , 2002, Adv. Eng. Softw..

[23]  Harish P. Cherukuri,et al.  Stability analysis of an explicit finite element scheme for plane wave motions in elastic solids , 2002 .

[24]  Eugenio Aulisa,et al.  Benchmark problems for wave propagation in elastic materials , 2009 .

[25]  Alain Combescure,et al.  A monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics , 2011 .

[26]  Julien Diaz,et al.  Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations , 2007, SIAM J. Sci. Comput..

[27]  A. Idesman,et al.  Finite element modeling of linear elastodynamics problems with explicit time-integration methods and linear elements with the reduced dispersion error , 2014 .

[28]  D. M. Trujillo An unconditionally stable explicit algorithm for structural dynamics , 1977 .

[29]  S. Yin A NEW EXPLICIT TIME INTEGRATION METHOD FOR STRUCTURAL DYNAMICS , 2013 .

[30]  Shen R. Wu,et al.  Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics , 2012 .

[31]  J. Marsden,et al.  Variational time integrators , 2004 .

[32]  Thomas J. R. Hughes,et al.  Implicit-Explicit Finite Elements in Transient Analysis: Stability Theory , 1978 .

[33]  Wim A. Mulder,et al.  Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media , 2013 .

[34]  Hoon Huh,et al.  A method for computation of discontinuous wave propagation in heterogeneous solids: basic algorithm description and application to one‐dimensional problems , 2012 .

[35]  Isaac Harari,et al.  Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics , 1997 .

[36]  K. C. Park,et al.  A variable-step central difference method for structural dynamics analysis — part 1. Theoretical aspects , 1980 .

[37]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .

[38]  Pol Duwez,et al.  The Propagation of Plastic Deformation in Solids , 1950 .

[39]  Ted Belytschko,et al.  Eigenvalues and Stable Time Steps for the Uniform Strain Hexahedron and Quadrilateral , 1984 .

[40]  Ludovic Noels,et al.  Comparative study of numerical explicit schemes for impact problems , 2008 .

[41]  R. L. Sierakowski,et al.  A new explicit predictor–multicorrector high-order accurate method for linear elastodynamics , 2008 .

[42]  A. Combescure,et al.  Coupling subdomains with heterogeneous time integrators and incompatible time steps , 2009 .

[43]  S. Krenk Dispersion-corrected explicit integration of the wave equation , 2001 .

[44]  G. Sala,et al.  AN APPROACH TO STATICAL AND QUASI-STATICAL NONLINEAR ANALYSIS OF STRUCTURES IN SMALL STRAINS AND FINITE ROTATIONS HYPOTHESES , 2013 .

[45]  Jintai Chung,et al.  Explicit time integration algorithms for structural dynamics with optimal numerical dissipation , 1996 .

[46]  Folco Casadei,et al.  Binary spatial partitioning of the central‐difference time integration scheme for explicit fast transient dynamics , 2009 .

[47]  Alexandre Ern,et al.  Time-Integration Schemes for the Finite Element Dynamic Signorini Problem , 2011, SIAM J. Sci. Comput..

[48]  G. Rio,et al.  Numerical damping of spurious oscillations: a comparison between the bulk viscosity method and the explicit dissipative Tchamwa–Wielgosz scheme , 2013 .

[49]  Kumar K. Tamma,et al.  Time discretized operators. Part 1: towards the theoretical design of a new generation of a generalized family of unconditionally stable implicit and explicit representations of arbitrary order for computational dynamics , 2003 .

[50]  Anthony Gravouil,et al.  Heterogeneous asynchronous time integrators for computational structural dynamics , 2015 .

[51]  Marcus J. Grote,et al.  High-order explicit local time-stepping methods for damped wave equations , 2011, J. Comput. Appl. Math..

[52]  K. Park Practical aspects of numerical time integration , 1977 .

[53]  Vitezslav Adámek,et al.  Analytical solution of transient in-plane vibration of a thin viscoelastic disc and its multi-precision evaluation , 2012, Math. Comput. Simul..

[54]  Jintai Chung,et al.  A new family of explicit time integration methods for linear and non‐linear structural dynamics , 1994 .

[55]  Hoon Huh,et al.  A time-discontinuous implicit variational integrator for stress wave propagation analysis in solids , 2011 .

[56]  Carlos A. Felippa,et al.  A variational principle for the formulation of partitioned structural systems , 2000 .

[57]  Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition , 2012 .

[58]  Ted Belytschko,et al.  Multi-time-step integration using nodal partitioning , 1988 .

[59]  T. Belytschko,et al.  Stability of explicit‐implicit mesh partitions in time integration , 1978 .

[60]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[61]  O. Zienkiewicz,et al.  A note on mass lumping and related processes in the finite element method , 1976 .

[62]  Galina V. Reshetova,et al.  Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media , 2015, J. Comput. Phys..

[63]  William J.T. Daniel,et al.  A partial velocity approach to subcycling structural dynamics , 2003 .

[64]  Wanming Zhai,et al.  TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE‐SCALE DYNAMIC PROBLEMS IN ENGINEERING , 1996 .

[65]  John A. Ekaterinaris,et al.  Effective Computational Methods for Wave Propagation , 2008 .

[66]  Jan Cerv,et al.  Rayleigh wave dispersion due to spatial (FEM) discretization of a thin elastic solid having non-curved boundary , 1996 .