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Geometric Implicit Function Modeling and Analysis Using R-functions  

Shin, Heon-Ju ((주)아이너스기술)
Sheen, Dong-Woo (서울대학교 수리과학부)
Kim, Tae-Wan (서울대학교 조선해양공학과 및 해양시스템공학연구소)
Publication Information
Korean Journal of Computational Design and Engineering / v.12, no.3, 2007 , pp. 220-232 More about this Journal
Abstract
Current geometric modeling and analysis are commonly based on B-Rep modeling and a finite elements method respectively. Furthermore, it is difficult to represent an object whose material property is heterogeneous using the B-Rep method because the B-Rep is basically used for homogeneous models. In addition, meshes are required to analyze a property of a model when the finite elements method is applied. However, the process of generating meshes from B-Rep is cumbersome and sometimes difficult especially when the model is deformed as time goes by because the topology of deforming meshes are changed. To overcome those problems in modeling and analysis including homogeneous and heterogeneous materials, we suggest a unified modeling and analysis method based on implicit representation of the model using R-function which is suggested by Rvachev. For implicit modeling of an object a distance field is approximated and blended for a complex object. Using the implicit function mesh-free analysis is possible where meshes are not necessary. Generally mesh-free analysis requires heavy computational cost compared to a finite elements method. To improve the computing time of function evaluation, we utilize GPU programming. Finally, we give an example of a simple pipe design problem and show modeling and analysis process using our unified modeling and analysis method.
Keywords
Approximated distance implicit function; R-function; heterogeneous material modeling; mesh-free analysis; GPU programming;
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Times Cited By KSCI : 2  (Citation Analysis)
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