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.
Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling
- 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.
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.
Modelling of crack propagation of gravity dams by scaled boundary polygons and cohesive crack model
- Authors: Shi, Mingguang , Zhong, Hong , Ooi, Ean Tat , Zhang, Chuhan , Song, Chongmin
- Date: 2013
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. 183, no. 1 (2013), p. 29-48
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- Description: Crack propagation in concrete gravity dams is investigated using scaled boundary polygons coupled with interface elements. The concrete bulk is assumed to be linear elastic and is modelled by the scaled boundary polygons. The interface elements model the fracture process zone between the crack faces. The cohesive tractions are modelled as side-face tractions in the scaled boundary polygons. The solution of the stress field around the crack tip is expressed semi-analytically as a power series. It reproduces the singular and higher-order terms in an asymptotic solution, such as the William's eigenfunction expansion when the cohesive tractions vanish. Accurate results can be obtained without asymptotic enrichment or local mesh refinement. The stress intensity factors are obtained directly from their definition and provide a convenient and accurate means to assess the zero-K condition, which determines the stability of a cohesive crack. The direction of crack propagation is determined from the maximum circumferential stress criterion. To accommodate crack propagation, a local remeshing algorithm that is applicable to any polygon mesh is augmented by inserting cohesive interface elements between the crack surfaces as the cracks propagate. Three numerical benchmarks involving crack propagation in concrete gravity dams are modelled. The results are compared to the experimental and other numerical simulations reported in the literature. © 2013 Springer Science+Business Media Dordrecht.
Crack propagation modeling with scaled boundary polygons
- Authors: Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Conference paper
- Relation: 1st Australasian Conference on Computational Mechanics, ACCM 2013 p. 719-724
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- Description: Crack propagation is modelled using scaled boundary polygons. The polygons discretise the computational domain and can be of any number of sides, leading to more flexible mesh generation. The scaled boundary finite element method is used to construct shape functions of the polygon elements. These shape functions form a partition of unity and are linearly complete. They can accurately model any kind of stress singularity without local mesh refinement or asymptotic enrichment functions. The scaled boundary shape functions enable the method to be further developed to model the response of heterogeneous and nonlinear materials. As the polygons can be of any number of sides, simple re-meshing algorithms can be devised to model crack propagation. Two numerical benchmarks are modeled to illustrate the salient features of the scaled boundary polygons.
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.
Crack propagation modelling in functionally graded materials using scaled boundary polygons
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Tin-Loi, Francis
- Date: 2015
- Type: Text , Journal article
- Relation: International Journal of Fracture Vol. 192, no. 1 (2015), p. 87-105
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- Description: A recently developed scaled boundary finite element formulation that can model the response of functionally graded materials is further developed to model crack propagation in two-dimensions. This formulation can accurately model the stress singularity at the crack tip in heterogeneous materials. The asymptotic behaviour at the crack tip is analytically represented in the scaled boundary shape functions of a cracked polygon. This enables accurate stress intensity factors to be computed directly from their definitions. Neither local mesh refinement nor asymptotic enrichment functions are required. This novel formulation can be implemented on polygons with an arbitrary number of sides. When modelling crack propagation, the remeshing process is more flexible and leads to only minimal changes to the global mesh structure. Six numerical examples involving crack propagation in functionally graded materials are modelled to demonstrate the salient features of the developed method. © 2015, Springer Science+Business Media Dordrecht.
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.
A quadtree-based scaled boundary finite element method for crack propagation modelling
- 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.
A quadtree-polygon-based scaled boundary finite element method for crack propagation modeling in functionally graded materials
- Authors: Chen, Xiaojun , Luo, Tao , Ooi, Ean Tat , Ooi, Ean Hin , Song, Chongmin
- Date: 2018
- Type: Text , Journal article
- Relation: Theoretical and Applied Fracture Mechanics Vol. 94, no. (2018), p. 120-133
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- Description: This paper presents a method to improve the computational efficiency of the scaled boundary finite element formulation for functionally graded materials. Both isotropic and orthotropic functionally graded materials are considered. This is achieved using a combination of quadtree and polygon meshes. This hybrid meshing approach is particularly suitable to be used with the SBFEM for functionally graded materials because of the significant amount of calculations required to compute the stiffness matrices of the polygons/cells in the mesh. When a quadtree structure is adopted, most of the variables required for the numerical simulation can be pre-computed and stored in the memory, retrieved and scaled as required during the computations, leading to an efficient method for crack propagation modeling. The scaled boundary finite element formulation enables accurate computation of the stress intensity factors directly from the stress solutions without any special post-processing techniques or local mesh refinement in the vicinity of the crack tip. Numerical benchmarks demonstrate the efficiency of the proposed method as opposed to using a purely polygon-mesh based approach. © 2018 Elsevier Ltd
Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon-quadtree meshes
- Authors: Ooi, Ean Tat , Natarajan, Sundararajan , Song, Chongmin , Ooi, Ean Hin
- Date: 2016
- Type: Text , Journal article
- Relation: International Journal of Impact Engineering Vol. 90, no. (2016), p. 154-164
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- Description: In this paper, we present an efficient computational procedure to model dynamic fracture within the framework of the scaled boundary finite element method (SBFEM). A quadtree data structure is used to discretise the domain, and 2:1 ratio between the cells is maintained. This limits the number of patterns in the quadtree decomposition and allows for efficient computation of the system matrices. The regions close to the boundary are discretised with arbitrary sided polygons so as to facilitate accurate modelling of the curved boundaries. The stiffness and the mass matrix over all the cells are computed by the SBFEM. Moreover, the semi-analytical nature of the SBFEM enables accurate modelling of the asymptotic stress fields in the vicinity of the crack tip. An efficient remeshing algorithm that combines the quadtree decomposition with simple Boolean operations is proposed to model the crack propagation. The remeshing is restricted only to a small region in the vicinity of the crack tip. The efficiency and the convergence properties of the proposed framework are demonstrated with a few benchmark problems. © 2015 Elsevier Ltd. All rights reserved.
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.
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 dual scaled boundary finite element formulation over arbitrary faceted star convex polyhedra
- Authors: Ooi, Ean Tat , Saputra, Albert , Natarajan, Sundararajan , Ooi, Ean Hin , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computational Mechanics Vol. 66, no. 1 (2020), p. 27-47
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- Description: A novel technique to formulate arbritrary faceted polyhedral elements in three-dimensions is presented. The formulation is applicable for arbitrary faceted polyhedra, provided that a scaling requirement is satisfied and the polyhedron facets are planar. A triangulation process can be applied to non-planar facets to generate an admissible geometry. The formulation adopts two separate scaled boundary coordinate systems with respect to: (i) a scaling centre located within a polyhedron and; (ii) a scaling centre on a polyhedron’s facets. The polyhedron geometry is scaled with respect to both the scaling centres. Polygonal shape functions are derived using the scaled boundary finite element method on the polyhedron facets. The stiffness matrix of a polyhedron is obtained semi-analytically. Numerical integration is required only for the line elements that discretise the polyhedron boundaries. The new formulation passes the patch test. Application of the new formulation in computational solid mechanics is demonstrated using a few numerical benchmarks. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
Crack propagation modeling in functionally graded materials using polygon elements modeled by the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Guo, ShuHong , Song, Chongmin
- Date: 2013
- Type: Text , Conference proceedings
- Relation: 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012; Sydney, NSW; Australia; 11th-14th December 2012; Published in From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM p. 133-138
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- Description: Functionally graded materials (FGMs) are multi-phased composites that are specifically engineered so that their material properties vary continuously in a predetermined direction. The heterogeneity in FGMs results in superior fracture resistance, making them suitable for use as medical implants and components in nuclear, aerospace and electro-mechanical industries. The degree to which the fracture resistance of FGMs can be improved is usually not known a priori. Understanding their fracture behaviour provides insights to design better FGMs and enables quantitative assessment of the structural integrity in manufactured FGM products. A novel methodology is developed in this study to model crack propagation in FGMs. It uses high order polygon elements that are modelled by the scaled boundary finite element method. The displacement and stress fields in each polygon are expressed using scaled boundary shape functions and corresponding nodal displacements. Material heterogeneity is modelled by locally fitting a polynomial curve in terms of scaled boundary finite element coordinates over each polygon. The developed method is very efficient in modelling singular stress fields in the vicinity of cracks. Stress intensity factors are evaluated directly from the singular modes in the scaled boundary finite element solutions to determine the crack propagation direction.A simple local remeshing algorithm for polygons is developed to accommodate crack propagation. Fracture analyses of FGMs are conducted on three numerical examples to validate the methodology and demonstrate its salient features. Fracture parameters e.g. stress intensity factors, critical failure load and crack propagation paths of FGM specimens can be obtained from these analyses. © 2013 Taylor & Francis Group.
- Description: From Materials to Structures: Advancement Through Innovation - Proceedings of the 22nd Australasian Conference on the Mechanics of Structures and Materials, ACMSM 2012
A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics
- Authors: Song, Chongmin , Ooi, Ean Tat , Natarajan, Sundararajan
- Date: 2018
- Type: Text , Journal article , Review
- Relation: Engineering Fracture Mechanics Vol. 187, no. (2018), p. 45-73
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- Description: The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semi-analytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygons to represent arbitrary geometric shapes leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility. © 2017 Elsevier Ltd
Hydraulic fracture at the dam-foundation interface using the scaled boundary finite element method coupled with the cohesive crack model
- Authors: Zhong, Hong , Li, Hongjun , Ooi, Ean Tat , Song, Chongmin
- Date: 2018
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 88, no. (2018), p. 41-53
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- Description: The scaled boundary finite element method coupled with the cohesive crack model is extended to investigate the hydraulic fracture at the dam-foundation interface. The concrete and rock bulk are modeled by the scaled boundary polygons. Cohesive interface elements model the fracture process zone between the crack faces. The cohesive tractions are modeled as side-face tractions in the scaled boundary polygons. The solution of the stress field around the crack tip is expressed semi-analytically as a power series. Accurate displacement field, stress field and stress intensity factors can be obtained without asymptotic enrichment or local mesh refinement. The proposed procedure is verified by the hydraulic fracture of a rectangular embankment on rigid foundation and applied to the modeling of hydraulic fracture on the dam-foundation interface of a benchmark dam. Different distributions of water pressure inside the crack are investigated. It is found that the water pressure inside the crack decreases the peak overflow to less than 20% of the case without water in the crack. Considering the water lag or not is significant to the response, while different distribution of pressure following the water lag region in the fracture process zone has negligible influence.
Adaptive analysis using scaled boundary finite element method in 3D
- Authors: Zhang, Junqi , Natarajan, Sundararajan , Ooi, Ean Tat , Song, Chongmin
- Date: 2020
- Type: Text , Journal article
- Relation: Computer Methods in Applied Mechanics and Engineering Vol. 372, no. (2020), p.
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- Description: In this paper, an adaptive refinement technique using the scaled boundary finite element method (SBFEM) is proposed. The salient feature of this technique is that it is not required to regenerate the mesh for the whole model during the iterations. To this end, a local mesh refinement strategy is implemented based on a polytree algorithm in three dimensions, which can be applied to polyhedral elements with arbitrary number of nodes, edges and faces. These elements constructed by the SBFEM can be used in analysis with their boundaries discretized only, which reduce the difficulty to connect elements with different sizes. An explicit residual based error indicator is developed using the discontinuity of the stress field to guide the adaptive mesh refinement. The accuracy and efficiency of the proposed method are demonstrated using five numerical examples, including complex geometry and stress singularity. © 2020 Elsevier B.V.
- Description: The work presented in this paper is partially supported by the Australian Research Council through Grant Number DP180101538 .
A quadtree-polygon-based scaled boundary finite element method for image-based mesoscale fracture modelling in concrete
- 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.
A direct time-domain procedure for the seismic analysis of dam–foundation–reservoir systems using the scaled boundary finite element method
- Authors: Qu, Yanling , Chen, Denghong , Liu, Lei , Ooi, Ean Tat , Eisenträger, Sascha , Song, Chongmin
- Date: 2021
- Type: Text , Journal article
- Relation: Computers and Geotechnics Vol. 138, no. (2021), p.
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- Description: In this paper, a direct time-domain procedure for the seismic analysis of dam–reservoir–foundation interactions is presented based on the scaled boundary finite element method (SBFEM). The SBFEM is a semi-analytical method and requires the discretization of boundary only. The geometric complexity in the bounded dam–reservoir–foundation system is easily handled in the SBFEM using quadtree meshes where each structural component can be discretized independently. The elastic wave fields in the unbounded foundation are rigorously captured through SBFE solutions in terms of displacement unit-impulse response functions, while the acoustic wave propagation in the semi-infinite reservoir is modelled by the SBFE-based doubly asymptotic open boundary. The input of seismic excitations is addressed by incorporating the Domain Reduction Method (DRM) into the SBFEM. Cracks are modelled efficiently and accurately by combining the SBFEM and quadtree meshes. The accuracy and efficiency of the proposed methodology is investigated by studying several benchmarks, Pine Flat dam and Jin'anqiao dam. © 2021 Elsevier Ltd