Stability Of Rectangular Plates Research Articles

OPTIMAL SUPPORT POSITIONING OF A RECTANGULAR PLATE IN A STABILITY PROBLEM UNDER TEMPERATURE FIELD EXPOSURE

Introduction . Thin plates are widely used structural elements in modern civil, mechanical, aeronautical, and marine engineering design. Alongside the temperature field, the middle plain of plates is subjected to uniformly distributed normal mechanical forces, with σφ intensity, which raises the stability problem of thin plates. The strength and stability of rectangular plates have been investigated by S.P. Timoshenko [1], S.A. Ambartsumyan [2] and others. In the field of design of thin structure elements, the optimal positioning of plate supports has been studied in the works of V.Ts. Gnuni [3], M.V. Belubekyan [4], and A.V. Eloyan [5, 6]. However, the problem of optimal support positioning has not been sufficiently studied, particularly regarding the thermoelastic stability of thin plates. The simultaneous exposure of mechanical forces and temperature field on a rectangular plate poses the issue of an efficient parameter с that determines the positions of transverse supports along the length of a plate thus ensuring the maximum buckling load. Aim . To calculate the optimal values of a parameter α = c/a in accordance with σ̅, h̅, values for different side ratios λ=a/b of a plate for specified temperature values. Materials and methods . Elastic isotropic plates were used, the maximum buckling load was determined. Results and conclusions . According to the results, the optimal location of plate supports for values λ = a/b–1/2,1 is determined by σ̅ = 3 β depending on the plate temperature. The maximum buckling load is determined when σ̅ = 3 β , h̅ = 0,01, w* = 1,772, α = 0,37, Т = 300 °С.

Aeroelastic analysis of rectangular plates coupled to sloshing fluid

In this study, an aeroelastic model that accounts for the fluid–structure interaction is developed to investigate vibration and stability of rectangular plates in contact with sloshing fluid on one side and under supersonic aeroelastic load on the other side. The fifth-order shear deformation theory, which is capable of considering rotary inertia and transverse shear stress, is employed to model the structure. Bulging and sloshing modes of the incompressible, inviscid and irrotational fluid are obtained with satisfying Laplace’s equation and fluid boundary conditions. The first-order piston theory is applied to consider the supersonic aeroelastic load. On the basis of Hamilton’s principle, the governing equations of the coupled fluid–structure system are derived and discretized using the Galerkin method. Numerical results for specific cases are compared with available results in the literature and an excellent agreement is observed. In the discussion section, influences of various parameters such as the dimensions of the fluid domain, plate dimensions and aerodynamic parameters on the natural frequencies and flutter behavior are studied.

Stability of rectangular plates with notch using FEM

Buckling behaviour analysis of thin-walled composite plate under an axial compressive force is presented. The plate with central notch is made of a carbon-epoxy composite – a laminate consisting of eight symmetrically oriented plies. This paper addresses an influence of notch on buckling behaviour of laminated composite plates. In this analysis, FEM was applied to perform parametric studies on various plates based on stacking sequences, shape of notch, and its size. Buckling behaviour of laminated composite plates under an axial compression load is studied using ABAQUSS software.

Combination of patch and wheel loads: Analytical approach to plate buckling

Past studies on the stability of rectangular plates under the influence of variable loads were based on assumptions of simplified stress distributions, which put the question of the accuracy of results thus obtained. The procedure of applying the exact stress functions in the problem of elastic stability of the plate with different boundary conditions under effects of patch and wheel loading is presented in this paper. Mathieu (1890) obtained the exact solution for the plane-strain state for a rectangular element for certain types of variable stresses on the boundaries. Baker at al (1993), following Mathieu.s results, analyzed the general problem of a rectangular plate loaded by completely arbitrary distributions of (normal and/or shear) stresses along the edges of the plate. Analytical approach used for determination of the critical load is based on well known Ritz energy technique. The strain energy due to bending of the plate is defined in the traditional way. On the other hand, the exact stress distribution of Mathieu.s theory of elasticity is introduced through the potential energy of the plate associated with the work done by external loads. Results for the critical load obtained by presented analytical approach are reaffirmed by numerical finite-element (FE) runs.

Stability of rectangular plates made of a laminated composite with components subject to long-term damage

The problem of bifurcational instability of rectangular plates made of laminated composites with components subject to long-term damage is formulated and solved by the proposed method. Numerical results are presented

Stability of plates from a granular composite with physically nonlinear inclusions and a damageable matrix

We present formulation and solution of the problem on the bifurcational stability of rectangular plates from granular composites with a damageable matrix and physically nonlinear inclusions.

Localization of eigenforms and limit transformations in problems of the stability of rectangular plates

Problems of the stability (buckling) of compressed rectangular plates are considered. It is assumed that evenly distributed compressive forces are applied to the opposite hinged edges, while the remaining two edges are not fastened and are free from external actions. It is shown that an increase in the length ratio of the hinged and unfastened sides in close proximity to the free boundary results in the localization of eigenforms corresponding to the lowest eigenvalues.

Influence of variable thickness on stability of rectangular plate under compression

This paper analyzes the stability of the elastic rectangular thin plates with sinusoidal changes in the plate thickness. The buckling load is defined in a weighted residual approach for different boundary conditions. The influence of the plate thickness variation and the edge ratio on the critical loads is investigated. The results are compared to the case of uniform thickness.

Dynamic stability of rectangular plates subjected to pulsating follower forces

Dynamic stability of rectangular plates subjected to pulsating follower forces

Effect of Discrete Rib Arrangement on the Stability of Rectangular Plates Reinforced by Orthogonal Ribs

Two variants (basic and approximate) of the stability analysis of hinged rectangular plates reinforced by orthogonal ribs are proposed. The necessity of allowing for the discreteness in the arrangement of the ribs is revealed with the help of numerical examples in determining both the parameters of critical stresses and buckling wave mode. The approximate procedure is constructed on the assumption that the tangent components of the displacement components may not be taken into account in the stability analysis of plates. This procedure permits us to accurately determine the parameter of critical stresses in a wide range of parameters of the ribs

Influence of the Aspect Ratio on the Dynamic Stability and Nonlinear Response of Rectangular Plates

The dynamic stability and nonlinear response of simply-supported rectangular plates subjected to parametric excitation are investigated. The large-deflection plate theory used in the analysis is derived in terms of the stress function F and lateral displacement w and is applied to rectangular plates with stress-free supported edges and uniformly stressed loaded edges. General rectangular plates are considered, the aspect ratio of the plate being regarded as an additional parameter of the system. Calculations are carried out for rectangular plates of various aspect ratios, and the relative importance of the principal regions of parametric instability associated with the lower mode shapes is clarified. The stationary response of the system within a principal region of instability is also evaluated. The results obtained indicate that the aspect ratio plays a crucial role in determining the stability of rectangular plates; elongated plates are more susceptible to various parametric resonances than square plates.

Stability of rectangular plates with cambered bitrapezoidal cross sections

This paper presents a theoretical moment-curvature relationship for rectangular plates having bitrapezoidal cross sections. It is shown that, for certain values of the cross-section camber and edge thickness, the plates exhibit a bending instability for some values of longitudinal curvature. Experimental results show good agreement between theory and experiment.

Buckling of Rectangular Plates with One Unsupported Edge, Compressed by Forces Distributed Along its Edges

The elastic stability of rectangular plates compressed in two perpendicular directions by forces uniformly distributed along the edges is considered. Edges x = 0 and x = a are simply supported, edge y = 0 is free and edge y = b is rigidly built-in (Fig. 1). Using the method described in a previous paper, after satisfying the boundary conditions at the edges of plate, the following transcendental equation is obtained:

Stability of Rectangular Plates Under Shear and Bending Forces

Abstract The author first discusses the problem of a plane, simply supported rectangular plate loaded by shearing forces in the plane of the plate on all four edges. There are two stiffeners attached one third and two thirds of the way along the plate. The critical load is calculated for various stiffener rigidities. Also, the rigidity necessary to keep the stiffeners straight when the plate buckles is found. This stiffener rigidity is found to be slightly larger than that necessary for a plate with one stiffener and the same panel dimensions as the plate with two stiffeners. The second problem discussed by the author is that of a plane, simply supported rectangular plate loaded by uniformly distributed edge shearing forces in the plane of the plate and linearly distributed tension and compression in the plane of the plate at the ends. The end forces vary from tension hσo, at one corner to—hσo, at the other corner, so that their resultant is a bending moment. The presence of the edge shearing forces is found to diminish the critical bending stress in this case. Calculations are made for various magnitudes of bending and shearing forces for plates of various proportions.