Fundamental solution based graded element model for steady-state heat transfer in FGM

Date

2012

Authors

CAO, Leilei
Wang, Hui
Qin, Qing Hua

Journal Title

Journal ISSN

Volume Title

Publisher

Springer

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.

Description

Keywords

Keywords: Boundary integrals; Domain integrals; Finite element models; Fundamental solutions; Generalized elements; graded element; Graded materials; Hybrid FEM; Interpolation function; Linear combinations; Material property; Numerical accuracy; Numerical results; functionally graded materials; graded element; heat conduction; hybrid FEM

Citation

Source

Acta Mechanica Solida Sinica

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

DOI

10.1016/S0894-9166(12)60034-2

Restricted until