Shear buckling of ship structures rectangular elements

Abstract

In the work to determine the spectrum of critical loads and the corresponding forms of a rectangular clamped panel (plate) buckling under the action of balanced tangential forces on its contour, the Bubnov-Galerkin method using polynomials in two coordinates is proposed. This problem of the ship skin element pure shift does not have an exact closed solution, and the known approximate solutions require an analysis of their accuracy and reliability. The aim of the work is to obtain and analyze analytical solutions using polynomials of various degrees. Approximating deflection functions satisfying all the boundary conditions of the problem are represented sequentially by polynomials of 10^th, 12^th, 14^th, 16^th and 18^th degrees in two coordinates with undefined coefficients. The solution of the main differential equation of the problem is found approximately in the integral sense, as a result of which homogeneous systems of linear algebraic equations with respect to unknown coefficients of polynomials are obtained. These systems contain a shear load as a parameter. To obtain eigenvalues (critical loads), the determinants of the systems are equated to zero. Numerical results are obtained in the Maple analytical computing system. For each approximation (polynomial), a power equation with respect to the critical load, the solution of which is paired values differing in signs is obtained. The forms of buckling are oblique waves. For a ship skin square panel, the first form of buckling is a single bulge along the diagonal of the panel. The second form is obtained in the form of two bulges directed in opposite directions (symmetrically-antisymmetrically with respect to the diagonals), etc. The numerical results are compared with the results of other authors. It is established that with an increase in the number of the polynomial terms, the initial critical loads and forms of buckling are specified, first of all.