Robust modelling of implicit interfaces by the scaled boundary finite element method
- Authors: Dsouza, Shaima , Pramod, A. L. N. , Ooi, Ean Tat , Song, Chongming , Natarajan, Sundararajan
- Date: 2021
- Type: Text , Journal article
- Relation: Engineering Analysis with Boundary Elements Vol. 124, no. (2021), p. 266-286
- Full Text: false
- Reviewed:
- Description: In this paper, we propose a robust framework based on the scaled boundary finite element method to model implicit interfaces in two-dimensional differential equations in nonhomegeneous media. The salient features of the proposed work are: (a) interfaces can be implicitly defined and need not conform to the background mesh; (b) Dirichlet boundary conditions can be imposed directly along the interface; (c) does not require special numerical integration technique to compute the bilinear and the linear forms and (d) can work with an efficient local mesh refinement using hierarchical background meshes. Numerical examples involving straight interface, circular interface and moving interface problems are solved to validate the proposed technique. Further, the presented technique is compared with conforming finite element method in terms of accuracy and convergence. From the numerical studies, it is seen that the proposed framework yields solutions whose error is O(h2) in L2 norm and O(h) in the H1 semi-norm. Further the condition number increases with the mesh size similar to the FEM. © 2021 Elsevier Ltd
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. Online first, no. 192 (2015), p. 87-105
- Full Text: false
- Reviewed:
- 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.
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
- Full Text: false
- Reviewed:
- 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.
Seismic response of non-structural components attached to reinforced concrete structures with different eccentricity ratios
- Authors: Aldeka, Ayad , Dirar, Samir , Chan, Andrew , Martinez-Vazquez, Pedro
- Date: 2015
- Type: Text , Journal article
- Relation: Earthquake and Structures Vol. 8, no. 5 (2015), p. 1069-1089
- Full Text: false
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- Description: This paper presents average numerical results of 2128 nonlinear dynamic finite element (FE) analyses of lightweight acceleration-sensitive non-structural components (NSCs) attached to the floors of one-bay three-storey reinforced concrete (RC) primary structures (P-structures) with different eccentricity ratios. The investigated parameters include the NSC to P-structure vibration period ratio, peak ground acceleration, P-structure eccentricity ratio, and NSC damping ratio. Appropriate constitutive relationships were used to model the behaviour of the RC P-structures. The NSCs were modelled as vertical cantilevers fixed at their bases with masses on the free ends and varying lengths so as to match the vibration periods of the P-structures. Full dynamic interaction was considered between the NSCs and P-structures. A set of seven natural bi-directional ground motions were used to evaluate the seismic response of the NSCs. The numerical results show that the acceleration response of the NSCs depends on the investigated parameters. The accelerations of the NSCs attached to the flexible sides of the P-structures increased with the increase in peak ground acceleration and P-structure eccentricity ratio but decreased with the increase in NSC damping ratio. Comparison between the FE results and Eurocode 8 (EC8) predictions suggests that, under tuned conditions, EC8 provisions underestimate the seismic response of the NSCs mounted on the flexible sides of the plan-irregular RC P-structures. © 2015 Techno-Press, Ltd.
Dynamic cohesive crack propagation modelling using the scaled boundary finite element method
- Authors: Ooi, Ean Tat , Yang, Zhenjun , Guo, Zaoyang
- Date: 2012
- Type: Text , Journal article
- Relation: Fatigue and Fracture of Engineering Materials and Structures Vol. 35, no. 8 (2012), p. 786-800
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- Description: This study develops a scaled boundary finite element method (SBFEM)-based approach for modelling fast cohesive crack propagation in quasi-brittle materials subjected to transient dynamic loadings. In this approach, the elastic bulk material is modelled by SBFEM subdomains and the cracks by nonlinear cohesive interface finite elements that are automatically inserted by a remeshing procedure. The global equation system is solved using an implicit time integration algorithm. Because all the solutions (displacements, stresses, velocities, accelerations) are semi-analytical in an SBFEM subdomain, this approach offers a few advantages over other methods, such as accurate calculation of dynamic stress intensity factors and T-stress without using fine crack-tip meshes, simpler remeshing, more accurate and efficient mesh mapping, and the need of much fewer degrees of freedom for the same accuracy. The approach is validated by modelling two concrete beams under impact, subjected to mode-I and mixed-mode fracture, respectively. © 2012 Blackwell Publishing Ltd.
A comprehensive method for analyzing the effect of geotextile layers on embankment stability
- Authors: Tolooiyan, Ali , Abustan, Ismail , Selamat, Mohamad , Ghaffari, Sh
- Date: 2009
- Type: Text , Journal article
- Relation: Geotextiles and Geomembranes Vol. 27, no. 5 (2009), p. 399-405
- Full Text: false
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- Description: Commercial software is used widely in slope stability analyses of reinforced embankments. Almost all of these programs consider the tensile strength of geotextiles and soil-geotextile interface friction. However, currently available commercial software generally does not consider the drainage function of nonwoven geotextile reinforcement. In this paper, a reinforced channel embankment reinforced by a nonwoven geotextile is analyzed using two methods. The first method only considers the tensile strength and soil-geotextile interface friction. The second method also considers the drainage function. In both cases, the reinforced embankment is modeled in rapid drawdown condition since this is one of the most important conditions with regard to stability of channel embankments. It is shown that for this type of application, modeling a nonwoven geotextile reinforced embankment using commercial software which neglects the drainage function of the geotextile may be unrealistic.