Polar-symmetric problem of elastic diffusion for isotropic multi-component plane

11th International Conference on "Mesh methods for boundary-value problems and applications"

Zemskov, A.V.^1 ; Tarlakovskii, D.V.^2

Moscow Aviation Institute, Moscow, Russia^1

Institute of Mechanics Lomonosov, Moscow State University, Moscow, Russia^2

关键词: Connected systems;    Equation of motion;    Hankel's transform;    Inverse Laplace transform;    Polar coordinate systems;    Quadrature formula;    Radial coordinates;    Stress-strain condition;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012101/pdf
DOI  :  10.1088/1757-899X/158/1/012101

来源: IOP

【 摘 要 】

The paper considers a polar-symmetric problem of finding a stress strain condition of a plane influenced by non-stationary volume elastic diffusion disturbances. The mathematical model is based on a connected system of equations of elastic diffusion in a polar coordinate system. The solution of the problem is sought in an integral for and presented in the form of convolutions of Green's function with the right side of equation of motion and mass transfer. Laplace time and Hankel's radial coordinate transformations are used to find the Green's functions. The inverse Laplace transform is done analytically by residue. The inverse Hankel's transform is done numerically by quadrature formulas.