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Extended Finite Element Method (XFEM) | |
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The structural optimization is a kind of methodology to find out optimal materials distributions in some engineering applications, in which usually the FEM is necessary to be implemented to do the sensitivity analysis. In level set method based framework, the optimal design is obtained in an iteration manner of evolving the boundary according to the normal velocity on it. In each iteration step before convergence, a sensitivity analysis is needed to update the velocity on the boundary for the next step. The XFEM provides a more reasonable technique for the sensitivity analysis in dynamic implicit boundary problems than many previous methods such as the density based method. The basic idea of XFEM is to augment the nodal shape function with an enrichment function on the elements along the boundary to model the arbitrarily evolving geometric features while on the other elements there is no further manipulation needed. This method has been favorably implemented in simulating the crack growth thus the remeshing process is not needed any more. | |
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| Comparison of Density method with XFEM. | |
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Example: Minimum mean compliance design problem of a short cantilever beam. |
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Initial Design (80〜40) |
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Optimal Design (80〜40) |
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| Strain energy density distribution along the boundary. | |
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| Density based method (40〜20) | |
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XFEM based method (40〜20) |
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