Steady and transient Green's functions for anisotropic conduction in an exponentially graded solid

Hsin Yi Kuo, Tungyang Chen

研究成果: Article同行評審

41 引文 斯高帕斯(Scopus)


The problem of the determination of Green's function in conduction for a rectilinearly anisotropic solid with an exponential grading along a certain direction is studied. Domains of an unbounded space and a half-space, either three-dimensional or two-dimensional, are considered. Along the boundary of the domain, homogeneous boundary conditions of the first and second kinds are imposed. We find interestingly that, under this specific type of grading, the Green's functions permit an algebraic decomposition, which will in turn greatly simplify the formulation. The method of Fourier transform is employed for the Green's function for a half-space or a half-plane. Although the derivation process is quite tedious, we show analytically that the inverse transform can be found exactly and their resulting expressions are surprisingly neat and compact. In addition, both steady-state and transient-state field solutions are considered. By taking Laplace transform with respect to the time variable, we show that the mathematical frameworks for the steady-state and transient-state Green's functions are entirely analogous. Thereby, the transient-state Green's function is readily obtained by taking Laplace inverse transform back to the time domain. These derived fundamental solutions will serve as benchmark results for modeling some inhomogeneous materials. In the absence of grading term, we have verified analytically that our solutions agree exactly with previously known Green's functions for homogeneous media.

頁(從 - 到)1111-1128
期刊International Journal of Solids and Structures
出版狀態Published - 2005 2月

All Science Journal Classification (ASJC) codes

  • 建模與模擬
  • 材料科學(全部)
  • 凝聚態物理學
  • 材料力學
  • 機械工業
  • 應用數學


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