Reproducing Kernel Particle Method And Its Applications

Reproducing Kernel Particle Method (RKPM) is one of the promising meshfreemethods with attractive features. It can avoid the computational difficulties caused bymesh distortion in large-deformation analysis, and avoid time-consuming remeshingfor moving discontinuity problems. Using smooth and continuous kernel functions,the solution obtained and its all order derivatives are continuous and with higheraccuracy. Moreover, its preprocessing is simpler, which could reduce the manualwork greatly.Since RKPM is a kind of Galerkin meshfree methods, in this thesis, penaltyfunction method is employed to enforce the essential boundary conditions,trapezoidal rule is used for the approximation of displacement field function, Gaussand Hammer quadratures are applied for the numerical integration of systemequation,self-adapting method is applied for confirming the support of the pointinterpolated. In this way the high accuracy of the results has been guaranteed.For simple domain rectangular background cells are constructed, while forcomplicated one, the background cells similar to finite element mesh is generated.Both schemes produce satisfying results.An object-oriented program of RKPM is worked out using Visual C++, whichcan be used for 2D small-deformation single- and multi-domain problems, and alsofor the 2D geometric nonlinear problem. The RKPM for geometric nonlinear analysisare formulated in the thesis, and the accuracy of the method and program is verifiedby some benchmark problems.This RKPM program has been applied to some 2D elastostatic problems, and theresults of numerical examples have shown that the RKPM is accurate and efficient.Thanks for the higher smoothness of the displacement results, it is easier to obtainaccurate stress results in RKPM, as shown in the example of multiply connectedregion problem. The examples of typical 2D geometric nonlinear problem haveshown that the results of RKPM are well agreed with the corresponding FEM results,and the RKPM avoid the mesh- dependence of the results.