Buckling of the cylindrical shell joint with annular plates under external pressure

By means of an asymptotic method the buckling under the uniform external pressure of the thin cylindrical shell supported by identical annular plates is analyzed. Boundary conditions on an internal parallel of the shell joined to a thin plate are obtained. At the edges of the shell the free support conditions are introduced. We seek the approximate solutions of the eigenvalue problem as a sum of slowly varying functions and edge effect integrals. On a parallel, where the plate joint with the shell, the main boundary conditions for the formulation of an eigenvalue problem of zero approximation are obtained. This problem describes also vibrations of a simply supported beam stiffened by springs. Its solution we seek as linear combinations of Krylov’s functions. It is shown, that in zero approximation it is possible to replace a narrow plate with a circular beam. At increase in width of a plate stiffness of the corresponding spring tend to a constant. It occurs because of localization plate deformations near to the internal edge of a plate. As an example the dimensionless critical pressure for the case when the shell is supported by one plate is found. The replacement of a narrow plate with a circular beam does not lead to appreciable change of the critical pressure, however for a wide plate the beam model gives the overestimated value of critical pressure.

Tectonic plates in 3D mantle convection model with stress- history-dependent rheology

Plate tectonics is a key feature of the dynamics of the Earth’s mantle. By taking into account the stress-history-dependent rheology of mantle materials, we succeeded in realistically producing tectonic plates in our numerical model of mantle convection in a three-dimensional rectangular box. The calculated lithosphere is separated into several pieces (tectonic plates) that rigidly move. Deformation of the lithosphere caused by the relative motion of adjacent plates is concentrated in narrow bands (plate margins) where the viscosity is substantially reduced. The plate margins develop when the stress exceeds a threshold and the lithosphere is ruptured. Once formed, the plate margins persist, even after the stress is reduced below the threshold, allowing the plates to stably move over geologic time. The vertical component of vorticity takes a large value in the narrow plate margins. Secondary convection occurs beneath old tectonic plates as two-dimensional rolls with their axes aligned to the direction of plate motion. The surface heat flow decreases with increasing distance from divergent plate margins (ridges) in their vicinity in the way the cooling half-space model predicts, but it tends towards a constant value away from ridges as observed for the Earth because of the heat transport by the secondary convection.

Tectonic plates in 3D mantle convection model with stress- history-dependent rheology

Plate tectonics is a key feature of the dynamics of the Earth’s mantle. By taking into account the stress-history-dependent rheology of mantle materials, we succeeded in realistically producing tectonic plates in our numerical model of mantle convection in a three-dimensional rectangular box. The calculated lithosphere is separated into several pieces (tectonic plates) that rigidly move. Deformation of the lithosphere caused by the relative motion of adjacent plates is concentrated in narrow bands (plate margins) where the viscosity is substantially reduced. The plate margins develop when the stress exceeds a threshold and the lithosphere is ruptured. Once formed, the plate margins persist, even after the stress is reduced below the threshold, allowing the plates to stably move over geologic time. The vertical component of vorticity takes a large value in the narrow plate margins. Secondary convection occurs beneath old tectonic plates as two-dimensional rolls with their axes aligned to the direction of plate motion. The surface heat flow decreases with increasing distance from divergent plate margins (ridges) in their vicinity in the way the cooling half-space model predicts, but it tends towards a constant value away from ridges as observed for the Earth because of the heat transport by the secondary convection.

The role of strain dependent rheology on formation of divergent plate boundaries

<p>Surface of the Earth is divided into distinct plates that move relative to each other. However, formation and evolution of new plate boundaries is still challenging to numerically produce and predict. In particular, regional lithospheric models as well as large scale convection models lack realistic strike slip plate boundaries that would arise self-consistently in such models. Here, we investigate the role of different rheologies on the inception and dynamic evolution of the new divergent plate boundaries and their offset by strike-slip faulting. We compare visco-plastic rheology and strain dependent rheology and their capacity to localise deformation into narrow plate limits. We use high-resolution 3D thermo-mechanical numerical models in  cartesian geometry to infer the conditions under which realistic divergent plate boundaries develop.</p>

Effect of Aspect Ratio and Installation Direction on Channel Flow Heat Transfer Performance under a Wide Range of Reynolds Number

In recent years, in the cooling technology for high-power electronic devices such as power transistors used for drive motor control of electric vehicles and hybrid vehicles, a method of flowing a cooling fluid to a cooling substrate having a fin structure has become the main technology. The structure of the cooling fluid flow path is a channel flow through multiple narrow plate gaps to secure a heat transfer area. In this study, the heat transfer characteristics when the aspect ratio of the channel having a flat rectangular cross-section was changed were investigated in detail by experiments. Moreover, the difference in the heat transfer characteristic at the time of making a rectangular flow path into vertical installation and horizontal installation was also investigated.

Models of riveting: asymptotic analysis of the Kirchhoff plates with Sobolev point conditions

The Sobolev embedding theorem implies the correct setting at isolated points of the Dirichlet condition or the transmission conditions which simulate contact welding, binding by bolts or screws and so on. We consider the problems on bending the Kirchhoff plate with periodically distributed point supports and the joint of two plates by rows of rivets. Asymptotic analyzes performed provide asymptotic expansions of solutions and error estimates, namely, the one-dimensional model of a narrow plate and the transmission conditions at the common edge of two plates. The results of homogenization differ seriously in the cases of one or several rows of supports and rivets. In particular, one-row riveting provides only hinge joint of the plates (jumps of the rotation angles are allowed) but two-row riveting provides almost complete clutch which all elastic fields become in main continuous at the common edge.

Metamorphism and the evolution of subduction on Earth

Subduction is a component of plate tectonics, which is widely accepted as having operated in a manner similar to the present-day back through the Phanerozoic Eon. However, whether Earth always had plate tectonics or, if not, when and how a globally linked network of narrow plate boundaries emerged are matters of ongoing debate. Earth's mantle may have been as much as 200–300 °C warmer in the Mesoarchean compared to the present day, which potentially required an alternative tectonic regime during part or all of the Archean Eon. Here we use a data set of the pressure (P), temperature (T), and age of metamorphic rocks from 564 localities that vary in age from the Paleoarchean to the Cenozoic to evaluate the petrogenesis and secular change of metamorphic rocks associated with subduction and collisional orogenesis at convergent plate boundaries. Based on the thermobaric ratio (T/P), metamorphic rocks are classified into three natural groups: high T/P type (T/P > 775 °C/GPa, mean T/P ~1105 °C/GPa), intermediate T/P type (T/P between 775 and 375 °C/GPa, mean T/P ~575 °C/GPa), and low T/P type (T/P < 375 °C/GPa, mean T/P ~255 °C/GPa). With reference to published thermal models of active subduction, we show that low T/P oceanic metamorphic rocks preserving peak pressures >2.5 GPa equilibrated at P–T conditions similar to those modeled for the uppermost oceanic crust in a wide range of active subduction environments. By contrast, those that have peak pressures <2.2 GPa may require exhumation under relatively warm conditions, which may indicate subduction of young oceanic lithosphere or exhumation during the initial stages of subduction. However, low T/P oceanic metamorphic rocks with peak pressures of 2.5–2.2 GPa were exhumed from depths where, in models of active subduction, the slab and overriding plate change from being decoupled (at lower P) to coupled (at higher P), possibly suggesting a causal relationship. In relation to secular change, the widespread appearance of low T/P metamorphism in the Neoproterozoic represents a “modern” style of cold collision and deep slab breakoff, whereas rare occurrences of low T/P metamorphism in the Paleoproterozoic may reveal atypical localized regions of cold collision. Low T/P metamorphism is not known from the Archean geological record, but the absence of blueschists in particular is unlikely to reflect secular change in the composition of the oceanic crust. In addition, the premise that the formation of lawsonite requires abnormally low thermal gradients and the postulate that oceanic subduction-related rocks register significantly lower maximum pressures than do continental subduction-related rocks, and imply different mechanisms of exhumation, are not supported. The widespread appearance of intermediate T/P and high T/P metamorphism at the beginning of the Neoarchean, and the subsequent development of a clear bimodality in tectono-thermal environments are interpreted to be evidence of the stabilization of subduction during a transition to a globally linked network of narrow plate boundaries and the emergence of plate tectonics.

Propagation of a strike-slip plate boundary within an extensional environment: the westward propagation of the North Anatolian Fault

We document the establishment of the Aegea–Anatolia/Eurasia plate boundary in Pliocene–Pleistocene time. Before 2 Ma, no localized plate boundary existed north of the Aegean portion of the Anatolia plate and the shear produced by the motion of Anatolia–Aegea with respect to Eurasia was distributed over the whole width of the Aegean – West Anatolian western portion. In 4.5 Ma, a shear zone comparable to the Gulf of Corinth was formed in the present Sea of Marmara. The initial extensional basins were cut by the strike-slip Main Marmara Fault system after 2.5 Ma. Shortly after, the plate boundary migrated west of the Sea of Marmara along the northern border of Aegea from the North Aegean Trough, to the Gulf of Corinth area and to the Kefalonia Fault. There, it finally linked with the northern tip of the Aegean subduction zone, completing the system of plate boundaries delimiting the Anatolia–Aegea plate. We have related the change in the distribution of shear from Miocene to Pliocene to the formation of a relatively undeforming Aegea block in Pliocene that forced the shear to be distributed over a narrow plate boundary to the north of it. We attribute the formation of this block to the northeastward progression of the oceanic Ionian slab. We propose that the slab cuts the overlying lithosphere from asthenospheric sources and induces a shortening environment over it.

Passive Control of Flow in an A-Pillar Region in the Presence of Uniform or Turbulent Upstream Flow

The flow at the level of A-pillar region is characterized by complex and unsteady three-dimensional separated areas. They are mainly responsible for pressure fluctuations which are the source aerodynamic noises radiated outward or transmitted in the passenger compartment. This noise can make the driver tired and stress the passengers in the cabin. Therefore, one of the technological challenges for ground vehicles is the reduction of noise generated by these aerodynamic sources. At the present time, active control devices are wanted to control the vortex and its interaction with the wall (lateral windows). However, fixed devices can also be installed to a form of passive control which will play on the relative position of the vortex and its dynamics. In the present work, simple geometric devices were installed on the A-pillar strut of a model body to modify the development of the conical vortex and its fluctuating pressure footprint. Two strategies were tested. The first consisted in a narrow plate running along the A-pillar, expected to modify the A-pillar strength and its position relative to the side wall. The second consisted in generating a secondary vortex, intense enough to interact with the main structure. The efficiency of these devices has been tested in the presence of a uniform upstream flow and a turbulent upstream flow. The isotropic and homogeneous turbulent flow was generated using a grid placed in the entry of test section, generating an intensity of 4% and an integral length scale of the magnitude of the A-pillar vortex diameter. For a uniform upstream flow, it was observed that the simple geometric devices used made the vortex core more energetic and coherent. Moreover, the group of devices acting as a vortex generator was able to very significantly reduce the coefficient of fluctuating pressure. Such an improvement was however not obtained in the presence of upstream turbulence.