Effective Meshless Method For Dynamic Analysis Of Elastic Media And Saturated Porous Media

Along with the behavior seismic design thought's appearance and the development, the pure strength judgment of foundation and earth structure under the earthquake already cannot meet the project needs. The method and the technology of hazard analysis, which takes the deformation as the primary control parameter, will be applied widely. This presents a new topic of study and the challenge for the existing soil dynamics theory. The finite element method (FEM) still has met many difficulties in computing the large deformation of soil under earthquake, though it has achieved great success in the engineering application. As an important complement of FEM, the meshless method has advantage in dealing with large deformation problems and attracts people's attention recently. Because of the low computational efficiency, the existing meshless method is difficult to popularize in large practical engineering. Therefore, it is very important to find high efficiency meshless method. Based on this, this paper introduces the ideal elastic soil and saturated soil and develops a high efficiency meshless method for dynamic analysis. The concrete work is as follows:(1) This paper develops the efficient and decoupled radial point interpolation meshless method based on global weak-forms (GRPIM) and radial point interpolation meshless method based on local weak-forms (LRPIM). Unknown variables are approximated by the radial point interpolation method. Discrete equations of dynamic response of elastic media and saturated porous media are deduced by global Galerkin weak-forms and local Galerkin weak-forms respectively. According to the precision requirement in wave motion simulation, a lumped-mass GRPIM and a lumped-mass LRPIM are derived. Then the time domain is discrete by the explicit integration procedures. A decoupled recurrence procedure for every degree is obtained.(2) A set of corresponding FORTRAN calculation program is written. In the end, two-dimensional and three-dimensional numerical examples demonstrate the precision and efficiency of the decoupled GRPIM and LRPIM. Two-dimensional and three-dimensional dynamic problems of elastic media and saturated porous media are analyzed by decoupled LRPIM, decoupled GRPIM, conventional LRPIM, conventional GRPIM and the finite element analysis software ANSYS, and the results and computational efficiency are compared and discussed. The results show that the decoupled GRPIM and LRPIM have the same precision as comparing with the conventional GRPIM and LRPIM, but their computational efficiency are increased greatly. The paper proves the feasibility and high efficiency of this decoupled meshless method.