Automatic two- and three-dimensional mesh generation based on fuzzy knowledge processing. (English) Zbl 0755.65117
Computational mechanics simulations have progressed dramatically, in particular after the appearance of supercomputers. Several tens of thousands of degrees of freedom (DOF) problems are currently regarded as nearly an upper limit for the finite element analysis on a popular supercomputer. In recent years, much attention has been paid to the fuzzy knowledge processing techniques, which allow computers to deal with “ambiguous” matters and processes.
The authors propose a novel finite element mesh generation algorithm based on the fuzzy knowledge processing technique. A number of local nodal patterns are stored in a nodal pattern database of the mesh generation system. These nodal patterns are determined a priori based on certain theories or past experience of experts of finite element method analyses. Each nodal pattern possesses a membership function and a procedure of node placement according to this function.
What a user has to do in a practical mesh generation process is to choose several local nodal points patterns properly and to designate the maximum nodal density of each pattern. The system places the chosen nodal patterns automatically in an analysis domain and on its boundary, and connects them smoothly by the fuzzy knowledge processing technique. Then triangular or tetrahedral elements are generated by means of the advancing front method.
The key issue of the present algorithm - to the authors’ opinion – is an easy control of complex two- or three-dimensional nodal density distribution by means of the fuzzy knowledge processing technique. The principal features of the algorithm are: a) quasi globally-optimum mesh subdivision can be obtained; b) only a fewer input data are necessary to generate complicated meshes.
The effectiveness of the present algorithm is demonstrated through several mesh generations for structures with a crack and a hole and those for structures with a junction. To demonstrate fundamental performances of the present algorithm the authors constructed a prototype system with an object-oriented language, Smalltalk-80 on a 32-bit microcomputer, Macintosh II.
The authors propose a novel finite element mesh generation algorithm based on the fuzzy knowledge processing technique. A number of local nodal patterns are stored in a nodal pattern database of the mesh generation system. These nodal patterns are determined a priori based on certain theories or past experience of experts of finite element method analyses. Each nodal pattern possesses a membership function and a procedure of node placement according to this function.
What a user has to do in a practical mesh generation process is to choose several local nodal points patterns properly and to designate the maximum nodal density of each pattern. The system places the chosen nodal patterns automatically in an analysis domain and on its boundary, and connects them smoothly by the fuzzy knowledge processing technique. Then triangular or tetrahedral elements are generated by means of the advancing front method.
The key issue of the present algorithm - to the authors’ opinion – is an easy control of complex two- or three-dimensional nodal density distribution by means of the fuzzy knowledge processing technique. The principal features of the algorithm are: a) quasi globally-optimum mesh subdivision can be obtained; b) only a fewer input data are necessary to generate complicated meshes.
The effectiveness of the present algorithm is demonstrated through several mesh generations for structures with a crack and a hole and those for structures with a junction. To demonstrate fundamental performances of the present algorithm the authors constructed a prototype system with an object-oriented language, Smalltalk-80 on a 32-bit microcomputer, Macintosh II.
Reviewer: G.Dimitriu (Iaşi)
MSC:
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
| 68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |
Keywords:
fuzzy knowledge processing; finite element mesh generation algorithm; local nodal patterns; finite element method; advancing front method; quasi globally-optimum mesh subdivision; effectiveness; performancesSoftware:
SmalltalkReferences:
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