A SUPERPOSITION METHOD FOR SOLVING A PROBLEM OF AN ELASTIC ISOTROPIC PARALLELEPIPED
This article introduces an algorithm for calculating impacts (values) of transcendental diﬀerential operators of the method of initial functions (MIF) in the Cartesian coordinate system for three-dimensional problems of the theory of elasticity on products of trigonometric functions. Using this algoritm three MIF solutions in the form of double trigonometric series of the corresponding coordinate variables with unknown coeﬃcients are built. Each of these solutions can satisfy arbitrary boundary conditions (power, kinematic, mixed) on the respective two opposite faces of the isotropic parallelepiped. The sum of these solutions in accordance with the method of superposition is a general solution for an elastic parallelepiped allowing to satisfy arbitrary boundary conditions on all its faces. A numerical-analytical solution for a particular problem is obtained ﬁnding the unknown coeﬃcients in the general solution solving the system of linear algebraic equation which is formed satisfying the given boundary conditions. An analysis of bending of a thick isotropic plate clamped on its four side faces under an uniformly distributed load on the upper horizontal face is carried out. The comparison of the results of ﬁnite element modeling using ANSYS with the analytical solution received shows some problems in FEM analysis of stresses on the faces clamped. Bibliogr. 17. Il. 5.