The solution of the plane problem of the theory of elasticity by the boundary elements method

摘要

An approach to solving the biharmonic equation of the plane problem of the theory of elasticity by the numerical-analytical method of boundary elements is developed. The reduction of the two-dimensional problem to the one-dimensional one was carried out by the KantorovichVlasov method. Systems of fundamental orthonormal functions and the Green function are constructed without any restrictions on the nature of the boundary conditions. A numerical example of solving a plane problem by the boundary element method for a rectangular plate is considered. The results are compared with the data of finite element analysis in the ANSYS program and those obtained by A.V. Aleksandrov.