Displacement calculated analytically

[graba]

Dear users,

right now I am struggling with calculations of the displacement in the analytically way. I am trying to accomplish this with help of the Eshelby's work (Eshelby's tensor). Right now I have a problem with Green's function. Displacement is expressed by Green's function, it looks like this (please see attachment).
Now I need Your help, because I don't know how to express Green's function from above equation in Matlab. Can anybody explain the Green's function from the simplest mathematical way?

 

[Valerie Park]

Green's function from the equation is essentially a mathematical tool used to solve equations involving differential operators. It is a solution to a differential equation that satisfies certain conditions at two points, allowing for the solution of the equation for any value of a parameter in between those two points. The Green's function can be used to calculate the displacement at any point in a system from the known displacement and force distributions at other points in the system.