Generalized von Kármán equations

AbstractIn a previous work, the first author has identified three-dimensional boundary conditions “of von Kármán's type” that lead, through a formal asymptotic analysis of the three-dimensional solution, to the classical von Kármán equations, when they are applied to the entire lateral face of a nonlinearly elastic plate.In this paper, we consider the more general situation where only a portion of the lateral face is subjected to boundary conditions of von Kármán's type, while the remaining portion is subjected to boundary conditions of free edge. We then show that the asymptotic analysis of the three-dimensional solution still leads in this case to a two-dimensional boundary value problem that is analogous to, but is more general than, the von Kármán equations. In particular, it is remarkable that the boundary conditions for the Airy function can still be determined solely from the data

Analytical and finite element modelling of long plate mode jumping behaviour

Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon that a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur

Analytical and finite element modelling of long plate mode jumping behaviour

Trapezoidal sheeting of thin-walled steel is applied frequently for roofing and cladding. As such, it is loaded by a concentrated load (at the support) and a bending moment. A recently developed model to predict the sheeting's failure behaviour leaves the question open whether mode jumping (the phenomenon that a plate dynamically changes its buckling mode during an increasing load) should be taken into account in the model. This article presents the analytical and finite element modelling of square and long plates, which, depending on the boundary conditions, may represent the compressed flange of trapezoidal sheeting. The analytical modelling is based on the combination of several displacement functions and using the principle of minimal potential energy. Hereafter the stability of each part of the resulting equilibrium curves is determined. A spin-off of the analytical model is an analytical expression for a current curve-fitted based prediction formula for the post/pre buckling stiffness ratio by Rhodes. Furthermore, the accuracy range of a solution by Williams and Walker for the far-post buckling behaviour can be confirmed. The finite element modelling has been carried out by implicit dynamic, and explicit (dynamic) simulations. Both for the load levels and the buckling mode sequences, the analytical and finite element models give equivalent results. It is concluded that for the specific boundary conditions that represent the situation of a compressed flange for trapezoidal sheeting, it is very likely that mode jumping will not occur

Towards passive station holding of autonomous underwater vehicles inspired by fish behaviour in unsteady flows

Some species of fish are able to alter their mode of swimming to interact with naturally produced vortices; the use of these gaits reduces the energy expended by the fish. To analyse the feasibility of autonomous underwater vehicles (AUV) replicating these gaits, a series of experiments are performed with unpowered rigid and flexible bodies positioned in the Kármán wake of a rigid cylinder. Simple motion capture techniques are used to capture the bodies’ lateral and upstream motion in the flow. The results demonstrate that manufactured bodies are capable of passively mimicking fish behaviours, to a limited extent. More importantly, it was concluded that while significant upstream movement was possible for a manufactured object, it was achievable irrespective of the stiffness of the material. For AUVs operating in unsteady flow regimes an ability to utilise energy saving gaits may improve the range or operational time

The post-buckled coupled mode interaction behaviour of thin-walled members in compression using finite element simulation

The work of this thesis sets out to give a clearer in-depth understanding of the failure mechanics of thin-walled compression members which are associated with complex interactions between the different buckling modes during the loading process. This thesis employs the finite element method in order to examine the effect of the modelling techniques imposed at the section junctions of short struts and to investigate the influence of the local and global end conditions with regard to support and loading on the compressive response of various sections, i.e. I-sections, plain channel sections, box-sections, and lipped channel sections. The thesis also details appropriate finite element modelling strategies and solution procedures taking due account of the influence of material nonlinearity and geometrical imperfections for the determination of the coupled mode interactive response of thin-walled compression members. A detailed account of the complete loading history of the compression members from the beginning of loading through to final collapse is given in the thesis. This involves elastic local buckling, nonlinear elastic and elasto-plastic post-buckling interaction behaviour and yield propagation leading to the development of an appropriate failure mechanism which causes final collapse and unloading. A new finite element modelling strategy has been developed in the thesis with particular reference to being able to deal with the classical assumption of the stress-free in-plane boundary conditions existing at the section junctions of short length strut members during post-local buckling. Also, for fixed-ended columns, with particular reference to singly-symmetric plain channel sections, it has been shown that column deflections are initiated from the onset of local buckling for the case of the constituent plate elements of the section being locally rotationally constrained at their ends. Such columns should not therefore be considered as an overall bifurcation problem of the locally buckled member. In the case of the pinned and fixed-ended boundary conditions of the columns, the finite element simulations are shown to be able to accurately describe the rather different complex failure mechanics with a high degree of imperfection sensitivity being shown to be in evidence for the pin-ended case. Considerably good agreement has been shown to occur with the independent simulations of other researchers using the finite strip method of analysis, with the analytical solution procedures of others and with the findings from independent test work and this has provided confidence in the viability and usefulness of the modelling strategies and solution procedures developed in this thesis

Nonlinear and Linearized Analysis of Vibrations of Loaded Anisotropic Beam/Plate/Shell Structures

L'abstract è presente nell'allegato / the abstract is in the attachmen

Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application

Nonlinear dynamic analysis of composite piezoelectric plates with graphene skin

This paper studies the nonlinear dynamical characteristic of a composite plate made of new three-phase materials which include the graphene (GP) combined with macro fiber composite (MFC) in the polymer. The GP is supposed to be uniformly dispersed in the upper and lower surfaces of the composite laminated plate with 1–3 mode of macro fiber. The cross-ply MFC composite laminated plate is subjected to transversal excitations. The constitutive laws for the MFC-GP composite material are obtained based on the rule of mixture for multi-components of composite material. The nonlinear governing equations of motion of the MFC-GP plate are derived by Hamilton's principle and the von Kármán geometrical kinematics. Galerkin's approach is employed to discretize the partial differential governing equations into a two-degree-of-freedom nonlinear system. Then, stability analysis is conducted to investigate the influences of various parameters on natural frequencies of the MFC-GP plate, with a particular focus on the effects of GP volume fraction, initial conditions and damping coefficients on nonlinear vibration behaviours of the composite plate

Joint experimental and numerical study of the influence of flame holder temperature on the stabilization of a laminar methane flame on a cylinder

The mechanisms controlling laminar flame anchoring on a cylindrical bluff-body are investigated using DNS and experiments. Two configurations are examined: water-cooled and uncooled steel cylinders. Comparisons between experimental measurements and DNS show good agreement for the flame root locations in the two configurations. In the cooled case, the flame holder is maintained at about 300 K and the flame is stabilized in the wake of the cylinder, in the recirculation zone formed by the products of combustion. In the uncooled case, the bluff-body reaches a steady temperature of about 700 K in both experiment and DNS and the flame is stabilized closer to it. The fully coupled DNS of the flame and the temperature field in the bluff-body also shows that capturing the correct radiative heat transfer from the bluff-body is a key ingredient to reproduce experimental results