The main goal of this work is the resolution of fluid structure interaction problems described with the Lagrangian formalism by means of a consistently derived monolithic approach. The use of a component-free derivation leads to a straightforward implementation of the formulation where only vectors and second-order tensors in R3 are required. Therefore, no basis or components have to be imposed ab initio for the discrete variational formulation as occurs when Voigt notation is employed. The computational framework adopted is the local maximum-entropy material point method (LME-MPM), a mesh-free technique that combines the material point sampling of the MPM and the LME, a spatial approximation technique with basis functions of class C∞. This framework sidesteps the use of expensive mesh refinement techniques, which are typically required when Lagrangian finite element method is employed. Finally, the effectiveness of this approach is illustrated against challenging fluid dynamic problems.
The main goal of this work is the resolution of fluid structure interaction problems described with the Lagrangian formalism by means of a consistently derived monolithic approach. The use of a component-free derivation leads to a straightforward implementation of the formulation where only vectors and second-order tensors in R3 are required. Therefore, no basis or components have to be imposed ab initio for the discrete variational formulation as occurs when Voigt notation is employed. The computational framework adopted is the local maximum-entropy material point method (LME-MPM), a mesh-free technique that combines the material point sampling of the MPM and the LME, a spatial approximation technique with basis functions of class C∞. This framework sidesteps the use of expensive mesh refinement techniques, which are typically required when Lagrangian finite element method is employed. Finally, the effectiveness of this approach is illustrated against challenging fluid dynamic problems. Read More
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