A field smoothing stabilization of particle methods in elastodynamics

One of the most important problems in solution of partial differential equations in their strong form with particle methods is the instability of results. A number of methods have been developed for elimination of this deficiency in past decade. Many of them, however, cannot be efficiently applied to all general engineering problems.In this paper, two new methods for removing the instability in particle methods are presented. The first method is based on an incremental form of the Navier equation in small deformations combined with the Newmark time integration scheme. The second method is based on the concept of field smoothing. This method stabilizes the solution by removing high frequency vibrations of field variables with a number of field smoothing techniques. This method is more general than the first one and may be applied to various engineering problems. The proposed methods have no requirements of considering any stabilizing terms in the main equations. Although the proposed approaches can be applied to any particle method, the CSPM particle method is adopted for detail discussion. Several illustrative examples are analyzed to assess the capability of the proposed approaches to enhance the stability of particle methods.