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2013 | Buch

Static and Dynamic Buckling of Thin-Walled Plate Structures

verfasst von: Tomasz Kubiak

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This monograph deals with buckling and postbuckling behavior of thin plates and thin-walled structures with flat wall subjected to static and dynamic load. The investigations are carried out in elastic range.

The basic assumption here is the thin plate theory. This method is used to determination the buckling load and postbuckling analysis of thin-walled structures subjected to static and dynamic load. The book introduces two methods for static and dynamic buckling investigation which allow for a wider understanding of the phenomenon. Two different methods also can allow uncoupling of the phenomena occurring at the same time and attempt to estimate their impact on the final result.

A general mathematical model, adopted in proposed analytical-numerical method, enables the consideration of all types of stability loss i.e.local, global and interactive forms of buckling. The applied numerical-numerical method includes adjacent of walls, shear-lag phenomenon and a deplanation of cross-sections.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

The subject of this monograph is a study of buckling and postbuckling behaviour of thin plates and thin-walled structures with flat walls, subjected to static and dynamic load.

Tomasz Kubiak

Chapter 2. Theory of Thin Plates for Laminates

Abstract

Thin isotropic, orthotropic or laminate plates with constant or widthwise variable material properties are considered in this monograph. Thin-walled beam-columns or girders composed of the above-mentioned plates are also analysed. In order to take into account all buckling modes (global, local and their interaction), the plate two-dimensional theory has been adopted to model the structures under analysis.

Tomasz Kubiak

Chapter 3. Analytical–Numerical Method

Abstract

The method proposed and explained below allows one to determine critical loads, natural frequencies and coefficients of the equation describing the postbuckling equilibrium path for thin orthotropic plates or girders, columns and beams composed of flat orthotropic plates (walls). This method also allows one to analyse a dynamic response of the plate structure subjected to pulse loading. Taking the deflections as a function of time and applying the relevant dynamic buckling criteria, it is possible to determine the dynamic critical load.

Tomasz Kubiak

Chapter 4. Finite Element Method

Abstract

The finite element method is used here to validate the analytical–numerical method presented in Chap. 3. The basic assumption and the used equations for thin plates in both the methods (ANM—the analytical–numerical method, FEM—the finite element method) are identical, but the way of solution is different. To apply a program based on the finite element method as a numerical experiment, confirming or validating the theoretical analysis or the analysis based on the analytical–numerical method, it is important to create an appropriate model. A properly chosen finite element type, a rational mesh density and appropriate boundary conditions play a significant role in obtaining the calculation results close to the reality.

Tomasz Kubiak

Chapter 5. Dynamic Buckling Criteria

Abstract

Dynamic stability, or better, dynamic buckling (sometimes referred to as a dynamic response) means a loss of stability of the structure subjected to pulse load. Especially, it can act along the axis of the column or in the plane of the plate. It should be mentioned that for the ideal uniformy compressed structures (without any geometrical imperfection) the critical buckling amplitude of pulse loading leads to infinity. Therefore, the dynamic buckling can be analysed only for structures with initial geometrical imperfections. In such a case, the critical value of dynamic load does not have a bifurcation character, thus it has to be determined on the basis of the assumed criterion. Some the most popular and some new criterion allowing to determine dynamic buckling is presented in this chapter.

Tomasz Kubiak

Chapter 6. Thin Plates

Abstract

The chapter is devoted to buckling, postbuckling behaviour and dynamic buckling of thin plates made of metals or composites modelled as orthotropic materials. The considered plates are simply supported on loaded edges and different boundary condition on longitudinal edges. They are subjected to uniform compression.

Tomasz Kubiak

Chapter 7. Thin-Walled Columns

Abstract

The chapter deals with static buckling, postbuckling behaviour and dynamic buckling of thin-walled column with open cross-section made of isotropic and orthotropic material. The analysed columns were subjected to compressed load. The results was obtained using finite element method and analytical-numerical method.

Tomasz Kubiak

Chapter 8. Girders, Beams Subjected to Pure Bending

Abstract

In this chapter, the behaviour of girders or beams subjected to pulse load causing pure bending is presented. Girders with square cross-sections and beams with channel sections are considered. The part of multi-segment girders between two diaphragms is taken into account. The structures under analysis are made of isotropic or orthotropic material. The calculations were made with finite element method software and analytical-numerical method—the obtained results were compared.

Tomasz Kubiak

Chapter 9. Thin-Walled Girders Subjected to Torsion

Abstract

The results of the dynamic buckling analysis of girders subjected to torsion are presented in this chapter. All the results of numerical calculations to be discussed further were obtained with finite element method commercial software. Girders with square cross-sections and different lengths were considered. A little attention is paid to thin-walled structures with flat wall subjected to bending or torsion. It was therefore decided to fill this gap by conducting an analysis of thin-walled girders with closed cross-section and behaviour of such structures subjected to torsion impulse of finite duration.

Tomasz Kubiak

Chapter 10. Thin-Walled Girders Subjected to Combined Load

Abstract

This chapter deals with dynamic response of thin-walled girders subjected to combined load (bending and/or twisting). The load was assumed as stepped dynamic pulse of finite duration. Numerical analysis was conducted with finite element method (FEM). Analysis has concentrated on thin-walled girders of length 200 mm and squared cross-section (100 × 100 mm) with 1 mm wall thickness. Different numerical models were compared and investigation of dynamic response of the structure under combined load was performed for different boundary conditions. The critical values of load were determined according to well-known criteria (Volmir, Budiansky-Hutchinson and Ari-Gur-Simonetta criterion).

Tomasz Kubiak

Titel: Static and Dynamic Buckling of Thin-Walled Plate Structures
verfasst von: Tomasz Kubiak
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-00654-3
Print ISBN: 978-3-319-00653-6
DOI: https://doi.org/10.1007/978-3-319-00654-3

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