Analytical solution of a two-dimensional elastostatic problem of functionally graded materials via the Airy stress function

H. Sakurai
2011 Materials Characterisation V   unpublished
Functionally Graded Materials (FGMs) possess properties that vary gradually as a function of spatial coordinates. They are different from conventional composite materials in that they have no distinct interfaces at which their material properties change abruptly. These FGMs are suitable for various applications, such as aerospace, nuclear fusion, biomaterial electronics, etc. In practice, applications of analytical solutions are limited. However, the analytical solutions are very important as
more » ... very important as standards for evaluating numerical simulation results and they are also important to mathematical understanding. Little research on the analytical solutions of two-dimensional elastostatic problems has been reported. Furthermore, few analytical solutions using Airy stress functions have been published. The purpose of this paper is to propose an analytical method for the two-dimensional elastostatic problems of FGMs using the Airy stress function. In the present investigation, FGMs in which the properties of the materials vary exponentially in one direction are examined. A few numerical examples are presented and the validity of the method is shown by comparisons with the results of past studies.
doi:10.2495/mc110111 fatcat:i3oaojaq2zcfdmb4mxcvyitlua