However, the techniques developed in this paper need to be generalized to three-dimensional domains before such a step may be implemented. This introduces spheres as a new class of ‘‘fi nite elements ’’ and opens up the possibility of developing an integrated computer aided design/engineering environment where the user has the option of using either the spheres or the more traditional fi nite elements or a combination of both to solve a speci fi c problem.

The superior node generation capabilities of a commercial fi nite element software can be harnessed and analysis results obtained using the method of fi nite spheres may now be directly compared with fi nite element results for exactly the same nodal con fi gurations. In this paper we have demonstrated how the data fl ow of a commercial fi nite element program, ADINA, can be used in the method of fi nite spheres in a general two-dimensional analysis. 11b we show the displacement solution results obtained by applying vertical displacement to the pole of a hemisphere using the point collocation-based method of fi nite spheres (with linear local basis). We have implemented the point collocation based method of fi nite spheres for real time simulation and display of deformation and tool tip reaction force for certain simple 3D geometries In Fig. It is observed that the method of fi nite spheres exhibits a superior convergence rate compared to the Galerkin fi nite element technique since approximation spaces exhibiting higher order continuity are used.

10c we compare the convergence in strain energy when the plate is discretized using Galerkin fi nite elements (linear) and the method of fi nite spheres (with linear local basis) when a h-type re- fi nement is performed. A discretization using 50 spheres is shown in Fig. Due to symmetry one quarter of the problem is discretized. A uniformly distributed tensile loading is applied along one of the sides of the plate. 10 we present the problem of a cantilever plate in plane strain conditions with a circular hole at its center.

The corresponding fi nite element meshes, generated using ADINA, are also shown. Figure 9 shows one quarter of an annulus discretized using 37 spheres. 8 a plate with two holes of different diameters is discretized using 175 spheres. examples demonstrating the techniques of generating a satisfactory cover using the ADINA input data fi le are presented in Fig.

Adina meshfree group