Methods of fundamental solutions in the mechanics of thin-walled structures

We present the foundations of the method of fundamental solutions in the mechanics of thin-walled structures and consider basic procedures of modeling that enable one to reduce mechanical problems to systems of partial differential equations with Dirac delta-functions on the right-hand sides. A method used for the construction of fundamental solutions is described. As examples, we consider the problem of action of point heat sources in a spherical orthotropic shell and the force problem for orthotropic shells with holes. The results of numerical calculations are presented in the form of plots.