A Reduction Method for Buckling Problems of Orthotropic Plates

1957 ◽  
Vol 8 (2) ◽  
pp. 145-156 ◽  
Author(s):  
P. Shuleshko
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Reduction Method ◽  
Isotropic Plate ◽  
Axial Loading ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Plate Buckling

SummarySeveral plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

Investigation of Vibration and Thermal Buckling of Nanobeams Embedded in An Elastic Medium Under Various Boundary Conditions

2015 ◽  
Vol 32 (3) ◽  
pp. 277-287 ◽  
Author(s):  
D. S. Mashat ◽  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Thermal Buckling ◽  
Governing Equations ◽  
Linear Temperature ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Dynamic Version ◽  
Beam Theories

AbstractAnalyses of free vibration and thermal buckling of nanobeams using nonlocal shear deformation beam theories under various boundary conditions are precisely illustrated. The present beam is restricted by vertically distributed identical springs at the top and bottom surfaces of the beam. The equations of motion are derived using the dynamic version of Hamilton's principle. The governing equations are solved analytically when the edges of the beam are simply supported, clamped or free. Thermal buckling solution is formulated for two types of temperature change through the thickness of the beam: Uniform and linear temperature rise. To validate the accuracy of the results of the present analysis, the results are compared, as possible, with solutions found in the literature. Furthermore, the influences of nonlocal coefficient, stiffness of Winkler springs and span-to-thickness ratio on the frequencies and thermal buckling of the embedded nanobeams are examined.

Vibration of a Fluid Conveying Pipe Carrying a Discrete Mass

1974 ◽  
Vol 96 (4) ◽  
pp. 268-272 ◽  
Author(s):  
T. T. Wu ◽  
P. P. Raju
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
General Expression ◽  
Normal Modes ◽  
Critical Value ◽  
Numerical Results ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Discrete Mass

This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

Vibration of Stiffened Plates

1964 ◽  
Vol 15 (3) ◽  
pp. 285-298 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
General Procedure ◽  
The Other ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions

SummaryThis paper presents a general procedure for calculating the natural frequencies of rectangular plates continuous over identical and equally spaced elastic beams which are simply-supported at their ends. Arbitrary boundary conditions are permissible on the other two edges of the plate. The results are compared with those obtained by using the orthotropic plate approximation for the system

On the Deflection of Rectangular Orthotropic Plates Under Lateral Loads

1964 ◽  
Vol 68 (643) ◽  
pp. 483-484
Author(s):  
N. R. Rajappa
Keyword(s):  
Isotropic Plate ◽  
The Other ◽  
Rectangular Plates ◽  
Lateral Loads ◽  
Orthotropic Plates ◽  
Characteristic Equations ◽  
Simply Supported ◽  
Elastically Restrained ◽  
Two Sides

Recently the use of Maclaurin’s series was illustrated for the analysis of orthotropic plates. Formulae connecting the deflection of orthotropic plates to that of the corresponding isotropic plate are established here, thus eliminating the need for solving the characteristic equations of orthotropic plates. Rectangular plates with two opposite sides simply-supported and one of the other two sides elastically restrained against rotation are considered.

scholarly journals Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

1998 ◽  
Vol 5 (5-6) ◽  
pp. 343-354 ◽  
Author(s):  
T.Y. Ng ◽  
K.Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Axial Loading ◽  
Various Boundary Conditions ◽  
Transverse Modes ◽  
First Approximation ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Parametric Response

In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

scholarly journals Nonlocal FEM Formulation for Vibration Analysis of Nanowires on Elastic Matrix with Different Materials

2019 ◽  
Vol 24 (2) ◽  
pp. 38 ◽  
Author(s):  
Büşra Uzun ◽  
Ömer Civalek
Keyword(s):  
Boundary Conditions ◽  
Nonlocal Elasticity Theory ◽  
Silver Nanowire ◽  
Small Scale ◽  
Weighted Residual Method ◽  
Simply Supported ◽  
Scale Parameters ◽  
Various Boundary Conditions ◽  
Winkler Elastic Foundation ◽  
Foundation Model

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW) are modeled as Euler–Bernoulli nanobeams with various boundary conditions such as simply supported (S-S), clamped simply supported (C-S), clamped–clamped (C-C), and clamped-free (C-F). The interactions between nanowires and medium are simulated by the Winkler elastic foundation model. The Galerkin weighted residual method is applied to the governing equations to gain stiffness and mass matrices. The results are given by tables and graphs. The effects of small-scale parameters, boundary conditions, and foundation parameters on frequencies are examined in detail. In addition, the influence of temperature change on the vibrational responses of the nanowires are also pursued as a case study.

scholarly journals Buckling Stability Assessment of Plates with Various Boundary Conditions Under Normal and Shear Stresses

2017 ◽  
Vol 7 (5) ◽  
pp. 2056-2061
Author(s):  
F. Riahi ◽  
A. Behravesh ◽  
M. Yousefzadeh Fard ◽  
A. Armaghani
Keyword(s):  
Boundary Conditions ◽  
Slenderness Ratio ◽  
Shear Stresses ◽  
Nonlinear Buckling ◽  
Various Boundary Conditions ◽  
Plate Buckling ◽  
Buckling Behavior ◽  
Buckling Stability ◽  
Plate Aspect Ratio ◽  
Normal And Shear Stresses

In the present paper, the buckling behavior of plates subjected to shear and edge compression is investigated. The effects of the thickness, slenderness ratio and plate aspect ratio are investigated numerically. Effects of boundary conditions and loadings are also studied by considering different types of supports and loading. Finally, the results of numerical methods are compared with the theoretical results. This work mainly investigates the buckling behavior of plates but also the capabilities of program of plate-buckling (PPB) and ABAQUS for performing linear and nonlinear buckling analyses. The results will be useful for engineers designing walls or plates that have to support intermediate floors/loads.

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