NODAL REACTIONS AND COEFFICIENTS OF THE STIFFNESS MATRIX OF A FINITE ELEMENT BASED ON THE REPRESENTATION OF DISPLACEMENTS BY POLYNOMIALS

Abstract

The study of prismatic bodies with constants along one of the coordinates of mechanical and geometric parameters is most appropriate to conduct on the basis of the semianalytical finite element method (NMSE). Its essence is a combination of finite element sampling and decomposition of displacements in the characteristic direction by a system of trigonometric coordinate functions.In [8, 15], a variant of the semivanalytic finite element method for the calculation of prismatic bodies when used as a system of coordinate functions of Fourier series was developed. The use of trigonometric series provides maximum efficiency of the semi-analytical finite element method, however, only the boundary conditions corresponding to the object's support on an absolutely rigid in its plane and flexible diaphragm can be satisfied at the ends of the body.As a result of the performed researches, the basis of the representation of displacements by polynomials is obtained, which allows to significantly expand the range of boundary conditions at the ends of the body. In this case, it isnot possible to reduce the solution of the initial spatial boundary value problem to a sequence of two-dimensional problems, so a reasonable choice of appropriate polynomials becomes especially important.Both 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 depend on their correct choice.In addition, the question of methods of integration in the calculation of the coefficients of the stiffness matrix of a finite element (CE), which is quite common, due to the significant complexity of this procedure.