Discrete element method has been widely adopted to simulate processes that are challenging to continuum-based approaches. However, its computational efficiency can be greatly compromised when large number of particles are required to model regions of less interest to researchers. Due to this, the application of DEM to boundary value problems has been limited. This paper introduces a three-dimensional discrete element–finite difference coupling method, in which the discrete–continuum interactions are modeled in local coordinate systems where the force and displacement compatibilities between the coupled subdomains are considered. The method is validated using a model dynamic compaction test on sand. The comparison between the numerical and physical test results shows that the coupling method can effectively simulate the dynamic compaction process. The responses of the DEM model show that dynamic stress propagation (compaction mechanism) and tamper penetration (bearing capacity mechanism) play very different roles in soil deformations. Under impact loading, the soil undergoes a transient weakening process induced by dynamic stress propagation, which makes the soil easier to densify under bearing capacity mechanism. The distribution of tamping energy between the two mechanisms can influence the compaction efficiency, and allocating higher compaction energy to bearing capacity mechanism could improve the efficiency of dynamic compaction.
A fast algorithm is proposed to integrate the trajectory of a low obiter perturbed by the earth's non-sphericity. The algorithm
uses a separation degree to define the low-degree and the high-degree acceleration components, the former computed rigorously,
and the latter interpolated from gridded accelerations. An FFT method is used to grid the accelerations. An optimal grid type
for the algorithm depends on the trajectory's permissible error, speed, and memory capacity. Using the non-spherical accelerations
computed from EGM96 to harmonic degree 360, orbit integrations were performed for a low orbiter at an altitude of 170 km.
For a separation degree of 50, the new algorithm, together with the predict-pseudo correct method, speeds up the integration
by 145 times compared to the conventional algorithm while keeping the errors in position and velocity below 10−4 m and 10−7 m/s for a 3-day arc.
Received: 28 July 1997 / Accepted: 1 April 1998 相似文献