Boundary integral based graded element for elastic analysis of 2D functionally graded plates

Wang, Hui; Qin, Qing Hua

doi:10.1016/j.euromechsol.2011.10.005

Cited by 38 publications

(13 citation statements)

References 23 publications

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“…As an alternative to the FEM/FDM and BEM, a new hybrid¯nite element approach, which is based on fundamental solutions, has been developed recently 18,19 and applied to heat transfer analysis in the human eye, 20 plane elastic problems in homogeneous 21,22 and heterogeneous media, 23 heat transfer analysis in¯ber-composites, 24 and nonlinear Poisson-type problems. 25 The hybrid¯nite element model mentioned above was referred to as HFS-FEM to distinguish it from other numerical algorithms, due to the use of fundamental solutions.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, it is versatile in generating multi-node elements and special purposed elements. 21,23,24 The satisfaction of the governing equations for the interior¯elds makes it possible to convert element domain integrals that appear in the hybrid variational functional into element boundary integrals. In addition, as the material de¯nition can be prescribed over element level, it is easy to apply the developed approach to multi-material problems such as the multi-layer skin tissues used in this study.…”

Section: Introductionmentioning

confidence: 99%

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A Fundamental Solution-Based Finite Element Model for Analyzing Multi-Layer Skin Burn Injury

Wang

Qin

2012

J. Mech. Med. Biol.

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To understand the physiology of tissue burns for successful clinical treatment, it is important to investigate the thermal behavior of human skin tissue subjected to heat injury. In this paper, a fundamental solution-based hybrid¯nite element formulation is proposed for numerically simulating steady-state temperature distribution inside a multilayer human skin tissue during burning. In the present approach, since only element boundary integrals are involved, the computational dimension is reduced by one as the fundamental solutions used analytically satis¯es the bioheat governing equation. Further, in multi-layer skin modeling, the burn is applied via a heating disk at constant temperature on a part of the epidermal surface of the skin tissue. Numerical results from the proposed approach are¯rstly veri¯ed by comparing them with exact solutions of a simple single-layered model or the results from conventional¯nite element method. Thereafter, a sensitivity analysis is carried out to reveal the e®ect of biological and environmental parameters on temperature distribution inside the skin tissue subjected to heat injury.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Fundamental Solution-Based Finite Element Model for Analyzing Multi-Layer Skin Burn Injury

Wang

Qin

2012

J. Mech. Med. Biol.

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“…As an alternative to HT-FEM, a novel hybrid finite formulation based on the fundamental solutions, called HFS-FEM, was developed for solving two-dimensional linear heat conduction problems (Wang and Qin 2009;Wang and Qin 2011a), and isotropic elastic (Wang and Qin 2011a), functionally graded elastic (Wang and Qin 2012) and piezoelectric problems (Cao et al 2012). In the approach, a linear combination of the fundamental solution at different source points located outside of the elements is used to approximate the unknown field within the element instead of the truncated Tcomplete functions used in HT-FEM.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Effective Thermal Conductivity of Fiber-Reinforced Composites

Cao

Qin

2012

IJAEC

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In this paper, effective thermal conductivity of fiber-reinforced composites are estimated by the newly developed hybrid finite element method (FEM). In the hybrid FEM, foundational solutions are employed to approximate the intra-element displacement field in any given element, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. The homogenization procedures using the representative volume element are integrated with the hybrid fundamental solution based finite element method (HFS-FEM) to estimate the effective thermal conductivity of the composites and to investigate the effect of fiber volume fraction and fiber arrangement pattern on the effective thermal conductivity. A special element with an inclusion is constructed by means of related special fundamental solutions. Due to the fact that the proposed special element exactly satisfy its boundary conditions along the fibre-matrix interface, only element boundary integrals are involved and significant mesh reduction can be achieved. Mesh regeneration may be avoided as well when the fiber volume fraction is slightly changed. The accuracy of the numerical results obtained by the proposed method is verified against with that obtained from commercial software package ABAQUS. The results indicate that the proposed method is efficient and accurate in analyzing the micromechanical thermal behavior of fiber-composites and has the potential to be scaled up to macro-scale modeling of practical problems of interest.

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“…Using a Fourier transform technique, these functions have been derived for exponentially graded media. Although extensive works have been developed to effectively model the constitutive behavior of the FG structures, most of these researches have been limited to elastic behavior analysis (Gao et al 2008;Wang and Qin 2012;Ashrafi et al 2013aAshrafi et al , 2013b.…”

Section: Introductionmentioning

confidence: 99%

A numerical boundary integral equation analysis for standard linear viscoelastic media made of functionally graded materials

Ashrafi

Shariyat

2014

Int J Mech Mater Eng

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Background: Although structures made of functionally graded materials have been studied by many researchers, no research may be found in literature on boundary element analysis of the functionally graded viscoelastic structures. Methods: In the present paper, a 2D boundary element formulation capable of modeling time-dependent functionally graded materials (FGM) is presented. A numerical implementation of the Somigliana identity in terms of the displacements is developed to solve 2D problems of the exponentially graded viscoelasticity. The FGM concept can be applied to various materials, for structural and functional purposes. In this model, only Green functions of the nonhomogeneous elastostatic problems are needed with material properties that vary continuously along a given dimension. Results and Conclusions: Results reveal that the boundary element approach can successfully be employed for the present complicated problem for arbitrary time histories of the applied loads and arbitrary boundary conditions, without the need to use relaxation functions or mathematical transformations.

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Boundary integral based graded element for elastic analysis of 2D functionally graded plates

Cited by 38 publications

References 23 publications

A Fundamental Solution-Based Finite Element Model for Analyzing Multi-Layer Skin Burn Injury

A Fundamental Solution-Based Finite Element Model for Analyzing Multi-Layer Skin Burn Injury

Evaluation of Effective Thermal Conductivity of Fiber-Reinforced Composites

A numerical boundary integral equation analysis for standard linear viscoelastic media made of functionally graded materials

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