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.

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.

Bend Flexibility Factors of Piping Elbows and Piping Elbows With Trunnion Attachments Using the Boundary Element Method

2009 ◽  
Author(s):  
Manuel Martinez ◽  
Johane Bracamonte ◽  
Marco Gonzalez
Keyword(s):  
Boundary Element Method ◽  
Numerical Method ◽  
Bending Moment ◽  
Piping System ◽  
Thin Walled Structures ◽  
Out Of Plane ◽  
Thin Walled ◽  
Plane Bending ◽  
Flexibility Factor ◽  
Element Method

Flexibility Factor is an important parameter for the design of piping system related to oil, gas and power industry. Elbows give a great flexibility to piping system, but where a trunnion is attached to an elbow in order to support vertical pipe sections, the piping flexibility is affected. Generally, determination of elbow flexibility factors has been performed by engineering codes such as ASME B31.3 or ASME B31.8, or using the Finite Element Method (FEM) and Finite Difference Method (FDM). In this work, bend flexibility factors for 3D models of piping elbows and piping elbows with trunnion attachments using the Boundary Element Method (BEM) are calculated. The BEM is a relatively new numerical method for this kind of analysis, for which only the surface of the problem needs to be discretized into elements reducing the dimensionality of the problem. This paper shows the simulation of 9 elbows with commercially available geometries and 29 geometries of elbows with trunnion attachments, 10 of them using commercial elbow dimensions, with applied in-plane and out-of-plane bending moments. Structured meshes are used for all surfaces, except the contact surface of elbow-trunnion joints, and no welded joints are simulated. The results show smaller values of flexibility factors of elbow and elbow–trunnion attachments in all loading cases if are compared to ASME B31.3 or correlations obtained from other works. The results also indicate that flexibility factor for elbow-trunnion attachment subjected to in-plane bending moment is greater than flexibility factor for out-of plane bending moment. Accuracy of BEM’s results were not good when flexibility characteristic values are lesser than 0.300, which confirm the problems of this numerical method with very thin-walled structures. The method of limit element could be used as tool of alternative analysis for the design of made high-pitched system, when the problem with very thin-walled structures is fixed.

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.

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).

scholarly journals Coupled Static and Dynamic Buckling Modelling of Thin-Walled Structures in Elastic Range Review of Selected Problems

2016 ◽  
Vol 10 (2) ◽  
pp. 141-149 ◽  
Author(s):  
Zbigniew Kołakowski ◽  
Andrzej Teter
Keyword(s):  
Numerical Method ◽  
Cross Sections ◽  
Bending Moment ◽  
Dynamic Buckling ◽  
Equilibrium Path ◽  
Compression Load ◽  
Thin Walled Structures ◽  
Post Buckling ◽  
Plates And Shells ◽  
Thin Walled

AbstractA review of papers that investigate the static and dynamic coupled buckling and post-buckling behaviour of thin-walled structures is carried out. The problem of static coupled buckling is sufficiently well-recognized. The analysis of dynamic interactive buckling is limited in practice to columns, single plates and shells. The applications of finite element method (FEM) or/and analytical-numerical method (ANM) to solve interaction buckling problems are on-going. In Poland, the team of scientists from the Department of Strength of Materials, Lodz University of Technology and co-workers developed the analytical-numerical method. This method allows to determine static buckling stresses, natural frequencies, coefficients of the equation describing the post-buckling equilibrium path and dynamic response of the plate structure subjected to compression load and/or bending moment. Using the dynamic buckling criteria, it is possible to determine the dynamic critical load. They presented a lot of interesting results for problems of the static and dynamic coupled buckling of thin-walled plate structures with complex shapes of cross-sections, including an interaction of component plates. The most important advantage of presented analytical-numerical method is that it enables to describe all buckling modes and the post-buckling behaviours of thin-walled columns made of different materials. Thin isotropic, orthotropic or laminate structures were considered.

scholarly journals The local theory of elastoplastic deformation processes and the stability beyond elastic limits of thin-walled structures subjected to complex loading

1992 ◽  
Vol 14 (1) ◽  
pp. 1-9
Author(s):  
Dao Huy Bich
Keyword(s):  
Constitutive Relations ◽  
Complex Loading ◽  
Local Theory ◽  
Rectangular Plates ◽  
Thin Walled Structures ◽  
Plastic Deformation Process ◽  
Deformation Processes ◽  
Thin Walled ◽  
The Stability ◽  
Loading Parameter

The paper is concerned with the complete constitutive relations of elasto-plastic deformation process theory. Using this theory the stability beyond elastic limits of thin-walled structures subjected to complex loading is analyzed. The proposed method of loading parameter is a combination of numerical and analytical solutions. Calculations have been carried out for rectangular plates and cylindrical shells in order to compare this method and its results with other theoretical and experimental works.

scholarly journals GLASS FIBER REINFORCED CONCRETE IN THIN-WALLED CONSTRUCTIONS

2019 ◽  
Vol 4 (4) ◽  
pp. 70-76
Author(s):  
Л. Панченко ◽  
Larisa Panchenko ◽  
Е. Ерижокова ◽  
E. Erizhokova
Keyword(s):  
Glass Fiber ◽  
Yield Criterion ◽  
Variable Parameter ◽  
Isoperimetric Problem ◽  
Fiber Reinforced Concrete ◽  
Rectangular Plates ◽  
Thin Walled Structures ◽  
Fiber Concrete ◽  
Thin Walled ◽  
Von Mises

Fibrous composites are progressive materials for buildings and structures. Structures based on them are characterized by high technical and economic characteristics. Glass fiber concrete is effective for thin-walled structures. Various principles of structural mechanics applied to fiber composites are pro-posed for solving design problems. The optimal configuration of the covering is determined by the sta-tionarity of its potential energy for given values of the calculated resistances of the material compo-nents. This formulation of the problem leads to a global minimum of the covering volume. In particu-lar, an axisymmetrically loaded spherical cover is considered; the optimal thickness is determined from the condition of equal resistance by the von Mises yield criterion. Types of elements for precast glass-fiber concrete of various spans are recommended. In addition, the shallow tunnels are consid-ered; they are a prevalent object of transport communications. The rationality of using the thin-walled spatial systems consisting of rectangular plates is established. The isoperimetric problem is solved for a given volume of material based on the generalized Lagrangian principles. The thickness of the rec-tangular plates of the spatial system of the tunnel is taken as a variable parameter.

scholarly journals Influence of the geometrical researches of surfaces of revolution and translation surfaces on design of unique structures

2019 ◽  
Vol 15 (4) ◽  
pp. 308-314 ◽  
Author(s):  
Gérard Léopold Gbaguidi Aisse
Keyword(s):  
Computer Modeling ◽  
Real Structure ◽  
Building Structures ◽  
Surfaces Of Revolution ◽  
Translation Surfaces ◽  
Fractal Surfaces ◽  
Thin Walled Structures ◽  
The World ◽  
Thin Walled ◽  
The Relationship

Aims of research. The use, design and analysis of architectural and building structures in the form of smooth and composite surfaces have become relevant and in demand lately, which determined the purpose of this article - to analyze the use of analytical surfaces given vector, parametric or explicit equations in real structures. Methods. The relationship between studies on the geometry of surfaces of revolution and transport and the creation of new forms of thin-walled structures and buildings is determined. An example of a real structure is given on each surface. The article does not consider composite, multifaceted, fractal surfaces, as well as surfaces that are not defined analytically. Results. It turned out that only a small number of considered surfaces of these two classes have found application in the world. At the end of the article, a bibliography is presented, which sets out the mathematical side of the design of analytical surfaces, their computer modeling, more detailed information about real structures in the form of the surfaces under consideration.

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