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.
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.
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 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.