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.
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.
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.
SBFEM for fracture analysis of piezoelectric composites under thermal load
- Authors: Li, Chao , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2015
- Type: Text , Journal article
- Relation: International Journal of Solids and Structures Vol. 52, no. 1 (2015), p. 114-129
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- Description: This paper extends a semi-analytical technique, the so-called scaled boundary finite element method (SBFEM), to analyze fracture behaviors of piezoelectric materials and piezoelectric composites under thermal loading. In this method, only the boundary is discretized leading to a reduction of the spatial dimension by one. The temperature field in the domain is obtained using the SBFEM and expressed as a series of power functions of the radial coordinate. The resulting stress and electric displacement distribution along the radial direction is represented analytically. This permits the generalized stress and electric displacement intensity factors to be directly evaluated from the solution by following standard stress recovery procedures in the finite element method (FEM). 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. © 2014 Elsevier 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.
Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation
- Authors: Natarajan, Sundararajan , Ooi, Ean Tat , Chiong, Irene , Song, Chongmin
- Date: 2014
- Type: Text , Journal article
- Relation: Finite Elements in Analysis and Design Vol. 85, no. (August 2014 2014), p. 101-122
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- Description: Three different displacement based finite element formulations over arbitrary polygons are studied in this paper. The formulations considered are the conventional polygonal finite element method (FEM) with Laplace interpolants, the cell-based smoothed polygonal FEM with simple averaging technique and the scaled boundary polygon formulation. For the purpose of numerical integration, we employ the sub-triangulation for polygonal FEM and classical Gaussian quadrature for the smoothed FEM and the scaled boundary polygon formulation. The accuracy and the convergence properties of these formulations are studied with a few benchmark problems in the context of linear elasticity and the linear elastic fracture mechanics. The extension of scaled boundary polygon to higher order polygons is also discussed.
Extension of the scaled boundary finite element method to treat implicitly defined interfaces without enrichment
- Authors: Natarajan, Sundararajan , Dharmadhikari, Prasad , Annabattula, Ratna , Zhang, Junqi , Ooi, Ean , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computers and Structures Vol. 229, no. (2020), p.
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- Description: In this paper, the scaled boundary finite element method (SBFEM) is extended to solve the second order elliptic equation with discontinuous coefficients and to treat weak discontinuities. The salient feature of the proposed technique is that: (a) it requires only the boundary to be discretized and (b) does not require the interface to be discretized. The internal boundaries are represented implicitly by the level set method and the zero level sets are used to identify the different regions. In the regions containing the interface, edges along the boundary are assigned different material properties based on their location with respect to the zero level set. A detailed discussion is provided on the implementation aspects, followed by a few example problems in both two and three dimensions to show the robustness, accuracy and effectiveness of the proposed approach in modelling materials with interfaces. The proposed technique can easily be integrated to any existing finite element code. © 2019 Elsevier Ltd
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.
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.
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.
Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials - a scaled boundary finite element approach
- Authors: Pramod, A. , Ooi, Ean Tat , Song, Chongmin , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article
- Relation: Composite Structures Vol. 206, no. (2018), p. 301-312
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- Description: The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique.