Resistance Of Plates Research Articles

Modes of Mantle Convection, Their Stability, and What Controls Their Existence

AbstractThe motion of Earth's tectonic plates is the surface expression of mantle convection beneath. Analytical convection models have attempted to relate observables, such as plate velocities and surface heat flow, with the thermo‐mechanical state of the mantle, and remain deeply influential in global geophysics. While such models tend to focus on describing the mantle's behavior today, there is evidence that suggests they may not be the best description for an earlier, hotter mantle. Early in Earth's history, higher temperatures may have led to different convective regimes that include active‐lid (today's form of convection), sluggish‐lid, and stagnant‐lid convection. In this study, we adopt and extend the analytical theory laid out by Crowley & O'Connell (2012, https://doi.org/10.1111/j.1365-246X.2011.05254.x) that self‐consistently characterizes the first two of these convection regimes. For a given thermo‐mechanical state, the theory predicts one to multiple solutions that each represent distinct modes of mantle convection. Here, we derive new scaling laws that connect these modes to the mantle's Rayleigh number and identify a new fundamental, dimensionless number, which we term the O’Connell number (named after Richard “Rick” J. O'Connell (1941–2015)), that describes a plate's resistance in context of the overall convection of the system. In addition, we identify two key bifurcations that bracket the Rayleigh‐O'Connell number space within which multiple solutions may exist. Finally, we remove the assumption of steady‐state in their original framework in order to perform a linear stability analysis to characterize the relative stability of each convection mode.

Experimental and numerical analysis of stiffened curved plates as bottom flanges of steel bridges

This paper deals with the experimental and numerical evaluation of the buckling behaviour and ultimate resistance of stiffened transversally curved panels subjected to uniform axial compression. Furthermore, a verification procedure for curved stiffened panels is proposed that gives a good estimation of the maximum loads obtained from experimental and numerical tests. The procedure is in line with the design methodology of EN 1993-1-5, accounting also for panel curvature. Nine large-scale tests were performed on longitudinally and transversally stiffened plates made of high strength steel, namely S500 and S700. They were subjected to compressive stresses up to collapse. The nine specimens comprised of flat and curved plates that differed in material grade and geometric parameters, such as panel thickness, aspect ratio, size and shape of stiffeners. The effects of different parameters on the plate's resistance to pure compression are discussed. Moreover, a numerical model built in the general-purpose code ABAQUS is presented and verified against the test results regarding initial stiffness, ultimate resistance and failure mode. Numerical simulations (FEA), based on the test panel geometry, the measured initial geometric imperfections and elasto-plastic material characteristics from tensile tests, demonstrate very good agreement with experimental results.

A mechanical model for thrust sheet deformation at a ramp

A theoretical model for deformation of a thrust sheet at a ramp which takes into account (1) viscous deformation within the upper plate, (2) plastic deformation within the fault zone, and (3) gravity shows that the upper plate's resistance to deformation can be an important impediment to thrust sheet movement. Using representative parameters for the Pine Mountain block of Kentucky, Virginia, and Tennessee, upper plate bending resistance is shown to be of the same order as fault zone drag. Gravity can be either an important resisting force or a moderate aid in the motion of the thrust sheet depending on how the paleotopography at the time of thrust sheet motion is reconstructed. Two end‐member cases are considered. (1) In the ‘no erosion’ case the surface of the block mimics the shape of the fault zone. In this case, gravity is the largest resistance to movement, greater than either internal deformation or fault zone drag. (2) In the ‘stacking’ case, erosion is assumed to alter the topographic profile of the block and overlying sheets in such a way as to provide a surface slope in the direction of movement. Gravity in this case aids movement of the Pine Mountain block but cannot provide all the work necessary to move the upper plate at a ramp. A tectonic push is also required. The bending stresses are a significant portion of the total stress field and are responsible for the existence of zones of both potential normal and potential reverse faults in the model. An element of the sheet situated on the lower or upper surface of the block will, in traveling from the bottom to the top of the ramp, experience both normal and reverse faulting regimes. This is perhaps an explanation for the complex association of normal and reverse faults found in some major thrust sheets.