Abstract
A good spatial discretization is of prime interest in the accuracy of the Finite Element Method. This paper presents a new refinement criterion dedicated to an h-type refinement method called Conforming Hierarchical Adaptive Refinement MethodS (CHARMS) and applied to solid mechanics. This method produces conformally refined meshes and deals with refinement from a basis function point of view. The proposed refinement criterion allow adaptive refinement where the mesh is still too coarse and where a strain or a stress field has a large value or a large gradient. The sensitivity of the criterion to the value or to the gradient ca be adjusted. The method and the criteria are validated through 2-D test cases. One limitation of the h-adaptive refinement method is highlighted: the discretization of boundary curves.
Highlights
Higher accuracy in Finite Element Method (FEM) can be obtained by adjusting spatial resolution of domain discretization
The general idea is to construct a hierarchy of nested meshes, where at a given level of refinement each basis functions can be expressed as a linear combination of basis functions associated to the immediate finer or coarser mesh
This refinement method is here used with new refinement criterion and is validated through 2-D test cases
Summary
Higher accuracy in Finite Element Method (FEM) can be obtained by adjusting spatial resolution of domain discretization. This method, initially developed in the framework of fluid mechanics [6, 16] and more recently applied to solid mechanics [10, 13], allows both (i) to preserve element shape quality while producing a conforming mesh and (ii) to perform local adaptive refinement and unrefinement This method deals with refinement from a basis function point of view and not from a geometrical point of view. The general idea is to construct a hierarchy of nested meshes, where at a given level of refinement each basis functions can be expressed as a linear combination of basis functions associated to the immediate finer or coarser mesh This refinement method is here used with new refinement criterion and is validated through 2-D test cases.
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