A scaled boundary polygon formulation for elasto-plastic analyses
- Ooi, Ean Tat, Song, Chongmin, Tin-Loi, Francis
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 268, no. (January 2014 2014), p. 905-937
- Full Text:
- Reviewed:
- Description: This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks.
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 268, no. (January 2014 2014), p. 905-937
- Full Text:
- Reviewed:
- Description: This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks.
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
- 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.
- 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.
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