The Stability in Bending of Slightly Corrugated Plates

1952 ◽  
Vol 56 (502) ◽  
pp. 782-788 ◽  
Author(s):  
D. G. Ashwell
Keyword(s):  
Elastic Plate ◽  
Arbitrary Shape ◽  
Bending Moment ◽  
Axis Parallel ◽  
Instability Characteristic ◽  
Rectangular Elastic Plate ◽  
Thin Walled ◽  
Corrugated Plates ◽  
The Stability ◽  
Finite Bending

A previous paper was concerned with the uniform finite bending of a flat rectangular elastic plate about an axis parallel to one of its pairs of opposite edges. Expressions were obtained for the shape assumed by sections of the plate containing the axis of curvature, and the applied bending moment. In the present paper the work is extended to deal with a plate having shallow regular corrugations of arbitrary shape running along it at right angles to the axis of curvature. Such a plate may be of interest as it exhibits the type of instability characteristic of curved thin-walled members. Its solution can be derived quickly from the previous work.

A characteristic type of instability in the large deflexions of elastic plates III. Curved rectangular plates in axial compression

1954 ◽  
Vol 222 (1148) ◽  
pp. 44-59 ◽  
Keyword(s):  
Axial Compression ◽  
Rectangular Plates ◽  
Bending Moments ◽  
Elastic Plates ◽  
Characteristic Type ◽  
Circular Tubes ◽  
Axis Parallel ◽  
Post Buckling ◽  
Thin Walled ◽  
The Stability

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Explicit Expressions for Buckling Analysis of Thin-Walled Beams Under Combined Loads with Laterally-Fixed Ends and Application to Stability Analysis of Saw Blades

2020 ◽  
pp. 2150032
Author(s):  
Van Binh Phung ◽  
Ngoc Doan Tran ◽  
Viet Duc Nguyen ◽  
V. S. Prokopov ◽  
Hoang Minh Dang
Keyword(s):  
Critical State ◽  
Bending Moment ◽  
Critical Issue ◽  
Eccentric Load ◽  
Concentrated Load ◽  
Combined Loads ◽  
Distributed Load ◽  
Thin Walled ◽  
The Stability ◽  
2D And 3D

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force [Formula: see text], bending moment [Formula: see text] and distributed load [Formula: see text] (or concentrated load [Formula: see text]) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads.

A characteristic type of instability in the large deflexions of elastic plates. I. Curved rectangular plates bent about one axis II. Flat square plates bent about all edges

1952 ◽  
Vol 214 (1116) ◽  
pp. 98-118 ◽  
Keyword(s):  
Bending Moment ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Surfaces Of Revolution ◽  
Characteristic Type ◽  
Axis Ii ◽  
Curved Structures ◽  
Thin Walled Structures ◽  
Instability Characteristic ◽  
Thin Walled

Part I . From a general equation governing the bending of thin elastic plates into certain types of surfaces of revolution are derived expressions for the behaviour of rectangular plates with initial curvatures, subjected to pure bending about one axis. It is found that such plates exhibit the type of instability characteristic of thin-walled structures which depend for their stiffness on curvature. Curves are drawn showing the deformation suffered by such plates, and an expression for the critical bending moment at which instability occurs is obtained. Experimental results show satisfactory agreement. Part II . The analysis of part I is extended to deal with the case of flat square or rectangular plates loaded by distributed bending moments applied to all four edges. Curves are drawn to describe their behaviour, and they are found to exhibit the characteristic instability displayed by thin-walled curved structures. Experimental verification is satisfactory.

scholarly journals INVESTIGATION OF THIN-WALLED COLUMN WITH VARIABLE I-SECTION STABILITY USING FINITE ELEMENT METHOD/PLONASIENĖS KINTAMOJO DVITĖJO SKERSPJŪVIO KOLONOS STABILUMO TYRIMAS BAIGTINIŲ ELEMENTŲ METODU

2000 ◽  
Vol 6 (2) ◽  
pp. 69-75
Author(s):  
Michail Samofalov ◽  
Rimantas Kačianauskas
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stability Analysis ◽  
Numerical Experiments ◽  
Relative Length ◽  
Bending Moment ◽  
Relative Height ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
The Stability

Thin-walled structures are widely used in building construction. Stability analysis [1–10] is of major importance to the design of thin-walled structures. This paper deals with the stability analysis of the thin-walled tapered column [11–18]. The aim is to investigate the influence of variation of the web height on the stability of column and combined action of axial force and plane bending moment. Critical state is defined by stability surface obtained by numerical experiments using the finite element method. Mathematical model of the linearised stability problem is presented as algebraic eigenvalue problem (1), where eigenvalues express the critical loading factor (2). Analytical solutions are known for particular cases of separate loading (4), (5). In this paper, the column with variable I-section is presented as assemblage of beam elements with constant section. Thin-walled beam element has 14 degrees of freedom (Fig 1), including linear displacements, rotations and warping displacements. Variation of cross-section of the column (Fig 2) is defined by relative height of web alb, were a and b are the height at the ends of column. Critical state is described by stability surface obtained using numerical experiments. Stability surface presents in the space of relative variation of height a/b, relative length and relative critical force and bending moment . Variation of section influences the critical bending moment only. The influence of finite element number on the with different relative height of web a/b is investigated numerically (Fig 3), and its variation of stability surface is presented in Fig 4. The numerical results show that variation of critical moment to relative web height a/b is linear (Fig 5). The shapes of buckling modes are presented in Fig 6. Variation of stability surface to relative length (6) is presented in Figs 7 and 8 and expressed by the simple expression (6) constructed on the basis of numerical experiments. Finally, the stability model (1) is compared with nonlinear calculations performed using program ANSYS [19] and shell finite elements (Figs 9 and 10).

Improved Generalized Procedure for Determining Critical State of a Thin-Walled Beam Under Combined Symmetric Loads

2019 ◽  
Vol 19 (08) ◽  
pp. 1950098 ◽  
Author(s):  
Phung Van Binh ◽  
Nguyen Viet Duc ◽  
Prokopov Vladimir Sergeevich ◽  
Dang Hoang Minh
Keyword(s):  
Bending Moment ◽  
Complex Loading ◽  
Computational Procedure ◽  
Beam Length ◽  
Concentrated Load ◽  
Internal Forces ◽  
Thin Walled ◽  
The Stability ◽  
External Loads

This paper presents an improved generalized procedure for dealing with the stability of thin-walled beams under combined symmetric loads based on the energy method. The differential equations for the case of complex loading conditions were developed using an axis transformation matrix. The work caused by external loads was related to the work of internal forces to simplify the computational procedure. The thin-walled beam subjected to axial force [Formula: see text], bending moment [Formula: see text] at both ends, and concentrated load [Formula: see text] at midspan was studied. The case of a concentrated load [Formula: see text] replaced by a distributed load [Formula: see text] over partial beam length was also examined. The stability region boundary of the beam was derived by two approaches: one was to estimate an approximate angle of twist prior to determination of the deflection and the other was to do it in the reverse way. Numerical results reveal that the first approach yields less error than the second; however, the outcome obtained by the former was more cumbersome than the latter. Above all, both approaches provided feasible results and are useful for further applications dealing with the stability analysis of thin-walled beams.

The stability of rectangular thin-walled profile with loading according to the scheme of pure bending

2020 ◽  
pp. 41-45
Author(s):  
V.B. Zylev ◽  
◽  
P.O. Platnov ◽  
I.V. Alferov ◽  
◽  
...  
Keyword(s):  
Pure Bending ◽  
Thin Walled ◽  
The Stability

scholarly journals The effect of flexural–torsional buckling on the stability of timber members: a case study

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Osama A. B. Hassan
Keyword(s):  
Axial Compression ◽  
Bending Moment ◽  
List Type ◽  
Torsional Buckling ◽  
Solution Methods ◽  
Simplified Solution ◽  
The Stability ◽  
Flexural Torsional Buckling ◽  
Building Engineering

Abstract This study investigates the stability of timber members subjected to simultaneously acting axial compression and bending moment, with possible risk for torsional and flexural–torsional buckling. This situation can occur in laterally supported members where one side of the member is braced but the other side is unbraced. In this case, the free side will buckle out of plane while the braced side will be prevented from torsional and flexural–torsional buckling. This problem can be evident for long members in timber-frame structures, which are subjected to high axial compression combined with bending moments in which the member is not sufficiently braced at both sides. This study is based on the design requirement stated in Eurocode 5. Solution methods discussed in this paper can be of interest within the framework of structural and building Engineering practices and education in which the stability of structural elements is investigated. Article Highlights This case study investigates some design situations where the timber member is not sufficiently braced. In this case, a stability problem associated with combined torsional buckling and flexural buckling can arise. The study shows that the torsional and/or flexural–torsional buckling of timber members can be important to control in order to fulfil the criteria of the stability of the member according to Eurocode 5 and help the structural engineer to achieve safer designs. The study investigates also a simplified solution to check the effect of flexural torsional buckling of laterally braced timber members.

Basic Concepts in the Stability Theory of Thin-walled Structures

2010 ◽  
Author(s):  
A. Guran ◽  
L. Lebedev ◽  
Michail D. Todorov ◽  
Christo I. Christov
Keyword(s):  
Stability Theory ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Basic Concepts ◽  
The Stability
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