An unconstrained integral approximation of large sliding frictional contact between deformable solids

International audienceThis paper presents a new integral approximation of frictional contact problems under finite deformations and large sliding. Similar to other augmented Lagrangian based formulations, the proposed method expresses impenetrability, friction and the relevant complementarity conditions as a non-smooth equation, consistently linearized and incorporated in a generalized Newton solution process. However, instead of enforcing the non-smooth complementarity equation in the already discretized system, a corresponding weak formulation in the continuous setting is considered and discretized through a standard Galerkin procedure. Such an integral handling of the contact and friction complementarity conditions, applied previously only to frictional contact problems under small deformations, is extended in the present paper to contact with Coulomb friction between solids undergoing large deformations. In total, the proposed method is relatively simple to implement, while its robustness is illustrated through numerical examples in two and three dimensions

Structural development of laminar flow control aircraft chordwise wing joint designs

For laminar flow to be achieved, any protuberances on the surface must be small enough to avoid transition to turbulent flow. However, the surface must have joints between the structural components to allow assembly or replacement of damaged parts, although large continuous surfaces can be utilized to minimize the number the number of joints. Aircraft structural joints usually have many countersunk bolts or rivets on the outer surface. To maintain no mismatch on outer surfaces, it is desirable to attach the components from the inner surface. It is also desirable for the panels to be interchangeable, without the need for shims at the joint, to avoid surface discontinuities that could cause turbulence. Fabricating components while pressing their outer surfaces against an accurate mold helps to ensure surface smoothness and continuity at joints. These items were considered in evaluating the advantages and disadvantages of the joint design concepts. After evaluating six design concepts, two of the leading candidates were fabricated and tested using many small test panels. One joint concept was also built and tested using large panels. The small and large test panel deflections for the leading candidate designs at load factors up to +1.5 g's were well within the step and waviness requirements for avoiding transition.The small panels were designed and tested for compression and tension at -65 F, at ambient conditions, and at 160 F. The small panel results for the three-rib and the sliding-joint concepts indicated that they were both acceptable. The three-rib concept, with tapered splice plates, was considered to be the most practical. A modified three-rib joint that combined the best attributes of previous candidates was designed, developed, and tested. This improved joint met all of the structural strength, surface smoothness, and waviness criteria for laminar flow control (LFC). The design eliminated all disadvantages of the initial three-rib concept except for unavoidable eccentricity, which was reduced and reacted satisfactorily by the rib supports. It should also result in a relatively simple low-cost installation, and makes it easy to replace any panels damaged in the field

Nonequilibrium Steady States of Driven Periodic Media

We study a periodic medium driven over a random or periodic substrate. Our work is based on nonequilibrium continuum hydrodynamic equations of motion, which we derive microscopically. We argue that in the random case instabilities will always destroy the LRO of the lattice. In most, if not all, cases, the stable driven ordered state is a transverse smectic, with ordering wavevector perpendicular to the velocity. It consists of a periodic array of flowing liquid channels, with transverse displacements and density (``permeation mode'') as hydrodynamic variables. We present dynamic functional renormalization group calculations in two and three dimensions for an approximate model of the smectic. The finite temperature behavior is much less glassy than in equilibrium, owing to a disorder-driven effective ``heating'' (allowed by the absence of the fluctuation-dissipation theorem). This, in conjunction with the permeation mode, leads to a fundamentally analytic transverse response for $T>0$. Our results are compared to recent experiments and other theoretical work.Comment: 39 PRB pages, RevTex and 9 postscript figures, uses multicol.st

Mapping rail wear transitions

This paper outlines work carried out to produce maps of rail material wear coefficients taken from laboratory tests run on twin disc and pin-on-disc machines as well as those derived from measurements taken in the field. Wear transitions are identified using the maps and defined in terms of slip and contact pressure. Wear regimes are related to expected wheel/rail contact conditions and contact points (rail head/wheel tread and rail gauge/wheel flange). Surface and sub-surface morphologies are discussed and comparisons are made between field and laboratory data

Mapping rail wear regimes and transitions

This paper outlines work carried out to produce maps of rail material wear coefficients taken from laboratory tests run on twin disc and pin-on-disc machines as well as those derived from measurements taken in the field. Wear regimes and transitions are identified using the maps and defined in terms of slip and contact pressure. Wear regimes are related to expected wheel/rail contact conditions and contact points (rail head/wheel tread and rail gauge/wheel flange). Surface morphologies are discussed and comparisons are made between field and laboratory data

Effective conductivity of composites of graded spherical particles

We have employed the first-principles approach to compute the effective response of composites of graded spherical particles of arbitrary conductivity profiles. We solve the boundary-value problem for the polarizability of the graded particles and obtain the dipole moment as well as the multipole moments. We provide a rigorous proof of an {\em ad hoc} approximate method based on the differential effective multipole moment approximation (DEMMA) in which the differential effective dipole approximation (DEDA) is a special case. The method will be applied to an exactly solvable graded profile. We show that DEDA and DEMMA are indeed exact for graded spherical particles.Comment: submitted for publication