Postbuckling Behavior of Rectangular Plates With Small Initial Curvature Loaded in Edge Compression—(continued)

1960 ◽  
Vol 27 (2) ◽  
pp. 335-342 ◽  
Author(s):  
Noboru Yamaki
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Ultimate Load ◽  
Numerical Solutions ◽  
Effective Width ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Shear Theory ◽  
Title Problem ◽  
Square Plate

In the previous paper [1], the title problem is theoretically treated under eight different boundary conditions and numerical solutions are obtained for the deflection, edge shortening, and effective width of the square plate in edgewise compression. As a continuation of this work, the stress state in the buckled plate is investigated and numerical results for the square plate are given graphically. Further the formulas for the ultimate load of the square plate in each case are derived by using the maximum-shear theory for the beginning of yielding and comparison is made with the previous results and experiments.

Postbuckling Behavior of Rectangular Plates With Small Initial Curvature Loaded in Edge Compression

1959 ◽  
Vol 26 (3) ◽  
pp. 407-414
Author(s):  
Noboru Yamaki
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Thin Plates ◽  
Large Deflections ◽  
Effective Width ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Initial Curvature ◽  
Special Cases ◽  
Fundamental Equations

Abstract The solution of Marguerre’s fundamental equations for large deflections of thin plates with slight initial curvature is presented for the case of a rectangular plate subjected to edge compression. The problem is solved under eight different boundary conditions, combining two kinds of loading conditions and four kinds of supporting conditions. Numerical solutions are obtained for square plates with and without initial deflection, and the connections of deflection, edge shortening, and effective width of the plate with applied loads are clarified. The solutions here obtained include as special cases those investigated by Levy and Coan.

Experiments on the Postbuckling Behavior of Square Plates Loaded in Edge Compression

1961 ◽  
Vol 28 (2) ◽  
pp. 238-244 ◽  
Author(s):  
Noboru Yamaki
Keyword(s):  
Boundary Conditions ◽  
Reasonable Agreement ◽  
Numerical Solutions ◽  
Experimental Results ◽  
Initial Deflection ◽  
Rectangular Plates ◽  
Maximum Deflection ◽  
Postbuckling Behavior ◽  
Different Boundary Conditions

In previous papers [1, 2], the postbuckling behavior of rectangular plates under edge compression has been studied theoretically under eight different boundary conditions, and numerical solutions are presented for square plates with and without initial deflection. To compare with these results, experiments were carried out by using aluminum square plates, and the relations of the maximum deflection, stresses, and strains at typical points in the plate with applied loads were determined under four different boundary conditions. It is found that the experimental results are in reasonable agreement with those theoretically predicted.

Thin Rectangular Plates on Elastic Foundation

1952 ◽  
Vol 19 (3) ◽  
pp. 361-368
Author(s):  
H. J. Fletcher ◽  
C. J. Thorne
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Numerical Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Transverse Loads ◽  
Sine Transform ◽  
Special Cases ◽  
Plates On Elastic Foundation

Abstract The deflection of a thin rectangular plate on an elastic foundation is given for the case in which two opposite edges have arbitrary but given deflections and moments. Six important cases of boundary conditions on the remaining two edges are treated. The solution is given for general transverse loads which are continuous in one direction and sectionally continuous in the other. By use of the sine transform the solution is obtained as a single trigonometric series. Numerical solutions are obtained for six special cases.

Three-dimensional static analysis of rectangular thick plates by using the meshless local Petrov—Galerkin method

2009 ◽  
Vol 223 (9) ◽  
pp. 1983-1996 ◽  
Author(s):  
R Vaghefi ◽  
G H Baradaran ◽  
H Koohkan
Keyword(s):  
Boundary Conditions ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
3D Analysis ◽  
Rectangular Plates ◽  
Weak Formulation ◽  
Heaviside Step Function ◽  
Thick Plates ◽  
Test Function ◽  
Aspect Ratios

In this article, a meshless local Petrov—Galerkin (MLPG) approach is developed for three-dimensional (3D) analysis of thick plates. Two different MLPG methods including MLPG1 and MLPG5 are employed to solve the elasto-static problems of thick plates. In MLPG1, a namely fourth-order spline function is considered as test function, while the Heaviside step function is employed as test function in MLPG5. Considering 3D equilibrium equations, the local symmetric weak forms are derived. The moving least-squares approximation is used to interpolate the solution variables and the penalty method is applied to impose the essential boundary conditions. In the present study, brick-shaped domains are chosen as local subdomains and support domains. The integrals appearing in the weak formulation are easily evaluated over brick-shaped subdomains and their boundaries. Considering the present approach, elasto-static deformations and stresses are analysed for thick rectangular plates with various boundary conditions and different aspect ratios. Excellent agreement is seen comparing the present results with the known analytical and numerical solutions in the literature.

scholarly journals A New Approach to the Analysis of Large Deflections of Plates

1955 ◽  
Vol 22 (4) ◽  
pp. 465-472
Author(s):  
H. M. Berger
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Flat Plate ◽  
Strain Energy ◽  
Numerical Solutions ◽  
Middle Surface ◽  
Large Deflections ◽  
Rectangular Plates ◽  
New Approach ◽  
Various Boundary Conditions

Abstract Simplified nonlinear equations for a flat plate with large deflections are derived by assuming that the strain energy due to the second invariant of the middle-surface strains can be neglected. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses for the circular plate and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.

EXPLICIT LOCAL BUCKLING ANALYSIS OF ROTATIONALLY- AND VERTICALLY-RESTRAINED ORTHOTROPIC PLATES UNDER UNIAXIAL COMPRESSION

2012 ◽  
Vol 12 (05) ◽  
pp. 1250038 ◽  
Author(s):  
XUPING HUO ◽  
PIZHONG QIAO
Keyword(s):  
Boundary Conditions ◽  
Uniaxial Compression ◽  
Numerical Solutions ◽  
Local Buckling ◽  
Potential Energy Function ◽  
Buckling Analysis ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Uniform Compression ◽  
Laminated Structures

In this paper, explicit local buckling analysis of orthotropic plates subjected to uniaxial compression with two loaded edges simply-supported and two unloaded edges supported by combined vertical and rotational restraining springs is presented. Based on the total potential energy function, the eigenvalue problem is formulated by treating the buckled shape functions as the admissible functions that satisfy the boundary conditions of the rectangular plates. Closed-form and approximate local buckling solutions of the combined rotationally- and vertically-restrained orthotropic plates, as well as explicit formulas for the critical buckling load and critical aspect ratio under the uniform compression, are obtained. By adjusting the stiffness of the rotational and vertical restraining springs, explicit local buckling solutions are established for eight simple cases of boundary conditions. To verify the explicit solutions, numerical analyses of orthotropic plates using the exact transcendental and finite element methods are conducted, for which reasonable agreement has been obtained between the explicit and numerical solutions, particularly for the simplified cases. The explicit solution obtained in this study can be used to facilitate the buckling analysis of composite laminated structures with different boundary conditions or joint connections as parts of stiffened and thin-walled structures by treating them as discrete plates with restrained boundary conditions.

scholarly journals Method of finite bodies for determination of the plane stressed state of rectangular plates with a rectangular hole

2019 ◽  
pp. 170-173
Author(s):  
V. P. Revenko
Keyword(s):  
Stress State ◽  
Quadratic Form ◽  
Boundary Conditions ◽  
Stressed State ◽  
Rectangular Plates ◽  
Rectangular Hole ◽  
Connected Surface ◽  
Ideal Contact ◽  
Finite Sum

The paper is devoted to the determination of the stress-deformed state of structurally heterogeneous bearing rectangular plates with a rectangular hole. The new analytical-numerical method (finite bodies) was used, to find the stress state of the plate with a hole. The method of finite bodies uses the conditional partition of the doubly-connected surface of the plate into simpler connected rectangular parts. On the lines of conditional contact, the conditions of ideal contact are taken into account, which ensure the equality of stresses, deformations and displacements. The perturbed stressed state, which is presented in the form of a series of functions, which is rapidly intercepted at a distance from the outline of the hole, is considered. A finite sum of solutions of a plane problem is used and the stress state of a perturbed state is given as a sum of a series for nonorthogonal functions. The components of vector of displacements and stresses are written. The determination of the coefficients of the sum of a series is based on the proposed method of satisfying all boundary conditions and the conditions of ideal contact to find the minimum of a generalized quadratic form. The numerical criterion for the convergence of the method is theoretically established. It is shown that the accuracy of satisfaction of boundary conditions and conditions of ideal contact is estimated by one number – the minimum of a generalized quadratic form.

Carrying capacity of edge-compressed rectangular plates

1980 ◽  
Vol 7 (1) ◽  
pp. 19-26
Author(s):  
A. N. Sherbourne ◽  
H. M. Haydl
Keyword(s):  
Carrying Capacity ◽  
Ultimate Load ◽  
Compressive Loading ◽  
Effective Width ◽  
Rectangular Plates ◽  
Rigid Plastic ◽  
Simply Supported ◽  
Elastic Loading ◽  
Special Case ◽  
Good Agreement

The carrying capacity of simply supported rectangular plates under uniaxial, in-plane compressive loading is investigated. The ultimate load is determined as the load corresponding to the intersection of an elastic loading line and a rigid–plastic unloading line. An attempt is made to formulate a plastic roof mechanism for the rectangular plate; the square buckle pattern mechanism for long plates is obtained as a special case. The effective width method is re-examined and is shown to give good agreement with experimental evidence. The recommendations of CSA S136-1974 are briefly reviewed in the light of the results obtained.

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

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