MODELING RAYLEIGH DAMPING AND VARIOUS RADIAL BASIS FUNCTIONS OF CYLINDERS MADE OF SATURATED POROUS MATERIALS USING MLPG METHOD UNDER DYNAMIC LOADING

Porous materials are widely applied in different engineering fields such as chemical engineering, materials engineering, environmental geomechanics, biomechanics, soil structure interaction and geomechanics. For this reason, dynamic and static analysis of the stress and strain of structures and continuum made of these materials have attracted the attention of researchers. To analyze these structures, numerical methods are required due to the fact that the governing equations are complicated. The meshless method was well implied for many structural problems in recent decades. In this method, the scattered nodes with regular or irregular distributions are used to discretize the field functions in local sub-domains. Because of using the nodes rather than the elements, the application of meshless method in some problems yields to more accurate results. To interpolate the fields' variables in terms of its nodal values, the radial point interpolation method (RPIM) with radial basis function (RBF) is used. The radial point interpolation method (RPIM) is employed to construct the shape functions. Because of the fact the interpolation function type affects the results of meshless approach, various interpolation functions are investigated. Then, the most proper one is selected for analyzing the porous material structure. To verify the presented method, the result of cylinders made of saturated porous materials using MLPG method under dynamic loading is compared to the analytical results. A good agreement between the presented method and analytical result is achieved. It is worthwhile to mention that damping should be included in dynamic analysis. Hence, the modeling of damping effect on the behavior of porous material is conducted. According to the obtained results, for the usual damping ratios of the porous materials, increasing the damping ratio leads to reduction in the displacement amplitude and stress. Also, it is observed that the period of the porous material are independent from its damping ratio.