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| Enriched meshless method based on partition of unity for a body with cracks |
| Received:March 04, 2011 Revised:September 15, 2011 |
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| DOI：10.7511/jslx20124006 |
| KeyWord:numerical simulation discontinuities partition of unity enriched meshless method stress intensity factor |
| Author | Institution |
| 马文涛 |
西安理工大学 土木建筑工程学院, 西安 ;宁夏大学 数学计算机学院, 银川 |
| 师俊平 |
西安理工大学 土木建筑工程学院, 西安 |
| 李宁 |
西安理工大学 土木建筑工程学院, 西安 |
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| Abstract: |
| Numerical simulation of discontinuities, especially for solving the dynamic cracks, is a hot and difficult problem. The meshless method based only on nodes is very suitable for solving those typical questions. A new method for crack approximation is introduced. Based on the idea of partition of unity, one Heaviside function accounting for the displacement discontinuity along the crack faces and four enriched functions near the crack tip in order to capture the singularity of the asymptotic crack tip displacement fields are enriched in the function of moving least square(MLS) approximation.Then the linear discrete system of equilibrium differential equations is derived by using the Galerkin method and the interaction integral method to evaluate the stress intensity factors is presented. Compared with other styles of enriched meshless, one advantage of this methods is that the visibility criterion is not to be used around the crack tip.Therefore, r1/2singularity is reproduced very well. The second advantage is that the domain of influence of the nodes not changed by the passage of the crack, holding the equations of sparsity, leading to rather high computations. Numerical simulations illustrate that the approach can effectively model the discontinuities, and it has practical merits. |
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