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| Natural element method based on the mean value theorem and point integration and its procedures |
| Received:December 06, 2007 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20095013 |
| KeyWord:natural element method weak form mean value theorem point integration procedure |
| Author | Institution |
| 覃立宁 |
福州大学 土木工程学院,福州 |
| 戴自航 |
福州大学 土木工程学院,福州 |
| 周瑞忠 |
福州大学 土木工程学院,福州 |
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| Abstract: |
| The Natural Element Method is a mesh-free method based on the evaluation of Partial Differential Equations by the Natural Neighbor Interpolation. It uses the Voronoi chart or Delaunay triangle as the background integration mesh. The mean value theorem is defined that the value of the center of a globe (or the center of a circle) in the unknown function definition domain is equal to the average or weighted average in spherical surface (or circumference). It is fully necessary for balance equation met by the unknown function. Using the mean value theorem and the point integration, the average strain value in evaluation domain is translated through divergence theorem into perimeter integration in domain circumferences. It improves the traditional integration format. The difference between Natural Element Method and other mesh-free methods is mainly in the following two aspects: one is using geometrical measure to get the natural adjacency shape function; the other is using the dummy point integration to form the stiffness matrix.The count cases show that this integration is an adapted numerical method which can greatly simplify the calculation of the program and improve the efficiency of computation. |