Abstract
The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.
Highlights
Интерес к работе сжатых подкрепленных пластин появился давно, однако только начиная с работ В.Т
Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections
An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points
Summary
Рассматривается шарнирно-опертая по торцам пластина, подкрепленная с одной стороны регулярным набором тонких прямоугольных ребер. Это позволяет исследовать устойчивость подкрепленной пластины при помощи анализа равновесия одного регулярного Т-образного фрагмента U σ L U ,U , где σ – тензор напряжений из решения линейной задачи равновесия пластины; σ – добавка при переходе в смежное равновесное состояние в случае бифуркационной потери устойчивости. В уравнения (9) и (10) входят значения критических параметров λ и λ , соответствующих общей форме изгиба и местному волнообразованию в пластине или ребрах. Эти величины находятся из решения линейной задачи на собственные значения. Если в правой части уравнения (12) стоит ноль, а в правой части уравнения (11) имеется несовершенство ξ 0 , пропорциональное параметру нагрузки, то бифуркационная задача реализуется как поиск критического значения нагрузки, при которой пластина с развивающимся начальным общим прогибом теряет устойчивость в виде волнообразования в пластине или в ребрах
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