2014 , Volume 19, № 5, p.24-36

Purpose.This work is aimed at the development of a modified method of collocation and least residuals and its application to solution of problems in mechanics of multilayered composite plates. Methodology. The basic idea of the modified method of collocations and least residuals lies in reduction of the grid cells number due to the higher accuracy of approximation of the solution in a single cell. For example, in the case of a rectangular initial area it is sufficient to use only one cell which coincides with the whole area. Higher accuracy of the approximation is achieved by a special choice of the collocation points in the nodes of the Chebyshev polynomial along with the basis functions in the form of a multiplication of Lagrange polynomials.Findings. The problems of bending of rectangular orthotropic and anisotropic laminated plates under transverse loads of any kind are both considered and solved. Solutions are obtained within the classical Kirchhoff-Love's laminated plate theory, Tymoshenko's theory and the Grigolyuk-Chulkov's theory of a broken line. A comparison of the numerical solutions with known analytical solutions is carried out for the case of orthotropic and anisotropic plates within 3D theory of elasticity under the special fixing and load. It is shown that the calculated characteristics of the stress-strain state are in good agreement for all the four theories considered above for the case of thin and very thin laminated plates, so the simplified theory is allowed to solve practical problems.Originality/value. For plates of medium thickness and thick plates, Kirchhoff-Love theory and the theory of Timoshenko distort the nature of the distribution of stresses and displacements in layered structures, so application of a more accurate theory becomes necessary. The presented modified method of collocation and least residuals showed high efficiency for solution of bending of multilayered anisotropic plates problems applied to the canonical squared and rectangular forms. There is reason to believe that it would be no less effective in dealing with a wider class of problems in the mechanics of composite structures, including multi-layer shells.