Buckling of Short Cylinders Under Combined Loading

1978 ◽  
Vol 45 (3) ◽  
pp. 574-578 ◽  
Author(s):  
R. C. Tennyson ◽  
M. Booton ◽  
K. H. Chan
Keyword(s):  
Experimental Data ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Combined Loading ◽  
Circular Cylinders ◽  
Simply Supported ◽  
Interactive Behavior ◽  
Major Significance ◽  
Z Parameter ◽  
Simultaneous Loading

This report presents theoretical and experimental data on the buckling of short, homogeneous, isotropic circular cylinders subjected to simultaneous loading of axial compression and hydrostatic pressure. Of major significance is the drastic change from “concave” to “convex” interactive behavior as the Z parameter is decreased. This phenomenon is demonstrated for both clamped and simply supported boundary conditions.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Effects of Boundary Conditions and Initial Out-of-Roundness on the Strength of Thin-Walled Cylinders Subject to External Hydrostatic Pressure

1956 ◽  
Vol 23 (3) ◽  
pp. 351-358
Author(s):  
G. D. Galletly ◽  
R. Bart
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Semiempirical Methods ◽  
Test Results ◽  
External Hydrostatic Pressure ◽  
Simply Supported ◽  
Small Deflection ◽  
The Difference ◽  
Deflection Theory ◽  
Theoretical Results

Abstract Using classical small-deflection theory, an investigation was made of the effects of boundary conditions and initial out-of-roundness on the strength of cylinders subject to external hydrostatic pressure. The equations developed in this paper for initially out-of-round cylinders with clamped ends, and a slightly modified form of the equations previously derived by Bodner and Berks for simply supported ends, were applied to some actual test results obtained from nine steel cylinders which had been subjected to external hydrostatic pressure. Three semiempirical methods for determining the initial out-of-roundness of the cylinders also were investigated and these are described in the paper. The investigation indicates that if the initial out-of-roundness is determined in a manner similar to that suggested by Holt then the correlation between the experimental and theoretical results is quite good. The investigation also indicates that while the difference in collapse pressures for clamped-end and simply supported perfect cylinders may be quite considerable, this does not appear to be the case when initial out-of-roundnesses of a practical magnitude are considered.

Bending of a thin circular plate under hydrostatic pressure over a concentric ellipse

1959 ◽  
Vol 55 (1) ◽  
pp. 110-120 ◽  
Author(s):  
W. A. Bassali
Keyword(s):  
Exact Solution ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Circular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Simply Supported ◽  
Thin Circular Plate ◽  
Thin Plate Theory

ABSTRACTAn exact solution in finite terms is derived within the limitations of the classical thin-plate theory, for the problem of a thin circular plate acted upon normally by hydrostatic pressure distributed over the area of a concentric ellipse, and subject to boundary conditions covering the usual rigidly clamped and simply supported boundaries.

Vibrations of an Incompressible Linearly Elastic Plate Using Discontinuous Finite Element Basis Functions for Pressure

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Lisha Yuan ◽  
Romesh C. Batra
Keyword(s):  
Finite Element ◽  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Plate Theory ◽  
Mass Matrix ◽  
Basis Functions ◽  
Mode Shapes ◽  
Normal Strain ◽  
Simply Supported ◽  
Transverse Normal Strain

Abstract We numerically analyze, with the finite element method, free vibrations of incompressible rectangular plates under different boundary conditions with a third-order shear and normal deformable theory (TSNDT) derived by Batra. The displacements are taken as unknowns at the nodes of a 9-node quadrilateral element and the hydrostatic pressure at four interior nodes. The plate theory satisfies the incompressibility condition, and the basis functions satisfy the Babuska-Brezzi condition. Because of the singular mass matrix, Moler's QZ algorithm (also known as the generalized Schur decomposition) is used to solve the resulting eigenvalue problem. Computed results for simply supported, clamped, and clamped-free rectangular isotropic plates agree well with the corresponding analytical frequencies of simply supported plates and with those found using the commercial software, abaqus, for other edge conditions. In-plane modes of vibrations are clearly discerned from mode shapes of square plates of aspect ratio 1/8 for all three boundary conditions. The magnitude of the transverse normal strain at a point is found to equal the sum of the two axial strains implying that higher-order plate theories that assume null transverse normal strain will very likely not provide good solutions for plates made of rubberlike materials that are generally taken to be incompressible. We have also compared the presently computed through-the-thickness distributions of stresses and the hydrostatic pressure with those found using abaqus.

Stochastic model of nonideal mixer. Boundary conditions in batch system

1984 ◽  
Vol 49 (2) ◽  
pp. 490-505
Author(s):  
Vladimír Kudrna ◽  
Pavel Hasal ◽  
Jiří Vlček
Keyword(s):  
Experimental Data ◽  
Stochastic Model ◽  
Boundary Conditions ◽  
Closed System ◽  
Batch System ◽  
Ideal Mixer

The earlier proposed general approach for description of the non-ideal mixer is coupled with corresponding boundary conditions for the closed system. Some simplifications in this procedure result in relations which are in agreement with experimental data.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

Vibrational Analysis of a Single-Layered Nanoporous Graphene Membrane

NANO ◽  
2016 ◽  
Vol 11 (04) ◽  
pp. 1650043 ◽  
Author(s):  
Haw-Long Lee ◽  
Win-Jin Chang
Keyword(s):  
Boundary Conditions ◽  
Vibrational Analysis ◽  
Atomic Scale ◽  
Good Correspondence ◽  
Graphene Layers ◽  
Simply Supported ◽  
Vibrational Behavior ◽  
Fundamental Frequencies ◽  
Nanoporous Graphene ◽  
New Applications

In this study, we use the atomic-scale finite element method to investigate the vibrational behavior of the armchair- and zigzag-structured nanoporous graphene layers with simply supported-free-simply supported-free (SFSF) and clamped-free-free-free (CFFF) boundary conditions. The fundamental frequencies computed for the graphene layers without pores are compared with the results of previous studies. We observe very good correspondence of our results with that of the other studies in all the considered cases. For the armchair- and zigzag-structured nanoporous graphenes with SFSF and CFFF boundary conditions, the frequencies decrease with increasing porosity. When the positions of the pores are symmetric with respect to the center of the graphene, the frequency of the zigzag nanoporous graphene is higher than that of the armchair one. To the best of our knowledge, this is first study investigating the relation between the vibrational behavior and porosity of nanoporous graphene layers, which is essential for tuning the material/structural design and exploring new applications for nanoporous graphenes.

Natural Frequencies of Parallelogrammic Plates Using Characteristic Orthogonal Polynomials in Rayleigh-Ritz Method

1992 ◽  
Author(s):  
L. T. Lee ◽  
W. F. Pon
Keyword(s):  
Boundary Conditions ◽  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Energy Functional ◽  
Comprehensive Treatment ◽  
Energy Functionals ◽  
Simply Supported ◽  
Cartesian Coordinate

Abstract Natural frequencies of parallelogrammic plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generalted by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. The strain energy functional and kinetic energy functionals are transformed from Cartesian coordinate system to a skew coordinate system. The natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods with all four edges clamped boundary conditions and greet agreements are found between them. The natural frequencies for parallelogrammic plates with other boundary conditions, such as four edges simply supported, clamped-free and simply supported-free, are also obtained. This method is considered as a better and accurate comprehensive treatment for this type of problems.

Standardization of Three Efficient Footbridges: Von Mises, Monocontentio and Bicontentio Prototypes.

2021 ◽  
Author(s):  
Mario Guisasola
Keyword(s):  
Boundary Conditions ◽  
Structural Characteristics ◽  
Structural Behavior ◽  
Bending Moments ◽  
Variable Depth ◽  
Constant Depth ◽  
Simply Supported ◽  
Vertical Walls ◽  
Basic Concepts ◽  
Von Mises

<p>The Von Mises, Monocontentio and Bicontentio footbridges are three parameterized metal bridge whose main structural characteristics are their variable depth depending on the applied stress and the embedding of abutments. Its use is considered suitable for symmetrical or asymmetrical topographies with slopes or vertical walls on one or both edges. The footbridges include spans spaced apart by 20 to 66 meters, and are between 2 to 4.5 meters wide.</p><p>Its design is based on five basic concepts: integration in the geometry of the environment; continuous search for simplicity; design based on a geometry that emanates from structural behavior; unitary and round forms; and long- lasting details.</p><p>The structural behavior of these prototypes has been compared with three types of constant-depth metal beams: the bridge simply supported, and the bridge embedded on one or both sides.</p><p>The embedding of abutments, and the adoption of a variation of depth adapted to the bending moments diagrams, allow for more efficient and elegant forms which are well-adapted to the boundary conditions.</p>

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