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This is an analytical study on Stokes flow through a tube of which the wall is patterned with periodic transverse grooves filled with an inviscid gas. In one period of the pattern, the fluid flows through an annular groove and an annular rib subject to no-shear and no-slip boundary conditions, respectively. The fluid may penetrate the groove to a certain depth, so there is an abrupt change in the cross section of flow through the two regions. The problem is solved by the method of domain decomposition and eigenfunction expansions, where the coefficients of the expansion series are determined by matching velocities, stress, and pressure on the domain interface. The effective slip length and pressure distributions are examined as functions of the geometrical parameters (tube radius, depth of fluid penetration into grooves, and no-shear area fraction of the wall). Particular attention is paid to the limiting case of flow through annular fins on a no-shear wall. Results are generated for the streamlines, resistance, and pressure drop due to the fins. It is found that the wall condition, whether no-shear or no-slip, will be immaterial when the fin interval is smaller than a certain threshold depending on the orifice ratio. [DOI: 10.1115/1.4002654]

The vibration of a free standing column under its own weight is studied. An intermediate support increases the fundamental frequency. The optimum location for the support is determined for clamped-free, pinned-free, and sliding-free columns. The problem is integrated by a simple accurate initial value method. Approximate and exact relations are also found. [DOI: 10.1115/1.4001511] Keywords: column, vibration, heavy, support

The vibration of a standing (or hanging) segmented column, affected by its own weight, is studied. The governing difference equations are solved numerically. The results tend to those of the continuous column as the number of segments tends to infinity. For the finite number of segments, the linear relation between frequency squared and self weight does not hold as in the continuous case. [DOI: 10.111511.4000843] Keywords: vibration, column, heavy, segmented

An infinite beam attached to an elastic foundation is buckled by an axial force. The beam is weakened by one or more joints or partial cracks. The governing equations are solved analytically and an exact nonlinear characteristic equation gives the buckling criterion. It is found that the buckling force depends on the foundation stiffness and the rotational resistance of the joints. The buckling modes are complex, and may be either antisymmetric or symmetric. DOI: 10.1061/(ASCE)EM.1943-7889.0000097 CE Database subject headings: Buckling; Beams; Elastic foundation; Joints. Author keywords: Buckling; Beam; Elastic foundation; Joint.

The flow through a symmetric, lens-shaped duct is solved by accurate Ritz and perturbation methods. The flow rate (resistance) is found for various thickness ratios. The flow rate is much better than friction factor-Reynolds number product as an index for duct flows, especially for the lens duct studied in this paper. The results are also important for the torsion of lens-shaped bars.

The buckling of a column affected by both an internal hinge and an elastic foundation is studied analytically. It is found that the elastic foundation raises the buckling force, but nonlinearly. The optimum locations for the hinge are determined.

In most publications on vibration of annular plates, the natural frequencies are only presented for inner radius as small as one-tenth of its outer radius, but there are hardly any results presented for cores smaller than this inner radius value. This is attributed to severe scaling problems upon using numerical techniques to obtain the fundamental frequency of plates when the inner radius becomes very small. This study aims to solve this class of plate vibration problem where the annular plates are thick and their core radii are much less than one-tenth of the outer radius. The analysis involved using the Mindlin plate theory so as to allow for the effects of transverse shear deformation and rotary inertia and the truncation of the terms in the Bessel functions defining the characteristic equations in order to overcome the scaling problem. Eventually, the fundamental frequency of a thick annular plate could be deduced as finite or zero when the inner radius approaches zero. DOI: 10.1061/(ASCE)0733-9399(2007)133:5(597) CE Database subject headings: Vibration; Plates; Frequency.

The slow film flow down a doubly periodic bumpy surface is studied for the first time. Perturbations on the primary variables and the complex boundary conditions lead to a system of successive equations. The secondary flow and the free surface shape depend on the wavelength of the bumps and a surface tension-inclination parameter There exists an optimum aspect ratio of the protuberances for maximal flow rate. [DOI: 10.1115/1.2060730]

The buckling problem of a column weakened at an interior location is studied for the first time. The weakness is modeled by a rotationally restrained junction. Exact buckling load values are obtained for the weakened column with various end conditions. Depending on the end conditions of the column, the buckling loads show sensitivity (and insensitivity) to junction location and rotational stiffness. The optimum location of the junction could be at the midpoint, at the ends, or somewhere in between. CE Database subject headings: Buckling; Columns; Joints.

This paper examines applicability and limitations of simplified models of elastic cylindrical shells for carbon nanotubes. The simplified models examined here include Donnell equations and simplified Flugge equations characterized by an uncoupled single equation for radial deflection. These simplified elastic shell equations are used to study static buckling and free vibration of carbon nanotubes, with detailed comparison to exact Flugge equations of cylindrical shells. It is shown that all three elastic shell models are in excellent agreement (with relative errors less than 5%) with recent molecular dynamics simulations for radial breathing vibration modes of carbon nanotubes, while reasonable agreements for various buckling problems have been reported previously for Donnell equations. For general cases of buckling and vibration, the results show that the simplified Flugge model, which retains mathematical simplicity of Donnell model, is consistently in better agreement with exact Flugge equations than Donnell model, and has a significantly enlarged range of applicability for carbon nanotubes. In particular, the simplified Flugge model is applicable for carbon nanotubes (with relative errors around 10% or less) in almost all cases of physical interest, including some important cases in which Donnell model results in much larger errors. These results are significant for further application of elastic shell models to carbon nanotubes because simplified shell models, characterized by a single uncoupled equation for radial deflection, are particularly useful for multiwall carbon nanotubes of large number of layers.

The difference equations governing the rotation of a segmented rod under axial force is formulated. The stability boundaries are found to be highly dependent on the number of links, the rotation rate and the compressive force. For a large number of links, the result approaches to that of the continuous elastic rod through some fractional power. The analysis is applicable to segmented drill shafts.

Blood flow in small curved tubes is modeled by the two-fluid model where a relatively cell-free fluid layer envelops a fluid core of higher viscosity. The parameters in the model are successfully curve fitted to experimental data for straight tubes. The curved tube equations are then solved by perturbation theory. It was found that curvature in general lowers the tube resistance, but increases the shear stress near the inside wall

This paper presents the Ritz method for buckling analysis of rectangular plates with an internal line hinge. The Ritz method involves the domain decomposition method to cater for the discontinuity of slope at the hinge line. The correctness of the Ritz formulation and solutions is confirmed by the exact solutions derived using the Levy method for plates with two opposite sides simply supported. Based on the Ritz method, buckling factors are generated for rectangular plates of various aspect ratios, hinge locations, and support and loading conditions. DOI: 10.1061/(ASCE)0733-9399(2003) 129:6(683) CE Database subject headings: Buckling; Plates; Hinges.

The viscous flow in a curved tube with partial slip on the boundary occurs in many practical situations. The problem is formulated in curved tube coordinates and solved by perturbation for small curvature. The mutual interaction of slip, curvature, and inertia causes changes in the axial flow, surface shear, and secondary flow. It is found that the net flow increases with increased slip and decreased Reynolds numbers.

Presented herein are exact stability criteria for Euler columns under intermediate and end concentrated axial loads. The stability criteria cover all combinations of classical boundary conditions, arbitrary location of the intermediate concentrated load, and ratios of the magnitude of the intermediate load to the end load. Also included is the buckling problem of a new class of Euler columns where one segment is in tension while the other segment in compression. CE Database subject headings: Columns; Buckling; Axial loads; Stability criteria.

Cutting test specimens from molded plaques is commonly used in mechanical testing. The mechanical properties of these cut specimens may be affected by cutting process as it could introduce extrinsic [...]

The radially symmetric, steady, slow viscous slip flow through a curved duct of rectangular cross section is studied. The Stokes equation is solved using eigenfunction expansions and Navier's slip condition. As slip is increased, the location of the maximum velocity moves from near center to the outer wall. The minimum velocity occurs at the inside corners. It is found that both slip and curvature promote the flow rate but not necessarily the mean velocity. [DOI: 10.1115/1.1445142]

This paper is concerned with the determination of the funicular shapes of submerged arches. A universal set of curves is generated, from which the shapes of funicular arches under hydrostatic forces may be extracted. The method of extraction of the funicular arch shape depends on the specified design parameters such as the water depth, arch height, and arch span. More importantly, this study shows that depending on the specification of the design parameters, there may not exist any funicular arch solution or there may be occasions in which there could be more than one funicular arch solution for the problem. DOI: 10.1061/(ASCE)0733-9445(2002)128:2(266) CE Database keywords: Arches; Hydrostatic pressure; Structural design.

Onset of convection in a fluid-saturated porous layer above a solid layer heated by constant flux is discussed. Thermoconvective stability of a porous layer over a solid layer is important in ocean floor hydrothermal systems and thermal insulation problems. The critical Rayleigh number for the porous layer increases with solid-layer thickness. That is the reverse of the case for constant-temperature heating. Topics include the impermeable top and constant-pressure top cases. Results are compared to those of R. McKibbin et al., 1983.

The torsion of a compound bar is studied by eigenfunction expansion and collocation. The bar has a regular polygonal cross section bonded with a circular core of different material. It is found that the torque is insensitive to the core size when the latter is less than 0.2 of the maximum dimension. Otherwise, the torque is highly dependent on the core size ratio and the shear moduli ratio of the two materials. The results obtained should be useful in the design of torsion members.

A study on dendritic alloy solidification was conducted to investigate the grain structural development and columnar-to-equiaxed transition during directional dendritic solidification using the NH4Cl-H2O model alloy. The experiment is the first phase of a continuing effort to ultimately model and simulate the columnar-to-equiaxed transition in the presence of crystal sedimentation and melt convection using a multiphase model developed by two researchers in a previous study.

Research is conducted to examine the thermal conductivity of composite materials. The process involves the development of closed-form solutions of the thermal effect of a composite with a single thin fiber. Numerical results for a composite containing an infinite staggered array of thin strips is then presented. Results reveal that stagger may be used to increase or decrease conducting without changing the amount of materials in the composite.

Research was conducted to study steam injection in a water-saturated two-dimensional reservoir utilizing a two-phase mixture model. Numerical analyses were based on the two-phase mixture model wherein boundary conditions were given in relation to the mixture pressure. Results showed that the cumulative displaced mass per unit of cross sectional area for various injection fluxes was directly proportional to time. They also indicated that superheated steam can help mobilize residual liquid to achieve complete recovery.

The efficient method of eigenfunction expansion and point match is used to solve the Stokes flow through a channel with transverse fins. Both in-phase and staggered fins are considered. Streamlines and resistances are found in terms of fin height and fin spacing. Extrapolating to large spacings, the added resistances due to a single pair of aligned fins and that of a single fin in a channel are obtained.

The boundary layer analysis of buoyancy-driven two-phase flow in capillary porous media reveals that the boiling boundary layer is wider than the condensing boundary layer. A two-phase crossflow pattern represents both the boiling and the condensing flow. The unsaturated flow theory is invalid for the condensing flow, and a two-phase model predicts the capillary effect on film condensation heat transfer.

Solutions to the Stokes equation for the rotation of finite, coaxial cylinders are achievable by integrating the concepts of domain decomposition, collocation, and eigenfunctions. A solid cylinder rotates within a larger, fluid-filled cylindrical enclosure. The method requires lesser computations compared to direct integrations and is useful for designing rotating cylinders at low Reynolds number. The case of a finite cylinder rotating in an infinite fluid is discussed.

The laminar, viscous flow between parallel plates with evenly spaced longitudinal ribs is solved by an eigenfunction expansion and point-match method. The ribs on both plates may be symmetrically placed or staggered. For a given pressure gradient, the mean velocity is plotted as a function of the geometric parameters. We find the wetted perimeter and the friction factor - Reynolds number product are unsuitable parameters for the flow through ducts of complex geometry.

A two-dimensional porous chamber which has a horizontal baffle extending from the side wall, exhibits convective unsteadiness. Steady low and high temperatures are reflected in the top and bottom respectively, but the side walls are insulated. The assumed steady baffle temperature affects the constancy of the chamber. A longer baffle does not guarantee steadiness but closeness of the center results in constancy. The upper part of the chamber reveals the beginning of the convection. The single cell is penetrated by increased baffle length, leading to four replicated cells indicating the beginning of the convection.

A viscous shear flow moves parallel to a wavy plate. Partial slip occurs on the wavy surface. The problem is solved by perturbation about a small amplitude parameter, namely, the amplitude to wavelength ratio. It is found that the interaction of waviness and slip decreases the apparent slip coefficient. [DOI: 10.1115/1.4002197] Keywords: viscous flow, slip, wavy, shear

THE THIRD HYPERVARIABLE REGION ([V.sub.3.)] of the human immunodeficiency virus-1 (HIV-1) external envelope glycoprotein (gp120) contains a cysteine loop that constitutes the PND [1-6]. A relatively conserved GPGR [7] sequence [...]

Blood flow in a small tube (30-1000 [micro]m) can be successfully modeled by the two-fluid model. The fully developed, constant heat flux convective heat transfer problem is studied. The velocity and temperature profiles are determined in closed form. Formulas for friction-factor-Reynolds number product, axial temperature gradient, and Nusselt number are found. [DOI: 10.1115/1.2898722] Keywords: blood flow, two fluid, heat

The temperature distribution of a curved barrier heated by constant flux on one side is studied. Both the right-angled corner and the rounded corner are solved by the method of domain decomposition and matching. It is found that hot spot temperatures may reach 2.5 times that of a fiat barrier but may be tempered with appropriate rounding at the corner: [DOI: 10.1115/1.1629105]

This paper studies the effect of a rotationally restrained base on the buckling of a standing column subjected to both its own weight and a tip load. The characteristic equation is derived analytically in terms of Bessel functions. The results show stability is greatly compromised when the base is not securely fixed. Rotational spring constants for some simple base constraints are estimated. DOI: 10.1061/(ASCE)0733-9399(2003)129:1(117) CE Database keywords: Columns; Buckling; Loads.

A long partially filled membrane container rests on an incline. The governing nonlinear equations are solved numerically. Similarity solutions that lead to universal shapes are found. The relationships among inclination, volume, and tension are illustrated. DOI: 10.1061/(ASCE)0733-9399(2002) 128:2(249) CE Database keywords: Membrane; Containers; Shape.

The bridle sling lifting of a flexible beam is analyzed. For a given sling length, the optimum attaching locations for minimal maximum bending are found.

The global critical load is an extremely useful index for flexible structures under large disturbances. The present technical note determines this index for a two-dimensional rigid solid supported by two flexible columns. The buckling and postbuckling problem is solved by a homotopy algorithm applied to a Galerkin formulation of the nonlinear elastica equations. The present results show the bifurcation curve is quite sensitive to an elevated mass center. The global buckling load is greatly reduced although the critical buckling load of linear stability analysis remains the same, showing that the linear stability index or bifurcation load is entirely erroneous in predicting the safe load under finite disturbances for flexible structures with elevated mass centers.

Study of the impact of longitudinal corrugations on torsional rigidity and maximum shear stress requires the perturbation theory as the basis of the solution. Exact solutions are established using conformal mapping, separation of variables and direct integration. The corrugations are the result of inaccurate machining.

A semianalytical technique, describing the diffusive transport across a wavy plate comprising annular sectors, reveals that the heat transfer is three times more at a concave site than in a convex site. Wavy plates have a greater surface area and flux transfer than a flat plate and are widely used in mechanical and biological systems. The wavy plates are applied to walls that increase heat transfer and the internal folds of the small intestine.

The optimum placement of heat sources to satisfy the minimum temperature requirements with the least total thermal energy input is analyzed. Models are derived for the placement of single, multiple and ring heat sources. Results show that the total minimum energy decreases as the number of sources increase. The use of multiple heating sources can result into savings of up to 25%. It is also more efficient to heat single larger areas than a number of smaller ones.

Functionally graded materials (FGMs) have been highly considered as candidate materials for applications in severe environments confronting modern technologies. The study reveals that by optimizing the processing conditions, and superheat, one can engineer a desired gradient in the solidified part.

The buckling of a circular plate on an elastic foundation is studied analytically. The buckling mode may not be axisymmetric as previously assumed. [DOI: 10.1115/1.1988347]

The eigen function and point-match method helps analyze the heat transfer across a bilayer composite cylinder with partial debonding. Presence of debonding leads to the generation of regions of high local temperatures near the inside surface. Increase in the inner radius increases the maximum temperature in cylinder with partial debonding.

A model is developed for the pressing of a two-dimensional thin sheet into a convex corner based on equations for a concave corner. Although general equations are the same, boundary conditions are different. Results show that an infinite pressure at a high rate is needed to force the sheet into a right angle. Thus, in designing pressure molds convex corners should first be rounded using the model at the highest possible pressure.