The Application Of Smoothed Particle Hydrodynamics Method In Structure Analysis

Weighted residual method with compactly supported functions which is the foundation of the meshless methods is presented in this paper.And some numerical approximate methods which are used usually in meshless methods are introduced, such as Kernel Particle method, Reproducing Kernel Particle method and Moving Least Square method. Meanwhile, several weighted residual methods, such as the collocation method, Galerkin method and Local Petrov-Galerkin method, are also described in this paper.The mathematic principle and the consistence conditions of Kernel Particle method are described emphatically, and the treatments of boundary condition and control function in elastic mechanics are deduced. Several numeric examples presented in this paper can verify that Smoothed Particle Hydronamics (SPH) method can solve one dimension problems of elastic mechanics, and the result calculated by SPH method has instability when problems are planar.Some corrected SPH methods are presented, such as Corrected Smoothed Particle Hydrodynamics (CSPH) method, Modified Smoothed Particle Hydrodynamics (MSPH) and collocation method with outer nodes. A series of numerical studies have been carried out to verify the performance of these approaches that can improve calculation accuracy and could be used successfully when the nodes are collocated unevenly. Finally, Galerkin method is introduced in SPH method to solve the instability problem. It is found that SPH method based on Galerkin method can solve planar problems successfully.