Scaled boundary polygons with application to fracture analysis of functionally graded materials
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 98, no. (2014), p.562-589
- Full Text: false
- Reviewed:
Automatic modelling of cohesive crack propagation in concrete using polygon scaled boundary finite elements
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2012
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 93, no. (2012), p. 13-33
- Full Text: false
- Reviewed:
- Description: An automatic cohesive crack propagation modelling methodology for quasi-brittle materials using polygon elements is presented. Each polygon is treated as a subdomain that is modelled by the scaled boundary finite element method (SBFEM). Generalised stress intensity factors (SIFs) based on matrix power function solutions of singular stress fields obtained from the SBFEM following standard finite element stress recovery procedures is used to evaluate the crack propagation criterion and determine the crack propagation direction. Interface elements model the fracture process zones and are automatically inserted into the polygon mesh as the crack propagates. A shadow domain procedure couples the polygons and interface elements. It computes the load-displacement response and crack propagation criterion, taking into account the cohesive tractions on the crack edges that are modelled as side-face tractions in the SBFEM. Cracks are propagated using a simple, yet flexible local remeshing procedure that can remesh any arbitrary polygon. Only minimal changes are made to the global mesh structure each time the remeshing algorithm is called. Five cohesive crack propagation benchmarks are modelled to validate the developed method and demonstrate its salient features. © 2012 Elsevier Ltd.
A scaled boundary finite element formulation with bubble functions for elasto-static analyses of functionally graded materials
- Authors: Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2017
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 60, no. 6 (2017), p. 943-967
- Full Text:
- Reviewed:
- Description: This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials. © 2017, Springer-Verlag GmbH Germany.
Dynamic crack propagation simulation with scaled boundary polygon elements and automatic remeshing technique
- Authors: Ooi, Ean Tat , Shi, Mingguang , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2013
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 106, no. (2013), p. 1-21
- Full Text: false
- Reviewed:
- Description: An efficient methodology for automatic dynamic crack propagation simulations using polygon elements is developed in this study. The polygon mesh is automatically generated from a Delaunay triangulated mesh. The formulation of an arbitrary n-sided polygon element is based on the scaled boundary finite element method (SBFEM). All kind of singular stress fields can be described by the matrix power function solution of a cracked polygon. Generalised dynamic stress intensity factors are evaluated using standard finite element stress recovery procedures. This technique does not require local mesh refinement around the crack tip, special purpose elements or nodal enrichment functions. An automatic local remeshing algorithm that can be applied to any polygon mesh is developed in this study to accommodate crack propagation. Each remeshing operation involves only a small patch of polygons around the crack tip, resulting in only minimal change to the global mesh structure. The increase of the number of degrees-of-freedom caused by crack propagation is moderate. The method is validated using four dynamic crack propagation benchmarks. The predicted dynamic fracture parameters show good agreement with experiment observations and numerical simulations reported in the literature. © 2013 Elsevier Ltd.
Polygon scaled boundary finite elements for crack propagation modelling
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis , Yang, Zhenjun
- Date: 2012
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 91, no. 3 (2012), p. 319-342
- Full Text: false
- Reviewed:
- Description: An automatic crack propagation modelling technique using polygon elements is presented. A simple algorithm to generate a polygon mesh from a Delaunay triangulated mesh is implemented. The polygon element formulation is constructed from the scaled boundary finite element method (SBFEM), treating each polygon as a SBFEM subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are computed directly from their definitions without any nodal enrichment functions. An automatic remeshing algorithm capable of handling any n-sided polygon is developed to accommodate crack propagation. The algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths. The efficiency of the polygon SBFEM in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack. Four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features. The predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature. © 2012 John Wiley & Sons, Ltd.
Construction of generalized shape functions over arbitrary polytopes based on scaled boundary finite element method's solution of Poisson's equation
- 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.