Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling
- Ooi, Ean Tat, Man, Hou, Natarajan, Sundararajan, Song, Chongmin
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin
- Date: 2015
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 144, no. (2015), p. 101-117
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- Description: A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique. © 2015.
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin
- Date: 2015
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 144, no. (2015), p. 101-117
- Full Text:
- Reviewed:
- Description: A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique. © 2015.
A quadtree-based scaled boundary finite element method for crack propagation modelling
- Ooi, Ean Tat, Man, Hou, Natarajan, Sundararajan, Song, Chongmin, Tin-Loi, Francis
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Conference paper
- Relation: 23rd Australasian Conference on the Mechanics of Structures and Materials, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, p. 813-818
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- Description: The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.
- Authors: Ooi, Ean Tat , Man, Hou , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Conference paper
- Relation: 23rd Australasian Conference on the Mechanics of Structures and Materials, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, p. 813-818
- Full Text:
- Reviewed:
- Description: The quadtree is a hierarchical-type data structure where each parent is recursively divided into four children. This structure makes it particularly efficient for adaptive mesh refinement in regions with localised gradients. Compared with unstructured triangles, mesh generation is more efficient using quadtree decompositions. The finite number of patterns in the quadtree decomposition makes it efficient for data storage and retrieval. Motivated by these advantages, a crack propagation modelling approach using a quadtree-based scaled boundary finite element method (SBFEM) is developed. Starting from the formulation of an arbitrary n-sided polygon element, each quadrant in the quadtree mesh is treated as a polygon within the framework of the SBFEM. Special techniques to treat the hanging nodes are not necessary. Moreover, the SBFEM enables accurate calculation of the stress intensity factors directly from its solutions without local mesh refinement or asymptotic enrichment functions. When a crack propagates, it is only necessary to split each quadrant cut by the crack into two. These quadrants are polygons that can be directly modelled by the SBFEM. Changes to the mesh are minimal. The efficiency of this approach is demonstrated using numerical benchmarks.
A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete
- Guo, H., Ooi, Ean Tat, Saputra, Albert, Yang, Zhenjun, Natarajan, Sundararajan, Ooi, Ean Hin, Song, Chongmin
- Authors: Guo, H. , Ooi, Ean Tat , Saputra, Albert , Yang, Zhenjun , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2019
- Type: Text , Journal article , acceptedVersion
- Relation: Engineering Fracture Mechanics Vol. 211, no. (2019), p. 420-441
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- Description: A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility.
- Authors: Guo, H. , Ooi, Ean Tat , Saputra, Albert , Yang, Zhenjun , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2019
- Type: Text , Journal article , acceptedVersion
- Relation: Engineering Fracture Mechanics Vol. 211, no. (2019), p. 420-441
- Full Text:
- Reviewed:
- Description: A quadtree-polygon scaled boundary finite element-based approach for image-based modelling of concrete fracture at the mesoscale is developed. Digital images representing the two-phase mesostructure of concrete, which comprises of coarse aggregates and mortar are either generated using a take-and-place algorithm with a user-defined aggregate volume ratio or obtained from X-ray computed tomography as an input. The digital images are automatically discretised for analysis by applying a balanced quadtree decomposition in combination with a smoothing operation. The scaled boundary finite element method is applied to model the constituents in the concrete mesostructure. A quadtree formulation within the framework of the scaled boundary finite element method is advantageous in that the displacement compatibility between the cells are automatically preserved even in the presence of hanging nodes. Moreover, the geometric flexibility of the scaled boundary finite element method facilitates the use of arbitrary sided polygons, allowing better representation of the aggregate boundaries. The computational burden is significantly reduced as there are only finite number of cell types in a balanced quadtree mesh. The cells in the mesh are connected to each other using cohesive interface elements with appropriate softening laws to model the fracture of the mesostructure. Parametric studies are carried out on concrete specimens subjected to uniaxial tension to investigate the effects of various parameters e.g. aggregate size distribution, porosity and aggregate volume ratio on the fracture of concrete at the meso-scale. Mesoscale fracture of concrete specimens obtained from X-ray computed tomography scans are carried out to demonstrate its feasibility.
Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation
- Xiao, B., Natarajan, Sundararajan, Birk, Carolin, Ooi, Ean Hin, Song, Chongmin, Ooi, Ean Tat
- Authors: Xiao, B. , Natarajan, Sundararajan , Birk, Carolin , Ooi, Ean Hin , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 124, no. 17 (2023), p. 3603-3636
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- Description: A general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well-known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well-established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near-incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed. © 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
- Authors: Xiao, B. , Natarajan, Sundararajan , Birk, Carolin , Ooi, Ean Hin , Song, Chongmin , Ooi, Ean Tat
- Date: 2023
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 124, no. 17 (2023), p. 3603-3636
- Full Text:
- Reviewed:
- Description: A general technique to develop arbitrary-sided polygonal elements based on the scaled boundary finite element method is presented. Shape functions are derived from the solution of the Poisson's equation in contrast to the well-known Laplace shape functions that are only linearly complete. The application of the Poisson shape functions can be complete up to any specific order. The shape functions retain the advantage of the scaled boundary finite element method allowing direct formulation on polygons with arbitrary number of sides and quadtree meshes. The resulting formulation is similar to the finite element method where each field variable is interpolated by the same set of shape functions in parametric space and differs only in the integration of the stiffness and mass matrices. Well-established finite element procedures can be applied with the developed shape functions, to solve a variety of engineering problems including, for example, coupled field problems, phase field fracture, and addressing volumetric locking in the near-incompressibility limit by adopting a mixed formulation. Application of the formulation is demonstrated in several engineering problems. Optimal convergence rates are observed. © 2023 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
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