Abstract
We present a promising approach to reduce the difficulties associated with meshing complex curved domain boundaries for higher-order finite elements. In this work, higher-order XFEM analyses for strong discontinuity in the case of linear elasticity problems are presented. Curved implicit boundaries are approximated inside an unstructured coarse mesh by using parametric information extracted from the parametric representation (the most common in Computer Aided Design CAD). This approximation provides local graded sub-mesh (GSM) inside boundary elements (i.e. an element split by the curved boundary) which will be used for integration purpose. Sample geometries and numerical experiments illustrate the accuracy and robustness of the proposed approach.
Highlights
High-order finite-element methods offer exceptional accuracy and higher rates of convergence by using coarse meshes
Moumnassi et al [1] developed a hybrid parametric/implicit representation well suited to methods based on fixed grids such as the extended finite element method (XFEM)
They showed that it was possible, using the so-called marching algorithm for automatic conversion from a parametric surface into a zero level set defined on a narrow band of the background mesh, and the algorithm to construct a finer graded sub-mesh (GSM) inside the split elements, to build an implicit computational domain independently of the finite element mesh size or its order of interpolation
Summary
High-order finite-element methods offer exceptional accuracy and higher rates of convergence by using coarse meshes. A large number of researchers have investigated a variety of concepts do not require the generation of a conforming mesh and modelling geometrical features independently of the finite element mesh used for analysis These concepts [1],[2],[3],[4] differ from each other on the following points : Types of numerical methods : eXtended finite element method (XFEM) [5], the generalized finite element method (GFEM) [6] and Finite Cell Method [2]. We use a background unstructured linear mesh that serves to construct the computational domain and serves for analysis by higher-order shape functions For this purpose, we use the implicit representation (Level Set Description) to define the geometrical features to represent domain boundaries and XFEM for analysis. To construct the curved domain with minimal dependence on this background mesh, we use the hybrid method proposed by Moumnassi et al [1] which exploits the advantages of the parametric and implicit (Level set) representations. It is more general in that it is possible to deal with arbitrary parametric definition of object (the most common in Computer Aided Design CAD), and more general background mesh grid (unstructured mesh)
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