Search results for "Buckling"
showing 10 items of 104 documents
Buckling and post-buckling analysis of cracked stiffened panels via an X-Ritz method
2019
Abstract A multi-domain eXtended Ritz formulation, called X-Ritz, for the analysis of buckling and post-buckling of stiffened panels with cracks is presented. The theoretical framework is based on the First-order Shear Deformation Theory and accounts for von Karman's geometric nonlinearities. The structure is modeled as assembly of plate elements. Penalty techniques are used to fulfill the continuity condition along the edges of contiguous elements and to satisfy essential boundary conditions requirements. The use of an extended set of approximating functions allows to model through-the-thickness cracks and to capture the crack opening and tip singular fields as well as the structural behav…
Nanomechanics of individual aerographite tetrapods
2017
Carbon-based three-dimensional aerographite networks, built from interconnected hollow tubular tetrapods of multilayer graphene, are ultra-lightweight materials recently discovered and ideal for advanced multifunctional applications. In order to predict the bulk mechanical behaviour of networks it is very important to understand the mechanics of their individual building blocks. Here we characterize the mechanical response of single aerographite tetrapods via in situ scanning electron and atomic force microscopy measurements. To understand the acquired results, which show that the overall behaviour of the tetrapod is governed by the buckling of the central joint, a mechanical nonlinear mode…
On the instability of an axially moving elastic plate
2010
Problems of stability of an axially moving elastic band travelling at constant velocity between two supports and experiencing small transverse vibrations are considered in a 2D formulation. The model of a thin elastic plate subjected to bending and tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of an analytical approach. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence (buckling). Then the static forms of instability are investigated, and critical regimes are studied as functions of geometric and mechanical problem param…
Some Optimization Problems
2013
In this chapter, the problems of safety analysis and optimization of a moving elastic plate travelling between two rollers at a constant axial velocity are considered. We will use a model of a thin elastic plate subjected to bending and in-plane tension (distributed membrane forces). We will study transverse buckling (divergence) of the plate and its brittle and fatigue fracture caused by fatigue crack growth under cyclic in-plane tension (loading). Our aim is to find the safe ranges of velocities of an axially moving plate analytically under the constraints of longevity and stability. In the end of this chapter, the expressions for critical buckling velocity and the number of cycles before…
Buckling and post-buckling analysis of cracked composite plates via a single-domain Ritz approach
2018
Thin and moderately thick composite multi-layered plates are widely employed in many engineering applications, especially in naval and aerospace structures. These structural components can experience in service the presence of cracks, generated for example by corrosion, fatigue or accidental external causes. Cracks can affect the load carrying capability, buckling and post-buckling behaviour of plates; therefore, their effects need to be investigated and taken into account for fail safe or damage tolerant design. Additionally, attention should be devoted to the interaction of cracks with buckling and post-buckling behaviour, as the energy release rate in post-buckling regimes can be adverse…
Buckling and nonlinear dynamics of elastically coupled double-beam systems
2016
Abstract This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary s…
Theoretical study on travelling web dynamics and instability under non-homogeneous tension
2013
Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibration…
Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid
2010
The out-of-plane instability of a moving plate, travelling between two rollers with constant velocity, is studied, taking into account the mutual interaction between the buckled plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the buckled plate (assumed cylindrical) is described by an integro-differential equation that includes the centrifugal force, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, and the bending force. The aerodynamic reaction is found analytically as a functional of the displacement. To find the critical divergence velocity of the moving plate and its corresponding buckling mode, an eigenvalue…
Direct observation of a buckling transition during the formation of thin colloidal crystals
2007
We have investigated a colloidal suspension in a thin wedge formed by two glass plates in the presence of a lateral pressure. Starting with a single hexagonal layer, with increasing separation between the glass plates additional layers are added. This process is accompanied by a number of structural transitions necessary to maintain a high packing fraction under the given boundary conditions. Besides the well-known sequence of hexagonal and quadratic phases, we observe two new phases which are identified with the buckling and the rhombic phase recently predicted by other authors.
Solitary Waves for the Assessment of Thermal Stress and Neutral Temperature in Slender Structures
2015
Slender columns and continuous welded rails subjected to compressive stress are common in many civil structures. The rapid in-situ measurement of this stress may be of interest to prevent structural anomalies such as buckling. In this article, the authors describe the coupling mechanism between highly nonlinear solitary waves (HNSWs) propagating along an L-shaped granular system and a beam in contact with the granular medium. The aim is the evaluation of HNSWs as a tool to measure stress in thermally loaded structures and to estimate the neutral temperature, i.e. the temperature at which this stress is null. The authors investigated numerically and experimentally one chain of spherical part…