Papers by Keyword: Point Collocation Method

Abstract: The analysis of sphere nonlocal elasticity is carried out by using the improved point collocation method. The approach is based on the Eringen’s model and two and three dimension problems are transformed to one dimension problems considering the polar symmetry. One dimension second order differential equation in terms of radial displacement is derived with domain integral. Due to the excellent accuracy of the point collocation method to one dimension differential equation using the radial basis function interpolation, the numerical solutions can be used as benchmarks. This approach can be easily extended to dynamic nonlocal elasticity and plasticity for sphere.

Abstract: Based on the MLS approximation, a meshless method for the numerical solution of the generalized Burger’s equation is presented in this paper. The nonlinear discrete scheme of the generalized equation is obtained, and is solved with the method of iteration. Compared with numerical methods based on mesh, the meshless method needs only the scattered nodes instead of meshing the domain of the problem. An example is given to demonstrate the accuracy of the proposed method. The numerical results agree well with the exact solutions.

Abstract: In this paper the spline subdomain approach is applied to the 2D simulations of the temperature distributions for composites containing a single rectangular particle with an interfacial thermal resistance at the interface between the particle and matrix. The bicubic B-splines are used to construct the trial functions for the approximations of the potential fields of composites. Applying the weighted residual point collocation method inside each subdomain and also on the boundaries between different subdomains, a system of linear algebraic equations is set up to determine the unknowns of the trial functions. The temperature distributions both inside the rectangular particle and along the interfaces under different interfacial contact conditions can be simulated approximately. Numerical results which are compared with the available solutions obtained by FEM method illustrate the accuracy and suitability of the present approach for steady-state conduction. Even in the adjacent areas of corners in the rectangular particle, the simulation results are also satisfactory.

Abstract: Point collocation methods have no mesh, no integration. While, the robustness of the point collocation methods is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important when using the point collocation methods. For boundary points, however, the positivity conditions cannot be satisfied, so that it is possible to get large numerical errors from the boundary points when using the point collocation methods. The author has proposed a point collocation method with a boundary layer of finite element. In this method, by introducing a boundary layer of finite element in boundary domain of workpiece, unsatisfactory issue of the positivity conditions of boundary points can be avoided, and the complicated boundary conditions can be easily imposed with the boundary layer of finite element. A forging process is analyzed by using the point collocation method with a boundary layer of finite element.