Various methods for solving the partial contact of surfaces with regularly periodic profiles -which might arise in analyses of asperity level contact, serrated surfaces or even curved structures -have previously been employed for elastic materials. A new approach based upon the summation of evenly spaced Flamant solutions is presented here to analyze periodic contact problems in plane elasticity. The advantage is that solutions are derived in a straightforward manner without requiring extensive experience with advanced mathematical theory, which, as it will be shown, allows for the evaluation of new and more complicated problems. Much like the contact of a single indenter, the formulation produces coupled Cauchy singular integral equations of the second kind upon transforming variables. The integral equations of contact along with both the boundary and equilibrium conditions provide the necessary tools for calculating the surface tractions, often found in closed-form for regularly periodic surfaces. Various loading conditions are considered, such as frictionless contact, sliding contact, complete stick, and partial slip. Solutions for both elastically similar and dissimilar materials of the mating surfaces are evaluated assuming Coulomb friction.
Elastic-plastic contact of a smooth sphere and a half-space with a real machined surface is simulated using an integration-based multilevel contact model. The total surface deflection is composed of bulk and asperity deformations. They are calculated at the global and the asperity level, respectively, which are connected through the asperity-supporting load. With this new model, the accurate contact area and contact pressure under a given load are quickly predicted using a relatively coarse grid system. The calculated load-area curve shows good agreement with the experimental data. Finally, the effects of the surface topography, including roughness and the asperity radius, upon the real contact area are analyzed.
Turtle visual cortex has three layers and receives direct input from the dorsolateral geniculate complex of the thalamus. The outer layer 1 contains several populations of interneurons, but their physiological properties have not been characterized. This study used intracellular recording methods followed by filling with Neurobiotin to characterize the morphology and physiology of two populations of layer 1 interneurons. Subpial cells have somata positioned in the outer third of layer 1 and dendrites confined within the band of geniculate afferents that runs from lateral to medial across visual cortex. Their dendrites are composed of a sequence of many beads or varicosities separated by intervaricose segments. They have membrane time constants of tau(o) = 45.5 +/- 5.2 ms and electrotonic lengths of 1.1 +/- 0.2. Subpial cells show spike rate adaptation in response to intracellular current pulses. Stellate cells have somata located in the inner two-thirds of layer 1 and, less frequently, in layers 2 and 3. Their dendrites extend in a stellate configuration across the cortex. They are smooth or sparsely spiny, but never bear distinct varicosities. They have membrane time constants of tau(o) = 155.1 +/- 12 ms and electrotonic lengths of 3.8 +/- 0.5. They show little spike rate adaptation in response to intracellular current pulses. The positions of the two populations of cells in visual cortex and their physiological properties suggest that subpial cells may participate in a feedforward inhibitory pathway to pyramidal cells, whereas stellate cells are involved in feedback inhibition to pyramidal cells.
The normal contact of a frictionless elastic coated cylinder indented by a flat rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. The boundary conditions are chosen such that the elastic layer rests on the cylindrical substrate. When the contact region is small compared to the radius of curvature of the coated cylinder, semi-analytical solutions are obtained by exploiting dual series equation techniques. The stresses on the surface are evaluated for plane strain. The results may have application to coated cylindrical structures, bimaterial inclusions, or pin-joint contact.
The normal contact of a frictionless, elastic curved beam indented by a flat, rigid surface is solved using a Michell–Fourier series expansion, which satisfies the mixed boundary value problem resulting from partial contact. When the contact region is small compared to the radius of curvature of the beam, semi-analytical solutions are obtained by exploiting dual series equation techniques. The relation between the level of loading and the extent of contact, as well as stress on the surface, are found for plane strain. The elasticity results extend Hertz line contact to finite thickness, curved beams. As the beam becomes thin, beam theory type behavior is recovered. The results may have application to finite-thickness wavy surfaces, cylindrical structures, or pressurized seals.
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