Оценка наибольшего собственного числа глобальной матрицы жесткости регулярной сетки

Abstract

The paper deals with condition of global stiffness matrices of regular mesh of finite elements. The estimation from above the greatest eigenvalue of such matrix offeres. The estimation is under construction on a local stiffness matrix of any finite element, hence, depends only from the size and the form of such element and does not depend on quantity of the final elements making a regular grid. At estimation construction the Gerschgorin’s theorem and that fact are used that local matrixes of rigidity of final elements of regular grids differ from each other only shift of blocks. On a numerical example it is shown that the constructed estimation possesses split-hair accuracy and at a considerable quantity of the elements entering into a grid, it is possible to consider it almost coinciding with the greatest own number. The behaviour of an estimation is shown at change of quality of the form of final elements.