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General Finite Element Methods with Special Focus on XFEM
This chapter summarizes the principles related to a wide spectrum of mesh-based methods that belong to the category of “general finite element methods (GFEMs)”. They are the most promising advanced CMs in explicitly handling local failure phenomena and meso-scale components (e.g. deformation localization bands, concrete cracks, structural planes, etc.) to give their detailed description using simple “finite element (FE)” mesh. Such a FE mesh may be generated beforehand to discretize the engineering structure concerned, where the deployment and size of FEs are dominated by the structure configuration and the gradient of field functions (e.g. strains and flow rates). The existence and evolution of local failure phenomena and meso-scale components are allocated within enriched elements. The basic variables within enriched element may be interpolated from the correspondent “enriched” nodal variables only (CEM), or from “enriched” nodal variables and basis functions together (XFEM). According to the virtual work or variational principle, the governing equations are established to solve these nodal variables. In this manner, less restraint is imposed on the mesh generation with considerable amount of heterogeneous components, which allows for a great simplification in the pre-process work towards the analysis for complex engineering structures. By the validation example of the 1-D discontinuous bar containing joint, it is clear that the FEM with joint element, the XFEM and the CEM with different enrichments will give identical outcomes. By the engineering example, it is shown that the GFEMs specified in this chapter already possess high ability to handle complex engineering issues, but the enriched sub-models for crack-tips are additionally demanded, which is cumbersome because of the repeated data mapping between the global mesh of arch dam and the local mesh containing crack-tip.
General Finite Element Methods with Special Focus on XFEM
This chapter summarizes the principles related to a wide spectrum of mesh-based methods that belong to the category of “general finite element methods (GFEMs)”. They are the most promising advanced CMs in explicitly handling local failure phenomena and meso-scale components (e.g. deformation localization bands, concrete cracks, structural planes, etc.) to give their detailed description using simple “finite element (FE)” mesh. Such a FE mesh may be generated beforehand to discretize the engineering structure concerned, where the deployment and size of FEs are dominated by the structure configuration and the gradient of field functions (e.g. strains and flow rates). The existence and evolution of local failure phenomena and meso-scale components are allocated within enriched elements. The basic variables within enriched element may be interpolated from the correspondent “enriched” nodal variables only (CEM), or from “enriched” nodal variables and basis functions together (XFEM). According to the virtual work or variational principle, the governing equations are established to solve these nodal variables. In this manner, less restraint is imposed on the mesh generation with considerable amount of heterogeneous components, which allows for a great simplification in the pre-process work towards the analysis for complex engineering structures. By the validation example of the 1-D discontinuous bar containing joint, it is clear that the FEM with joint element, the XFEM and the CEM with different enrichments will give identical outcomes. By the engineering example, it is shown that the GFEMs specified in this chapter already possess high ability to handle complex engineering issues, but the enriched sub-models for crack-tips are additionally demanded, which is cumbersome because of the repeated data mapping between the global mesh of arch dam and the local mesh containing crack-tip.
General Finite Element Methods with Special Focus on XFEM
Springer Tracts in Civil Engineering
Chen, Shenghong (author)
2023-01-01
68 pages
Article/Chapter (Book)
Electronic Resource
English
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