Abstract
SPH (smoothed particle hydrodynamics) is one of the oldest meshless methods used to simulate mechanics of continuum media. Despite its great advantage over the traditional grid-based method, implementing boundary conditions in SPH is not easy and the accuracy near the boundary is low. When SPH is applied to problems for elasticity, the displacement or stress boundary conditions should be suitably handled in order to achieve fast convergence and acceptable numerical accuracy. The GFDM (generalized finite difference method) can derive explicit formulae for required partial derivatives of field variables. Hence, a SPH–GFDM coupled method is developed to overcome the disadvantage in SPH. This coupled method is applied to 2-D elastic analysis in both symmetric and asymmetric computational domains. The accuracy of this method is demonstrated by the excellent agreement with the results obtained from FEM (finite element method) regardless of the symmetry of the computational domain. When the computational domain is multiply connected, this method needs to be further improved.
Highlights
Smoothed particle hydrodynamics (SPH) is a Lagrangian and mesh-free technique for computational modeling of continuum systems such as solids and fluids
In order to verify the accuracy of generalized finite difference method (GFDM)-SPH coupled method proposed in the previous section, two benchmark test examples are examined for both symmetric and asymmetric computational domains
We demonstrate the applicability of the SPH–GFDM coupled method for the analysis of 2-D elastic problems
Summary
Smoothed particle hydrodynamics (SPH) is a Lagrangian and mesh-free technique for computational modeling of continuum systems such as solids and fluids. With the increasing application of SPH to more and more engineering problems, many challenges have emerged in dealing consistently with boundary conditions. These difficulties are mainly caused by two aspects. The shape of the boundary of the computational domain is usually complicated in practical engineering problems For those particles near the boundary, their support domain will be truncated. Due to these difficulties, the accuracy of the SPH approximation is reduced dramatically near the boundary and these will have an influence on the overall accuracy of the simulation. Proper boundary treatments have been an ongoing concern for the successful implementation of the SPH method
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