An h-hierarchical adaptive scaled boundary finite element method for elastodynamics
- Authors: Yang, Zhenjun , Zhang, Zihua , Liu, Guohua , Ooi, Ean Tat
- Date: 2011
- Type: Text , Journal article
- Relation: Computers and Structures Vol. 89, no. 13-14 (2011), p. 1417-1429
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- Description: A posteriori h-hierarchical adaptive scaled boundary finite element method (ASBFEM) for transient elastodynamic problems is developed. In a time step, the fields of displacement, stress, velocity and acceleration are all semi-analytical and the kinetic energy, strain energy and energy error are all semi-analytically integrated in subdomains. This makes mesh mapping very simple but accurate. Adaptive mesh refinement is also very simple because only subdomain boundaries are discretised. Two 2D examples with stress wave propagation were modelled. It is found that the degrees of freedom needed by the ASBFEM are only 5%-15% as needed by adaptive FEM for the examples. © 2011 Elsevier Ltd. All rights reserved.
Modelling dynamic crack propagation using the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Yang, Zhenjun
- Date: 2011
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 88, no. 4 (2011), p. 329-349
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- Description: This study presents a novel application of the scaled boundary finite element method (SBFEM) to model dynamic crack propagation problems. Accurate dynamic stress intensity factors are extracted directly from the semi-analytical solutions of SBFEM. They are then used in the dynamic fracture criteria to determine the crack-tip position, velocity and propagation direction. A simple, yet flexible remeshing algorithm is used to accommodate crack propagation. Three dynamic crack propagation problems that include mode-I and mix-mode fracture are modelled. The results show good agreement with experimental and numerical results available in the literature. It is found that the developed method offers some advantages over conventional FEM in terms of accuracy, efficiency and ease of implementation. © 2011 John Wiley & Sons, 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
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- 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.
2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM
- Authors: Li, Chao , Song, Chongmin , Man, Hou , Ooi, Ean Tat , Gao, Wei
- Date: 2014
- Type: Text , Journal article
- Relation: International Journal of Solids and Structures Vol. 51, no. 11-12 (June 2014), p. 2096-2108
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- Description: The dynamic stress and electric displacement intensity factors of impermeable cracks in homogeneous piezoelectric materials and interface cracks in piezoelectric bimaterials are evaluated by extending the scaled boundary finite element method (SBFEM). In this method, a piezoelectric plate is divided into polygons. Each polygon is treated as a scaled boundary finite element subdomain. Only the boundaries of the subdomains need to be discretized with line elements. The dynamic properties of a subdomain are represented by the high order stiffness and mass matrices obtained from a continued fraction solution, which is able to represent the high frequency response with only 3-4 terms per wavelength. The semi-analytical solutions model singular stress and electric displacement fields in the vicinity of crack tips accurately and efficiently. The dynamic stress and electric displacement intensity factors are evaluated directly from the scaled boundary finite element solutions. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.
A scaled boundary polygon formulation for elasto-plastic analyses
- 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
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- 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.
Virtual and smoothed finite elements : A connection and its application to polygonal/polyhedral finite element methods
- Authors: Natarajan, Sundararajan , Bordas, Stéphane , Ooi, Ean Tat
- Date: 2015
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 104, no. 13 (2015), p. 1173-1199
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- Description: We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O(dofs)1.1 in case of the conventional polygonal FEM, while it scales as O(dofs)0.7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. © 2015 John Wiley & Sons, Ltd.
Construction of high-order complete scaled boundary shape functions over arbitrary polygons with bubble functions
- Authors: Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 108, no. 9 (2016), p. 1086-1120
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- Description: This manuscript presents the development of novel high-order complete shape functions over star-convex polygons based on the scaled boundary finite element method. The boundary of a polygon is discretised using one-dimensional high order shape functions. Within the domain, the shape functions are analytically formulated from the equilibrium conditions of a polygon. These standard scaled boundary shape functions are augmented by introducing additional bubble functions, which renders them high-order complete up to the order of the line elements on the polygon boundary. The bubble functions are also semi-analytical and preserve the displacement compatibility between adjacent polygons. They are derived from the scaled boundary formulation by incorporating body force modes. Higher-order interpolations can be conveniently formulated by simultaneously increasing the order of the shape functions on the polygon boundary and the order of the body force mode. The resulting stiffness-matrices and mass-matrices are integrated numerically along the boundary using standard integration rules and analytically along the radial coordinate within the domain. The bubble functions improve the convergence rate of the scaled boundary finite element method in modal analyses and for problems with non-zero body forces. Numerical examples demonstrate the accuracy and convergence of the developed approach. Copyright (c) 2016 John Wiley & Sons, Ltd.
A novel scaled boundary finite element formulation with stabilization and its application to image-based elastoplastic analysis
- Authors: He, Ke , Song, Chongmin , Ooi, Ean Tat
- Date: 2018
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 115, no. 8 (2018), p. 956-985
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- Description: Digital images are increasingly being used as input data for computational analyses. This study presents an efficient numerical technique to perform image-based elastoplastic analysis of materials and structures. The quadtree decomposition algorithm is employed for image-based mesh generation, which is fully automatic and highly efficient. The quadtree cells are modeled by scaled boundary polytope elements, which eliminate the issue of hanging nodes faced by standard finite elements. A novel, simple, and efficient scaled boundary elastoplastic formulation with stablisation is developed. In this formulation, the return-mapping calculation is only required to be performed at a single point in a polytope element, which facilitates the computational efficiency of the elastoplastic analysis and simplicity of implementation. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed technique for performing the elastoplastic analysis of high-resolution images.
Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method
- Authors: Hirshikesh , Pramod, Aladurthi , Annabattula, Ratna , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2019
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 355, no. (2019), p. 284-307
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- Description: In this work, we propose an adaptive phase field method (PFM) to simulate quasi-static brittle fracture problems. The phase field equations are solved using the scaled boundary finite element method (SBFEM). The adaptive refinement strategy is based on an error indicator evaluated directly from the solutions of the SBFEM without any need for stress recovery techniques. Quadtree meshes are adapted to perform mesh refinement. The polygons with hanging nodes in the quadtree decomposition are treated as n−sided polygons within the framework of the SBFEM and do not require any special treatment in contrast to the conventional finite element method. Several benchmark problems are used to demonstrate the robustness and the efficacy of the proposed technique. The adaptive refinement strategy reduces the mesh burden when adopting the PFM to model fracture. Numerical results show an improvement in the computational efficiency in terms of the number of elements required in the standard PFM without compromising the accuracy of the solution.
Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes
- Authors: Aladurthi, Lakshmi , Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2019
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 119, no. 13 (2019), p. 1379-1394
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- Description: In this paper, a purely displacement-based formulation is presented within the framework of the scaled boundary finite element method to model compressible and nearly incompressible materials. A selective reduced integration technique combined with an analytical treatment in the nearly incompressible limit is employed to alleviate volumetric locking. The stiffness matrix is computed by solving the scaled boundary finite element equation. The salient feature of the proposed technique is that it neither requires a stabilization parameter nor adds additional degrees of freedom to handle volumetric locking. The efficiency and the robustness of the proposed approach is demonstrated by solving various numerical examples in two and three dimensions.
An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method
- Authors: Mathew, Tittu , Pramod, A. L. N. , Ooi, Ean Tat , Natarajan, Sundararajan
- Date: 2020
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 367, no. (2020), p.
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- Description: This paper serves to extend the existing literature on the Stochastic Galerkin Scaled Boundary Finite Element Method (SGSBFEM) in two ways. The first part of this work deals with the formulation of multiple non-correlated Gaussian random fields using the conventional Karhunen–Loéve expansion technique and its forward propagation through the Spectral Stochastic Scaled Boundary Finite Element setting using the polynomial surface fit method in terms of the scaled boundary coordinates. The advantages in adopting such a forward propagation technique in capturing the statistical moments of Quantities of Interest (QoI) across the domain, are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs. The second contribution is the extension of the proposed forward Uncertainty Quantification (UQ) to take into account multiple independent random fields, followed by Polynomial Chaos Expansion (PCE) based sensitivity analysis. Both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing SGSBFEM in the literature. Moreover, the stochastic results are validated for all the numerical examples using the Monte Carlo method. © 2020 Elsevier B.V.
Application of scaled boundary finite element method for delamination analysis of composite laminates using cohesive zone modelling
- Authors: Garg, Nikhil , Prusty, Gangadhara , Ooi, Ean Tat , Song, Chongmin , Pearce, Garth , Phillips, Andrew
- Date: 2020
- Type: Text , Journal article
- Relation: Composite Structures Vol. 253, no. (2020), p. 1-10
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- Description: In this paper, the scaled boundary finite element method (SBFEM) is evaluated for two-dimensional delamination analysis of composite laminates. The delamination phenomenon was studied using cohesive zone modelling (CZM). A bi-linear (triangular) traction-separation law was used to describe the interface behaviour, which was modelled using zero-thickness interface elements. Local arc-length solution technique was used to solve the non-linearity due to the interface behaviour. In this research, pure Mode I and Mode II as well as mixed mode delamination studies have been conducted using the SBFEM formulation. A variety of numerical experiments were performed. Good agreement was observed between the SBFEM simulation and the available numerical and experimental results in the open literature. A comparison between the SBFEM and other traditional methods shows that the presented formulation can solve the same physical problem with a reduction in the computational cost by more than half. The study highlights the advantages of SBFEM over other methods for modelling delamination in composite laminates using CZM.
- Description: This project is conducted within the ARC Training Centre for Automated Manufacture of Advanced Composites (IC160100040), supported by the Commonwealth of Australia under the Australian Research Council's Industrial Transformation Research Program.
Application of adaptive phase-field scaled boundary finite element method for functionally graded materials
- Authors: Pramod, Aladurthi , Hirshikesh , Natarajan, Sundararajan , Ooi, Ean Tat
- Date: 2021
- Type: Text , Journal article
- Relation: International Journal of Computational Methods Vol. 18, no. 3 (2021), p.
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- Description: In this paper, an adaptive phase-field scaled boundary finite element method for fracture in functionally graded material (FGM) is presented. The model accounts for spatial variation in the material and fracture properties. The quadtree decomposition is adopted for refinement, and the refinement is based on an error indicator evaluated directly from the solutions of the scaled boundary finite element method. This combination makes it a suitable choice to study fracture using the phase field method, as it reduces the mesh burden. A few standard benchmark numerical examples are solved to demonstrate the improvement in computational efficiency in terms of the number of degrees of freedom. © 2021 World Scientific Publishing Company.