Geodesic
The outer layer method for solving boundary value problems of the elasticity theory
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 289-296

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This paper presents an algorithm for solving boundary value problems of the elasticity theory, suitable to solve contact problems and those whose scope of deformation contains thin layers of a medium. The solution is represented as a linear combination of subsidiary solutions and fundamental solutions to the Lame equations. Singular points of fundamental solutions of the Lame equations are located as an external layer of the deformation around the perimeter. Coefficients of the linear combination are determined by minimizing deviations of a linear combination from the boundary conditions. To minimize deviations, the conjugate gradient method is applied. Examples of calculations for mixed boundary conditions are presented. 
@article{SJVM_2017_20_3_a4,
     author = {V. I. Mashukov},
     title = {The outer layer method for solving boundary value problems of the elasticity theory},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {289--296},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a4/}
}
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V. I. Mashukov. The outer layer method for solving boundary value problems of the elasticity theory. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 20 (2017) no. 3, pp. 289-296. http://geodesic.mathdoc.fr/item/SJVM_2017_20_3_a4/