Solving the problem of bending plate finite element method using splines of the 5th degree on the triangular grid

Abstract

Splines are involved in a large number of physical processes. Using splines for research biharmonic problem is widely used in practice, particularly in the study of the deflection plates. Many exact solutions have been developed for isotropic linear elastic thin plates; most of them can be found in the monographs Tymoshenko (Tymoshenko and Woinowsky-Krieger, 1959). In this paper we propose a scheme for solving biharmonic problem for a rectangular plate in the case of boundary conditions that match the conditions of rigid support plate in the form of a spline of the 5th degree, which provides an approximate solution of a class affiliation  These polynomials are not used previously for the biharmonic equation. The article was considered the application of the formulas for the construction of a polynomial of the fifth degree taken from [1] biharmonic problem. An experiment was conducted that compares the current solution with polynomials, which were obtained by the formulas [1] to the square area. As has been taken exact solutions formula (a) in work [3] on the field . The area was divided into two, four, eight triangles. The experiment showed greater than a partition area into triangles, the smaller the error.