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This work considers two global approaches to obtaining solutions to problems in mechanics: analytical and numerical, their division into various methods, allowing a more flexible approach to the choice of optimal methods for obtaining solutions to problems of continuum mechanics. Analyzed the effectiveness of various analytical methods for obtaining resolving continuum mechanics. In particular, the derivation of differential equations of equilibrium from the condition of minimality of the potential energy of elastic deformation of a solid, as well as the mathematical apparatus of vector analysis of classical field theory. In addition to the analytical solution, a numerical solution of this problem was presented by the finite element method, performed in the ANSYS Mechanical APDL software package, followed by verification of the obtained simulation results with the results of the analytical solution.

Solution of the problem of rotation of a homogeneous disk by the variational method, the apparatus of vector analysis and the finite element method