2D static Green's function for an inhomogeneous elastic solid

作者：Watanabe Kazumi^*

来源：Zeitschrift fur Angewandte Mathematik und Mechanik, 2010, 90(2): 151-160.

DOI：10.1002/zamm.200900367

• Green's function
• inhomogeneity
• elastic solid
• exact solution

An exact closed form 2D Green's function for an inhomogeneous elastic solid is presented. Assuming a unidirectional exponential inhomogeneity, the Green's function is expressed in terms of the modified Bessel function of the second kind It is pointed out that the decomposition of the Green's function into the grading and non-grading terms is impossible in the sense of the closed form Solution. An exponential decay of the Green's function is also found at the far-field, although the logarithmic singularity at the far-field exists in the homogeneous 2D solid In addition, it is shown that a biaxial inhomogeneity can be reduced to the unidirectional inhomogeneity and the present Green's function covers both uni- and bi-axial inhomogeneities.

• 出版日期2010-2