Asymmetric Green's functions for exponentially graded transversely isotropic substrate-coating system

作者：Akbari F; Khojasteh A^*; Rahimian M

来源：Journal of Central South University, 2018, 25(1): 169-184.

DOI：10.1007/s11771-018-3727-6

• functionally graded material
• transversely isotropic
• bi-material
• Green's function
• coating-substrate
• displacement potential

By virtue of a complete set of two displacement potentials, an analytical derivation of the elastostatic Green's functions of an exponentially graded transversely isotropic substrate-coating system is presented. Three-dimensional point-load and patch-load Green's functions for stresses and displacements are given in line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations, with utilizing Fourier series and Hankel transforms. As illustrations, the present Green's functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green's functions. Because of complicated integrand functions, the integrals are evaluated numerically and for numerical computation of the integrals, a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration. Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions. Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green's functions that the effect of degree of variation of material properties will be recognized.

• 出版日期2018-1