RKPM Analysis Of Circular Plates On Winkler Foundation

Reproducing kernel particle method(RKPM) is developed from smoothed particlehydrodynamic method(SPH), reproducing kernel particle method is based onModified kernel function, and it is formed by Taylor series expansion. As a kind ofmeshless methods, reproducing kernel particle method is a method without theproblems such as mesh generation and mesh aberration compared with Finite elementmethod, as a result, this method is of unique advantages in the engineering analysis.Based on full study of RKPM and circular foundation plates, this article studied the useof RKPM in analysis of circular foundation plates.Firstly, this article studied the approximation scheme of field function and thestructure of the shape function, then; the1st and2nd derivatives to the shape function ofreproducing kernel particle method are deduced and introduced boundary conditions.Then, anther theory—elastic plate theory is analyzed. Displacement control equationand internal force calculation equation of circular foundation plates is given. At last,RKPM analysis of circular foundation plate bending on Winkler foundation is built.Analyzed a circular foundation plate with the program, EFMPRF, which is programmedin FORTRAN, and compared with references or results of ANSYS. We find thatreproducing kernel particle method can be used in analysis of elastic plate on Winklerfoundation. For a better understanding of the factors affect accuracy of the reproducingkernel particle method, we adjust the node distribution and the cell structure, andcompared the calculated results with the results of commercial finite element software.We find that if the nodes are distributed uniformly and be Consistent with the cellstructure, the result is of good accuracy. In addition, the problem of Boundary warpingcan be solved if we put more nodes on the boundary. In the last chapter, we adjust theparameter of the program, including the number of gauss point, size of influencedomain and scanning step. We find that if we use more gauss points, the result ofinternal force is of better accuracy. The size of the influence domain should beappropriate, Otherwise the program could stop or the accuracy will degrade. Scanningstep can also affect the accuracy and the time of the program takes.