Local Loss Of Stability Research Articles

Experimental and Numerical Analysis of a Composite Thin-Walled Cylindrical Structures with Different Variants of Stiffeners, Subjected to Torsion.

The aim of the study was to determine the impact of the use of isogrid stiffeners on the stress and displacement distribution of a thin-walled cylindrical shell made of layered composites subjected to torsion. It also strives to define criteria for assessing the results of non-linear numerical analysis of models of the examined structures by comparing them with the results of the model experiment. The study contains the results of experimental research using models made of glass–epoxy composites and the results of numerical analyses in non-linear terms. The experiment was carried out using a special test stand. The research involved two types of considered structures. The results of the research allowed to create the concept of an adequate numerical model in terms of the finite element method, allowing to determine the distribution of stress and strain in the components of the studied structures. Simultaneously, the obtained conformity between the results of non-linear numerical analyses and the experiment allows to consider the results of analyses of the modified model in order to determine the properties of different stiffening variants as reliable. The presented research allows to determine the nature of the deformation of composite thin-walled structures in which local loss of stability of the covering is acceptable in the area of post-critical loads.

Mathematical model of deformation of orthotropic shell structures under dynamic loading with transverse shears

Thin-walled orthotropic shell structures are used in various fields of engineering, and the process of their deformation is essentially non-linear, which significantly complicates their analysis. A technique for numerically investigation of the process of deformation of such structures under dynamic loading is proposed in this article. The computational algorithm is based on the L.V. Kantorovich method and Rosenbrock method for solution of a stiff ODE system.A new variation of the mathematical model is based on the functional of total deformation energy, takes into account geometrical nonlinearity, transverse shears, orthotropy of the material, and rotational inertia, and may be used for a study of shells of different geometric forms. Dimensionless parameters are used.The proposed model and the use of mentioned methods allows to produce the most accurate calculations of the buckling of shell structures.The applicability of this technique is shown: the results of calculations are given for orthotropic shallow shells of double curvature having a square base with cylindrical and conical panels. The load values are derived for local and total stability loss, for structures made of four different materials. The effect of the rate of loading on the obtained values is shown.

Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem

A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.

Application of 3D Digital Image Correlation for Development and Validation of FEM Model of Self-Supporting Arch Structures

Many building structures, due to a complex geometry and non-linear material properties, are cumbersome to analyze with finite element method (FEM). A good example is a self-supporting arch-shaped steel sheets. Considering the uncommon geometry and material profile of an arch (due to plastic deformations, cross section of a trough, a goffer pattern), the local loss of stability can occur in unexpected regions. Therefore, the hybrid experimental-numerical methodology of analysis and optimization of arch structures have been proposed. The methodology is based on three steps of development and validation of a FEM with utilization of a digital image correlation (DIC) method. The experiments are performed by means of 3D DIC systems adopted sequentially for each measurement step conditions from small size sections, through few segment constructions up to full scale in situ objects.

The application of thin-walled integral constructions in aviation as exemplified by the SAT-AM project

The high level of durability and reliability is a strict requirement for today's aircraft constructions. The most important aspect is the mass of the structure which has a decisive influence on both the volatile and technical properties of an aircraft as well as its economical operation. Modern aircraft structures, or more precisely their load-bearing structures, are almost exclusively manufactured as thin-walled ones which meet the requirement to minimize the mass of the structure. While the local loss of coverage stability is permissible under operating load conditions, exceeding critical load levels of the structural skeleton elements (e.g. frames, stringers) is practically synonymous with some destruction of the structure. It results in a necessity for the continual improvement of both design methods and the improvement of structural solutions of aviation structures. By reducing the thickness of the cover and, at the same time, introducing densely spaced stiffening longitudinal elements, a structure with considerably higher critical loads can be obtained and, consequently, a more favorable distribution of gradients and stress levels which directly contributes to an increase in fatigue life. This paper attempts to analyze the above-mentioned problem more closely, using the example of a densely ribbed rectangular plate.

Static analysis and stability of the steel framework

The use of sheet metal plates for frame supports minimizes the thickness of the web, whose carrying capacity is only used in shear zones as a shear resistance, while in the center zones of the spans, where the bending moments dominate, and the lateral force tends to zero - the web's carrying capacity is minimized. Sheet metal binders exhibit a high supercritical load capacity, which is particularly noticeable when using rigid belts and slim webs, the shear loads for this type of sheet metal can be significantly higher than the critical loads specified for ideal plate models and webs. An analysis of the stability of the flat frame with carrier elements of I-section in the elastic range, including the ribbing of the web of co-lumns, as a counteracting the phenomenon of local loss of web stability. Studies on the effects of concentrations on general structural, torsion and torsional collapse were performed. The analysis used bar and shell calculation models, which allows analysis of the local loss of stability of the individual sections of the sheet metal section.

Necessary height of the vertical stiffeners in steel silos on discrete supports

The steel silos are interesting complex facilities. In order to ensure unloading of whole amount of stored product by gravity, the steel silos are often placed on supporting frame structure. Values of stresses in the joints between the thin walled shell and supporting frame elements are very high. It can causes local loss of stability in the shell. To prevent its local buckling, many designers put stiffening elements above the supports. Here the question is how high should be the stiffening elements? The right solution is that they should reach that level till which the values of the meridional normal stresses above the supports and in the middle between them are equalized. Under this level the cylindrical shell will be considered as a ring beam, stiffened by elements above the supports. Above it, the cylinder can be calculated as continuously supported shell. But where is this level? A lot of researchers worked on values and way of distribution of normal meridional stresses above the supports of the cylindrical shells. As a result of their efforts are determined critical height Hcr of the shell and the ideal position HI of intermediate stiffening ring. But these heights are considerably different between each other. To which of them our vertical stiffening elements should achieve?

Flow impact on granular force chains and induced instability

With today's discrete element modeling (DEM) coupled with pore-scale finite volume (PFV) scheme, the impact of an internal fluid flow on the mechanical stability of a granular material is assessed at the scale of a three-dimensional representative elementary volume. To isolate the specific impact of the fluid on the contact network, a granular sample in which rattlers have been initially removed is considered while a fluid pressure drop is applied under constant mechanical loading. Although the initial state is reputed to be unstable according to the second-order work criterion, it is shown that (i) an internal fluid flow is able to trigger the underlying instability on its own and (ii) the flow direction has no influence because of local fluid force fluctuations. In addition, the microscale mechanisms occurring during the sample collapse are investigated and it is shown that the fluid perturbation induces a decrease in kinematic constraints around force chains, which is characteristic of a local loss of stability.

Modelling the failure of near-edge impacted carbon fibre-reinforced composite subjected to shear loading

The failure of an impacted carbon fibre-reinforced composite is analysed, where a double impact near the edge of a large centre hole and subsequent shear loading are simulated. Three levels of impact with energies of 15 J, 25 J and 50 J are investigated, along with an impact-free panel used as control. The numerical finite-element (FE) method together with cohesive zone modelling is employed. The composite material is represented by the three-dimensional ply-by-ply FE model. The numerical results of the impacts are compared with respect to the damaged areas as described in the FE model and it is found that only the 50 J impact causes the impactor to penetrate the composite. Subsequent shear loading shows two failures during loading. The first is caused by a local loss of stability in the impacted region whereas the second is a failure in the tension diagonal of the panel. The load carrying capacity, when compared to the impact-free panel, shows on average, a reduction of 37% at the first failure. The FE modelling technique utilizing the ply-by-ply 3D model and cohesive zone representing the ply interactions is successfully adopted to simulate the shear test of the near-edge impacted composite. However, the behaviour of the compression region including the impact zone does not entirely agree with that experimentally observed during the shear test. In future studies, the compressive strength and local loss of stability should be more precisely addressed.

Analysis of Nonclassical Fracture Problems for Prestressed Bodies with Interacting Cracks

We consider two types of nonclassical fracture mechanisms, namely, the fracture of cracked bodies with initial (residual) stresses acting along the crack planes and the fracture of solids under compression along parallel cracks. To investigate nonaxisymmetric and axisymmetric problems for infinite solids containing two parallel coaxial cracks or a periodic set of coaxial parallel cracks, we use a combined analytic-numerical method within the framework of the three-dimensional linearized mechanics of solids. The analysis involves the representation of stresses and displacements in the linearized theory via harmonic potential functions. With the use of the integral Fourier–Hankel transformations, the problems are reduced to the solution of Fredholm integral equations of the second kind. This approach allows us to investigate problems in a unified general form for compressible and noncompressible homogeneous isotropic or transversely isotropic elastic bodies with an arbitrary structure of the elastic potential, and the material specification of the model is carried out only in the stage of numerical analysis of the resolving equations obtained in the general form. The effects of initial stresses on the stress intensity factors are analyzed for highly elastic materials and layered composites (modeled as transversely isotropic elastic bodies). The “resonance-like” effects are revealed when compressive initial stresses reach the values corresponding to the local loss of stability of the material in the vicinity of cracks, which, according to the indicated combined method, allows one to determine the critical (limiting) load parameters under the conditions of compression of the body along the cracks. The conclusions concerning the dependences of the stress intensity factors and critical (limiting) parameters of compression on the geometric parameters of the problems are formulated as well as concerning the dependences on physical and mechanical characteristics of the materials.

Modal and stability analysis of structures in periodic elastic states: application to the Ziegler column

We present a spectral method to compute the transverse vibrational modes, or Floquet Forms (FFs), of a 2D bi-articulated bar in periodic elastic state due to an end harmonic compressive force. By changing the directional nature of the applied load, the trivial straight Ziegler column exhibits the classic instabilities of stationary states of dynamical system. We use this simple structure as a numerical benchmark to compare the various spectral methods that consist in computing the FFs from the spectrum of a truncated Hill matrix. We show the necessity of sorting this spectrum and the benefit of computing the fundamental FFs that converge faster. Those FFs are almost-periodic entities that generalize the concept of harmonic modal analysis of structures in equilibria to structures in periodic states. Like their particular harmonic relatives, FFs allow to get physical insights in the bifurcations of periodic stationary states. Notably, the local loss of stability is due to the frequency lock-in of the FFs for certain modulation parameters. The presented results could apply to many structural problems in mechanics, from the vibrations of rotating machineries with shape imperfections to the stability of periodic limit cycles or of any slender structures with tensile or compressive periodic elastic stresses.

Vertical stiffeners and internal pressure - influencing factors on distribution of meridional stresses in steel silos on discrete supports

Steel silos are interesting, complicated facilities. In order to ensure unloading of whole amount of stored product by gravity, they are often placed on supporting structure. Values of stresses in joints between thin sheets and supporting frame elements are very high, which could cause local loss of stability in thin shells. Many researchers have worked on values and distribution of the meridional stresses in that joints. Their traditional approach is to divide in their minds cylindrical shell on two parts - discretely supported ring beam and continuously supported shell above it. As a result of their efforts critical height of shell Hcr and ideal position of intermediate stiffening ring on shell are determined. The scientific results are based on semi-membrane theory of Vlasov, in which influence of vertical stiffeners and internal pressure is not accounted. On other hand all steel silos are loaded with an internal pressure and majority of them have vertical stiffeners above supports. Is it possible the obtained scientific results to be applied to these silos? In a present article the author will show that stiffeners and pressure should not be ignored in an analysis.

Computation of Thin-Walled Cross-Section Resistance to Local Buckling with the Use of the Critical Plate Method

Abstract Thin-walled bars currently applied in metal construction engineering belong to a group of members, the cross-section res i stance of which is affected by the phenomena of local or distortional stability loss. This results from the fact that the cross-section of such a bar consists of slender-plate elements. The study presents the method of calculating the resistance of the cross-section susceptible to local buckling which is based on the loss of stability of the weakest plate (wall). The “Critical Plate” (CP) was identified by comparing critical stress in cross-section component plates under a given stress condition. Then, the CP showing the lowest critical stress was modelled, depending on boundary conditions, as an internal or cantilever element elastically restrained in the restraining plate (RP). Longitudinal stress distribution was accounted for by means of a constant, linear or non-linear (acc. the second degree parabola) function. For the critical buckling stress, as calculated above, the local critical resistance of the cross-section was determined, which sets a limit on the validity of the Vlasov theory. In order to determine the design ultimate resistance of the cross-section, the effective width theory was applied, while taking into consideration the assumptions specified in the study. The application of the Critical Plate Method (CPM) was presented in the examples. Analytical calculation results were compared with selected experimental findings. It was demonstrated that taking into consideration the CP elastic restraint and longitudinal stress variation results in a more accurate representation of thin-walled element behaviour in the engineering computational model.

Evaluation of stress-strain state of gas pipeline section with local stability loss

Evaluation of stress-strain state of gas pipeline section with local stability loss

Computer simulation of local and global buckling of thin-walled shells

Stability of thin-walled structures is investigated on the basis of the geometrically nonlinear theory of shells. This allows us to monitor a series of shell deformation processes under different load changes. The local and general loss of stability can be determined by observing changes in the shape of the shell curved surface before and after critical loads. The shell material can be isotropic or orthotropic, but linear-elastic. A mathematical model of deformation of a shell is the functional of total potential energy of deformation of the shell. Two methods are applied to minimize the total energy functional of deformation of the shell. One is based on the method of L-BFGS with discrete approximation of the unknown functions by NURBS-surfaces. This enables taking into account various forms of fixing of the shell contour and the complex shape of this circuit. The other employs the Ritz method and the best parameter continuation method in the continuous approximation of the unknown displacement functions and the angles of rotation of the normal. This technique allows us to find the upper and lower critical loads and the bifurcation point. A combination of these techniques makes it possible to study both the subcritical and supercritical behavior of the structure and to identify the local and global buckling of the shell and their relationship. On the curve of equilibrium states versus “load q - deflection W ” one can see all moments of buckling of the shell caused by “swatting” of some part of it. Thus, after each buckling a significant change in the shape of the curved surface is observed. For illustration purposes the changes in the shell shape at subcritical and supercritical stages are plotted against its three-dimensional surface. After the general loss of stability the shell deforms under loading without any significant change in its shape, i.e. it behaves as a plate.

Engineering stress solutions for bolted and pressurized steel structures

Two geometrical models of bolted connections and pressurized containers are suggested. A unified analytical procedure for stresses is developed based on the Huber–Mises–Hencky yield criterion, elastic–perfectly plastic material behavior and plane stress assumption. To determine the minimum distance between centers of fasteners in bolted connections the limit load-carrying capacity criterion is proposed. The results obtained agree well with AISC specifications and on the safe side. For pressurized containers it is shown that stress distributions depend on Poisson's ratio which should be taken into account in a stability analysis since these structures are mostly vulnerable to the local loss of geometric stability.

Commentary on “Biochemical and Immunomorphological Evaluation of Hepatocyte Growth Factor and c-Met Pathway in Patients with Critical Limb Ischemia”: Regenerative Therapy of Chronically Ischaemic Wounds: Land in Sight?

This issue of the European Journal of Vascular and Endovascular Surgery features interesting basic research that explores molecular mechanisms behind an important yet unsolved clinical problem of vascular care: the lost regenerative competence of chronically ischaemic wounds. We all have been challenged by trophic tissue defects in patients with chronic critical limb ischaemia (CLI) that after some time seem to turn to an inert state, which may persist even if revascularisation of the macro-circulation is feasible, not to speak of situations where it is not. Complementary regenerative therapy is definitively needed. The author’s approach to explore the human hepatocyte growth factor (HGF)/Met proto-oncogene signalling pathway is compelling. Activated Met signalling plays an important role (albeit only in animal models) in numerous regenerative processes, including skin wound repair, and it is indirectly regulated by tissue hypoxia via hypoxia inducible factor-1 (HIF-1). Consistently, the HGF/Met axis was indeed downregulated in non-healing CLI wounds in the present study. The authors saw this as a reflection of decreased HGF serum levels and a local loss of HIF-1 stability. If this were true, therapeutic application of HGF might help reactivate normal wound healing in CLI, an intriguing finding! The question, however, is whether the presented data really suggest such a fly interpretation. The number of investigated specimens was very limited, and without a specific power analysis it remains somewhat unclear how many parameters were investigated, which increases the risk of a chance finding. Moreover, from the snapshot information alone, it is impossible to determine which came first: the decreased HGF serum levels, the increased HIF-1 RNA expression, or the local loss of c-Met activation? Thus, already the study design obviates any inference of causality. But, most importantly, the choice of the control group may raise concerns. Assuming a localised adverse

The plastic loss of stability of a thin-walled tube under axial compression

A theoretical model of the plastic shaping of ring folds in the axial compression of a thin-walled tube with smooth plates after local loss of stability is presented. The initial stage of the shaping is calculated using membrane theory of a rigid-plastic envelope under the von Mises plasticity condition, taking into account the deformation strengthening and the change in the wall thickness. The final stage is calculated using moment theory with the finite curvature of the curvilinear parts of the folds. The calculated forms of the folds and the force-displacement dependences when there is loss of stability agree satisfactorily with experimental data.

Numerical analysis of the stability of a multi-element rod structure under disproportionate loading

We study the stress-strain state and the process of stability loss for a multi-element rod structure supported by pillars, whose subsidence is prescribed. A numerical model is developed to reveal structure elements with lost stability. The calculated results corresponding to the stability loss process are compared with the data on stability loss obtained by engineering methods. Critical impacts that cause complete and local stability loss in the structure are determined.

3D Analyses of the symmetric local stability loss of the circular hollow cylinder made from viscoelastic composite material

The 3D approach was employed for investigations of the symmetric local stability loss of the circular hollow cylinder made from the viscoelastic composite materials. This approach is based on investigations of the development of the initial rotationally symmetric infinitesimal local imperfections of the circular hollow cylinder within the scope of 3D geometrically nonlinear field equations of the theory of viscoelasticity for anisotropic bodies. The numerical results of the critical force and critical time are presented and discussed. For comparison and estimation of the accuracy of the results given by the 3D approach, the same problem is also solved by using various approximate shell theories. The viscoelasticity properties of the plate material are described by the fractional–exponential operator. The numerical results and their discussion are presented for the case where the cylinder is made of a uni-directional fibrous viscoelastic composite material. In particular, it is established that the difference between the critical times obtained by employing 3D and third order refined shell theories becomes more non-negligible if the values of the external compressive force are close to the critical compressive force which is obtained at t=∞ (t denotes a time).