Geometry-related Treatments for Three-dimensional Meshless Method
Ming-Hsiao Lee; and Wen-Hwa Chen;

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 61, No. 3, pp. 249-272, 2010
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Keywords meshless, geometry treatment, triangulated surface, multi-material
Abstract The meshless method has a distinct advantage over other methods in that it requires only nodes without an element mesh which usually induces time-consuming work and inaccuracy when the elements are distorted during the analysis process. However, the element mesh can provide more geometry information for numerical simulation, without the need to judge if the nodes or quadrature points are inside the analysis domain which happens in the meshless method, since the analysis domain is defined by the element's edges or faces and the quadrature points are all inside the elements. Because the analysis model with only nodes for the meshless method lacks these types of geometry-related information, some difficulties are usually encountered during the numerical simulation, especially, for the cases with three-dimensional irregular-shaped analysis domains. Therefore, two types of domain and boundary representations, say, constructive solid geometry scheme and triangulated surface boundary scheme, are employed in this work. To further deal with those geometry-related issues required for the meshless method, several efficient check mechanisms are also devised. With those proposed geometry schemes and check mechanisms, both three-dimensional irregular-shaped and multi-material problems can be easily handled with the meshless method. Several demonstrative cases prove the effectiveness of the proposed techniques.
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