Numerical and Analytical Investigation of Stability of the Reinforced Plate

2021 ◽  
Vol 23 (4) ◽  
pp. B278-B287
Author(s):  
Gaik A. Manuylov ◽  
Sergey B. Kositsyn ◽  
Irina E. Grudtsyna
Keyword(s):  
Potential Energy ◽  
Nonlinear Analysis ◽  
Critical Points ◽  
Analytical Investigation ◽  
Equilibrium States ◽  
Stress Fields ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Initial Imperfections ◽  
Reinforced Plate

The work is aimed at the construction of an algorithm for studying the equilibrium states of a reinforced plate near critical points, using the first (cubic terms) nonlinear terms of the potential energy expansion. Using geometrically nonlinear analysis of displacement, deformation and stress fields, the Eigenforms of buckling were calculated and bifurcation solutions and solutions for equilibrium curves with limit points were constructed depending on the initial imperfections.

scholarly journals Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

2021 ◽  
Vol 17 (1) ◽  
pp. 3-18
Author(s):  
Gaik A. Manuylov ◽  
Sergey B. Kositsyn ◽  
Irina E. Grudtsyna
Keyword(s):  
Numerical Solution ◽  
Nonlinear Analysis ◽  
Critical Loads ◽  
Wave Formation ◽  
Geometrically Nonlinear ◽  
Stiffened Plate ◽  
Geometrically Nonlinear Analysis ◽  
Initial Imperfections ◽  
Bifurcation Points ◽  
Limit Points

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.

Geometrically Nonlinear Analysis in the Vicinity of Critical Points by the Generalized Inverse

1989 ◽  
Vol 4 (4) ◽  
pp. 181-191 ◽  
Author(s):  
Yasuhiko Hangai ◽  
Xiao-Guang Lin
Keyword(s):  
Nonlinear Analysis ◽  
Critical Points ◽  
Bifurcation Point ◽  
Limit Point ◽  
Analytical Method ◽  
Generalized Inverse ◽  
Equilibrium Path ◽  
Geometrically Nonlinear ◽  
Equilibrium Equations ◽  
Geometrically Nonlinear Analysis

In the geometrically nonlinear analysis for equilibrium paths, the determinant of the tangent stiffness matrix at the critical point becomes zero so that a numerically unstable situation appears in the vicinity of critical points. To avoid such a situation, many numerical methods including the arc-length method and the perturbation method have been developed. In this paper, an analytical method to pursue the geometrically nonlinear equilibrium paths in the vicinity of critical points such as limit point and bifurcation point is presented by using the generalized inverse. In the first part, the perturbation equations for the incremental equilibrium equations are derived. Then, critical points on the equilibrium path are classified into limit point and bifurcation point by using the existence condition of solution. In the second part, an analytical method for post-critical paths beyond critical points is presented by means of the generalized inverse. In the final part, the application of the present method to the post-buckling analysis of a shallow arch and cable domes subjected to the symmetrical loads is shown.

Sign in / Sign up

Export Citation Format

Share Document