CALCULATED RELATIONS OF THE SEMI-ANALYTICAL FINITE ELEMENT METHOD OF PRISMATIC BODIES FOR A FINITE ELEMENT BASED ON THE REPRESENTATION OF DIS-PLACEMENTS BY POLYNOMIALS

Abstract

In article [8, 10], a variant of the semi-analytical finite element method for the calculation of prismatic bodies was developed using the Fourier series function as a coordinate system. The use of trigonometric series ensures maximum efficiency of the semi-analytical finite element method, however, at the ends of the body it is possible to satisfy only the boundary conditions corresponding to the support of the object on an absolutely rigid in its plane and flexible diaphragm. As a result of the performed researches the basis of representation of movements by polynomials is received that allows to expand considerably a range of boundary conditions on end faces of a body. In this case, it is not possible to reduce the solution of the original spatial boundary value problem to a sequence of two-dimensional problems, so a reasonable choice of appropriate polynomials becomes especially important. Their correct choice depends on the conditionality of the matrix of the system of separate equations and, consequently, the convergence of integration algorithms for its solution, and the universality of the approach to the possibility of satisfying different variants of boundary conditions at the ends of the body.