Discontinuous deformation analysis(DDA) is a numerical method for analyzing the deformation of block system. It employs unified dynamic formulation for both static and dynamic analysis, in which the so-called kinetic ...Discontinuous deformation analysis(DDA) is a numerical method for analyzing the deformation of block system. It employs unified dynamic formulation for both static and dynamic analysis, in which the so-called kinetic damping is adopted for absorbing dynamic energy. The DDA dynamic equations are integrated directly by the constant acceleration algorithm of Newmark family integrators. In order to have an insight into the DDA time integration scheme, the performance of Newmark time integration scheme for dynamic equations with kinetic damping is systematically investigated, formulae of stability, bifurcation, spectral radius, critical kinetic damping and algorithmic damping are presented. Combining with numerical examples, recognition and suggestions of Newmark integration scheme application in the DDA static and dynamic analysis are proposed.展开更多
While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. ...While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.展开更多
基金supported by the Fundamental Research Funds for Central Public Welfare Research Institutes(Grant No.CKSF2014053/CL)
文摘Discontinuous deformation analysis(DDA) is a numerical method for analyzing the deformation of block system. It employs unified dynamic formulation for both static and dynamic analysis, in which the so-called kinetic damping is adopted for absorbing dynamic energy. The DDA dynamic equations are integrated directly by the constant acceleration algorithm of Newmark family integrators. In order to have an insight into the DDA time integration scheme, the performance of Newmark time integration scheme for dynamic equations with kinetic damping is systematically investigated, formulae of stability, bifurcation, spectral radius, critical kinetic damping and algorithmic damping are presented. Combining with numerical examples, recognition and suggestions of Newmark integration scheme application in the DDA static and dynamic analysis are proposed.
基金supported by the National Basic Research Program of China("973"Project)(Grant Nos.2011CB013505&2014CB047100)the National Natural Science Foundation of China(Grant No.11172313)
文摘While the classical discontinuous deformation analysis(DDA) is applied to the analysis of a given block system, one must preset stiffness parameters for artificial springs to be fixed during the open-close iteration. To a great degree, success or failure in applying DDA to a practical problem is dependent on the spring stiffness parameters, which is believed to be the biggest obstacle to more extensive applications of DDA. In order to evade the introduction of the artificial springs, this study reformulates DDA as a mixed linear complementarity problem(MLCP) in the primal form. Then, from the fact that the block displacement vector of each block can be expressed in terms of the contact forces acting on the block, the condensed form of MLCP is derived, which is more efficient than the primal form. Some typical examples including those designed by the DDA inventor are reanalyzed, proving that the procedure is feasible.
