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Fundamental Solution Based Graded Element Model for Steady-State Heat Transfer in FGM

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Abstract

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials (FGMs). The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the inter-element boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element (FE) model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional FEM and boundary element method (BEM). Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.

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Authors and Affiliations

  1. Key Laboratory for Highway Construction Technology and Equipment of Ministry of Education, Chang’an University, Xi’an, 710064, China

    Leilei Cao

  2. School of Engineering, Australian National University, Canberra, ACT, 0200, Australia

    Leilei Cao, Hui Wang & Qing-Hua Qin

  3. College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou, 450052, China

    Hui Wang

Authors
  1. Leilei Cao
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  2. Hui Wang
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  3. Qing-Hua Qin
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Corresponding author

Correspondence to Qing-Hua Qin.

Additional information

The research in this paper is partially supported by the Special Fund for Basic Scientific Research of Central Colleges, Chang’an University (Project No. CHD2011JC150) and the National Natural Science Foundation of China (No. 11102059).

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Cao, L., Wang, H. & Qin, QH. Fundamental Solution Based Graded Element Model for Steady-State Heat Transfer in FGM. Acta Mech. Solida Sin. 25, 377–392 (2012). https://doi.org/10.1016/S0894-9166(12)60034-2

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  • DOI: https://doi.org/10.1016/S0894-9166(12)60034-2

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