دانلود رایگان مقاله روش ساده برای شبیه سازی عددی با سطوح تراشیده CAD

Abstract

In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its simplicity and ease of implementation into existing Finite Element (FEM) or Boundary Element (BEM) software. The method is first verified with classical test examples in structural mechanics. Then two practical applications are presented one using the FEM, the other the BEM, that show the applicability of the method.

6. Summary and conclusions

A novel approach to trimming was presented. The main advantage of the method lies in its simplicity and ease of implementation into existing software. The method is currently restricted to cases with two trimming curves. However, as has been demonstrated, practical applications exist, where this is the case. Our main interest lies in the application of the BEM to the simulation of underground excavations, where benefits of the method can be seen. The geometry of the underground excavation depicted in Fig. 16 for example is ideally suited to the proposed algorithm. Using a conventional BEM simulation, it has been found difficult to generate a mesh from the CAD data, as elements with bad aspect ratios appeared and had to be repaired. Since the trimming information provided by the CAD program only involves two trimming curves in this case, this application lends itself well to the proposed simulation approach. Extensions of the method are possible. In fact, Gordon–Coons patches (see [15]) provide a framework where four curves can be used to define a surface. One may thus construct an arbitrary patch with four trimming curves in the u, v-parameter space. Multiple holes may be considered by using a subdivision of the mapping area. Trimming plays an important role in realizing the dream of a direct connection between CAD and simulation, without the intermittent step of mesh generation. It is hoped that our contribution provides impetus for an – much needed – increase in research activity in this area.