Computation of dynamic stress intensity factors in cracked functionally graded materials using scaled boundary polygons
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Date: 2014
- Type: Text , Journal article
- Relation: Engineering Fracture Mechanics Vol. 131, no. (2014), p. 210-231
- Full Text: false
- Reviewed:
- Description: In this paper, the recently developed scaled boundary polygons formulation for the evaluation of stress intensity factors in functionally graded materials is extended to elasto-dynamics. In this approach, the domain is discretized using polygons with arbitrary number of sides. Within each polygon, the scaled boundary polygon shape functions are used to interpolate the displacement field. For uncracked polygons, these shape functions are linearly complete. In a cracked polygon, the shape functions analytically model the stress singularity at the crack tip. Therefore, accurate dynamic stress intensity factors can be computed directly from their definitions. Only a single polygon is necessary to accurately compute the stress intensity factors. To model the material heterogeneity in functionally graded materials, the material gradients are approximated locally in each polygon using polynomial functions. This leads to semi-analytical expressions for both the stiffness and the mass matrices, which can be integrated straightforwardly. The versatility of the developed formulation is demonstrated by modeling five numerical examples involving cracked functionally graded specimens subjected to dynamic loads. © 2014 Elsevier Ltd.
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
- Full Text: false
- Reviewed:
- 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.
Scaled boundary polygons with application to fracture analysis of functionally graded materials
- Authors: Chiong, Irene , Ooi, Ean Tat , Song, Chongmin , Tin-Loi, Francis
- Type: Text , Journal article
- Relation: International Journal for Numerical Methods in Engineering Vol. 98, no. (2014), p.562-589
- Full Text: false
- Reviewed: