Modelado de Multifractura Discreta en Materiales Quasi-Frágiles Monografía

Abstract

In this work, a new modal reanalysis algorithm based on AMLS method is proposed for local, nontop ological,high rank modifications. Instead of using some perturbation technique[44, 85] or using the Kirsch Combined method[223, 226], the proposed reanalysis procedure uses AMLS method to perform the reanalysisexp lo itin g the concept of substructure. The modification affects a particular path on the hierarchical partitiontree, which traces back from the modified nodes to the root node. In our proposed modal reanalysis algorithmonly the modified substructures and affected substructures due to the propagation need to be recalculated.

This algorithm can significantly improve the efficiency compared to the full recalculation. Some of the advantages are:

1. Larger substructure size increases moderately the accurate of the AMLS method. For medium substructure size, the efficiency of AMLS method can be improved using a sparse linear solver and sparse eigen solver.

2. If the modified substructures are recalculated using exact method, the reanalysis does not affect the precision of the final results by AMLS method. The eigen-values computed are accurate as the precision of AMLS method is.

3. The amplitude of modification is not limited to small modification change, as being required by approximate method.

4. It is only required to identify the corresponding modified and affected sub-structures for performing the recalculation and save the data of the non-modified sub-structures. In the worst case, the computational cost is no more than the fresh AMLS-solution.

5. It is more suitable for large-scale eigen value problem with local high-rank modifications.

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