A hierarchical h adaptivity methodology based on element subdivision

Ródenas, Juan José; Albelda, José Luis; Tur, M.; Fuenmayor, F. J.

doi:10.18273/revuin.v16n2-2017024

Cited by 5 publications

(4 citation statements)

References 26 publications

(29 reference statements)

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“…Obviously, TO driven by FE analyses is also prone to experiencing such problems. Algorithms that consider h-adaptive mesh refinement based on the estimated quality of the FE solution are well-established techniques [22][23][24][25][26] that improve the quality of the solution (evaluated by error estimation techniques) refining the meshes in the regions where the FE solution is less accurate. Mesh optimality criterion (like minimization of the number of elements in the new mesh to obtain a prescribed error level, or equi-distribution of the error in the elements of the new mesh 27 ) can be used in h-refinement processes to create computationally efficient meshes to improve the performance of FE analyses.…”

Section: Introductionmentioning

confidence: 99%

Improvement in 3D topology optimization with h‐adaptive refinement using the Cartesian grid Finite Element Method

Muñoz

Albelda

Ródenas

et al. 2021

Numerical Meth Engineering

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The growing number of scientific publications on topology optimization (TO) shows the great interest that this technique has generated in recent years. Among the different methodologies for TO, this article focuses on the well‐known solid isotropic material penalization (SIMP) method, broadly used because of its simple formulation and efficiency. Even so, the SIMP method has certain drawbacks, namely: lack of precision in definition of the edges of the optimized geometry and final results strongly influenced by the discretization used for the finite element (FE) analyses. In this article, we propose a combination of techniques to limit the effect of these drawbacks and, thus, to improve the behavior of TO. All these techniques are based on the use of the Cartesian grid finite element method (cgFEM), an immersed boundary method whose Cartesian grid structure and hierarchical data structure makes it specially appropriate for TO. All the proposed techniques are framed under the concept of mesh refinement. First, we propose the use of two meshes, the FE analysis mesh, and a finer mesh for integration and evaluation of sensitivities, to improve the resolution of the final solution at a marginal computational cost. Then we propose two h‐adaptive mesh refinement strategies. The first one will tend to refine the elements having intermediate density values and will have the effect of sharpening the definition of the edges of the optimized geometry. We will clearly show that if the accuracy of the FE analyses is not taken into account, stress constrained TO will generate solutions that, once manufactured, will not satisfy the constraints. Hence, we also propose an h‐refinement strategy based on the estimation of the discretization error in energy norm.

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Section: Introductionmentioning

confidence: 99%

Improvement in 3D topology optimization with h‐adaptive refinement using the Cartesian grid Finite Element Method

Muñoz

Albelda

Ródenas

et al. 2021

Numerical Meth Engineering

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“…In this article we adopt a so-called hierarchical mesh refinement scheme [29,30] which consists in directly subdividing elements requiring refinement. This strategy generally results in optimal refined meshes and enables to better control the mesh refinement thanks to an explicit hierarchical data-structure.…”

Section: Introductionmentioning

confidence: 99%

A unified framework for the computational comparison of adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locally adaptive multigrid methods versus h-adaptive methods

Koliesnikova

Ramière

Lebon

2021

Journal of Computational Physics

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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“…In order to introduce local mesh refinement, the h-adaptivity could be applied. The h-adaptivity has been proven to be an effective tool to enhance local accuracy while keeping computational costs low, as can be seen in several research works on the simulation of cracks [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Combining h-adaptivity with the Element Splitting Method for Crack Simulation in Large Structures

Shu-min¹,

Braun²,

Herrnring³

et al. 2021

Preprint

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H-adaptivity is an effective tool to introduce local mesh refinement in FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures such as ship hulls. In engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called ‘h-adaptive element splitting’ (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that consist of structured coarse meshes. By employing the mesh refinement introduced in this paper, very small cracks are well represented in large structures.

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A hierarchical h adaptivity methodology based on element subdivision

Cited by 5 publications

References 26 publications

Improvement in 3D topology optimization with h‐adaptive refinement using the Cartesian grid Finite Element Method

Improvement in 3D topology optimization with h‐adaptive refinement using the Cartesian grid Finite Element Method

A unified framework for the computational comparison of adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locally adaptive multigrid methods versus h-adaptive methods

Combining h-adaptivity with the Element Splitting Method for Crack Simulation in Large Structures

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