Multiple isoparametric finite element method for nonhomogeneous media

Li, Chunyu; Zou, Zhenwei; Zhang, Duan

doi:10.1016/s0093-6413(00)00073-2

Cited by 28 publications

(10 citation statements)

References 5 publications

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“…͑24͒ requires derivatives at element integration points of the compliance-and constitutive-tensor components. We interpolate specified nodal material properties E͑x͒ and ͑x͒ and compute their X 1 -derivatives at integration points using standard isoparametric interpolation ͑e.g., Li et al 2000; Kim and Paulino 2002b͒:…”

Section: Computation Of Material-property Derivativesmentioning

confidence: 99%

Computation of Mixed-Mode Stress Intensity Factors for Cracks in Three-Dimensional Functionally Graded Solids

2006

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This work applies a two-state interaction integral to obtain stress intensity factors along cracks in three-dimensional functionally graded materials. The procedures are applicable to planar cracks with curved fronts under mechanical loading, including crack-face tractions. Interaction-integral terms necessary to capture the effects of material nonhomogeneity are identical in form to terms that arise due to crack-front curvature. A discussion reviews the origin and effects of these terms, and an approximate interaction-integral expression that omits terms arising due to curvature is used in this work to compute stress intensity factors. The selection of terms is driven by requirements imposed by material nonhomogeneity in conjunction with appropriate mesh discretization along the crack front. Aspects of the numerical implementation with ͑isoparametric͒ graded finite elements are addressed, and examples demonstrate the accuracy of the proposed method.

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Section: Computation Of Material-property Derivativesmentioning

confidence: 99%

Computation of Mixed-Mode Stress Intensity Factors for Cracks in Three-Dimensional Functionally Graded Solids

2006

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“…The term homogeneous element here describes an element with all integration points assigned a common property value; the term graded element here describes an element with integration points that may have different property values. Many researchers, including Williamson and Rabin (1992), Lee and Erdogan (1995), Anlas et al (2000), Li et al (2000), Santare and Lambros (2000), Bruck and Gershon (2002), and Kim and Paulino (2002c) apply homogeneous and graded elements to model uncracked FGMs. With increasing mesh refinement, solutions generated with homogeneous and graded elements converge at a rate dependent upon the severity of material gradients and the quadrature schemes (Kim and Paulino, 2002c).…”

Section: Finite Element Analysis Including Graded Materials Propertiesmentioning

confidence: 99%

“…With analyst-specified nodal values for the properties, interpolation using element shape functions determines property values at integration points. For its generality and accuracy (Li et al, 2000;Kim and Paulino, 2002c), the current study employs the nodal-values approach.…”

Section: Finite Element Analysis Including Graded Materials Propertiesmentioning

confidence: 99%

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

Walters

Paulino

Dodds

2004

International Journal of Solids and Structures

140

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“…where = ln ( / )/ln (r /r ) Here Ei and Eo denote the modulus of elasticity of the inner and outer surfaces, respectively [27]. It has been shown that using continuously varying properties of inhomogeneous materials in iso-parametric Finite Element formulation does not cause any computational issue [15].…”

Section: Problem Formulationmentioning

confidence: 99%

Speeding up the Stress Analysis of Hollow Circular FGM Cylinders by Parallel Finite Element Method

Gharebaghi

Niknam

2019

NMCE

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In this article, a parallel computer program is implemented, based on Finite Element Method, to speed up the analysis of hollow circular cylinders, made from Functionally Graded Materials (FGMs). FGMs are inhomogeneous materials, which their composition gradually varies over volume. In parallel processing, an algorithm is first divided to independent tasks, which may use individual or shared data. Such tasks could be simultaneously executed. In this paper, a parallel Finite Element software is developed to perform the analysis on a multiprocessor system. The software parallelizes every time-consuming task of the algorithm, if possible. As an application, the analysis of a thick hollow cylinder, made from FGM, is performed to evaluate the capability of the software. The results show not only the software is authoritative of analyzing large-scale problems, but also it is 2.4 times faster than the serial version. Although such speedup is achieved using eight processors, the number of processors could be increased utilizing computer networks. According to the results, it could be concluded that the speedup increases when the number of processors increases. However, because of some technical limits and overheads such as data traffic among the processors, the speedup approaches its maximum for a certain number of processors.

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Multiple isoparametric finite element method for nonhomogeneous media

Cited by 28 publications

References 5 publications

Computation of Mixed-Mode Stress Intensity Factors for Cracks in Three-Dimensional Functionally Graded Solids

Computation of Mixed-Mode Stress Intensity Factors for Cracks in Three-Dimensional Functionally Graded Solids

Stress-intensity factors for surface cracks in functionally graded materials under mode-I thermomechanical loading

Speeding up the Stress Analysis of Hollow Circular FGM Cylinders by Parallel Finite Element Method

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