Non-rectangular Cross-sections Research Articles

Transverse energy loss slope in meandering channels

Limited research has been conducted on transverse energy loss in meandering channels. Previous studies made assumptions regarding a linear vertical profile of transverse velocity and rectangular cross sections with horizontal transverse beds, neglecting the effects of nonlinear transverse velocity profiles and transverse bed slopes that contribute to topographic steering. In this study, a novel expression for the transverse energy loss slope is derived analytically. This expression incorporates a nonlinear vertical distribution for transverse velocity and considers non-rectangular cross sections, thereby improving the computation of roughness coefficients in curved channels. A topographic steering number is introduced, which indicates the presence of topographic steering when it exceeds unity. The developed equation rectifies the previous underestimation of sinuosity in natural rivers when compared to existing equations. Additionally, an expression for superelevation is derived, accounting for channel roughness and transverse bed slope, unlike previous equations. The study reveals that roughness can significantly affect the height difference between outer and inner banks. Under higher roughness conditions, the height difference can exceed predictions from existing formulas by up to 50%. This emphasizes the importance of considering roughness effects in accurately estimating superelevation. The developed equations are validated through comparisons with available field, laboratory, and numerical data.

Enhancing the Mechanical Properties of Auxetic Metamaterials by Incorporating Nonrectangular Cross Sections into Their Component Rods: A Finite Element Analysis

Herein, four prevalent architectures of metamaterials, namely, the arc‐star, star, reentrant, and antichiral models, are examined to study the effects of the cross‐sectional shapes of component rods on the stiffness and Poisson's ratios of the materials. Four differently sized cross sections of rods are designed, and two types of cross‐sectional geometries—square and I‐shaped—are adopted. Aspect ratios of 0.5, 0.75, and 1 are considered for the I‐shaped cross‐sectional models. A total of 64 metamaterial models are analyzed. The results show that the stiffness and negative Poisson's ratios of the metamaterials depend primarily on their architectures. For example, the antichiral model exhibits approximately 13 times more stiffness than its arc‐star counterpart. The cross‐sectional geometries of the component rods also play an essential role in the mechanical behaviors of the metamaterials. For instance, the antichiral architecture, which consists of bars with an I‐shaped section that has a width‐to‐height ratio of 0.5, has an elastic modulus 9 times greater than that of the model composed of bars with a square cross section. This study shows that it is possible to design metamaterials several times stronger simply by changing the shape of the cross section of their constituent elements without compromising on their lightweight property.

A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges.

In the European standards specifying disc spring manufacturing, geometry, shape and characteristic, an edge rounding is prescribed. Common methods for the calculation of disc spring characteristics, even in these standards, are based on a rectangular cross-section. This discrepancy can lead to a considerable divergence of the computed characteristic from the characteristic determined by testing. In literature, this divergence has not yet been examined with regard to rounded edges. In this paper, a new method addressing this problem is introduced. For this purpose, the geometry of idealized disc springs is parameterized. Based on four edge radii and two angles of the inner and outer faces, equations to compute the initial cone angle and the lever arm are introduced. These equations are used to formulate an algorithm to adapt other computation methods to non-rectangular cross-sections and rounded edges. The method is applied to the formulas by Almen–Laszlo, Curti–Orlando, Zheng and those by Kobelev. FE simulations of disc springs with rounded edges and a non-rectangular cross-section were used to verify the new formulas. The results show that the introduced method can be applied to known characteristic computation methods and result in a model expansion taking cross-section variations into account. The adjusted characteristics show more accurate alignment to the FE simulation for the cross-section variations investigated. These findings not only close the geometric gap between the manufacturing guidelines and the computation on an analytical basis, they also define a new parameter space for designs of disc springs and a corresponding force computation method to optimize spring characteristics.

Fin Cross-Section Shape Influence on Short Channel Effects of MuGFETs

Multiple-gate FETs is normally constructed on pre-etched silicon fins. These devices often present casual width variations along the silicon height; mostly caused by technological limitations of the fin definition process, due to non-ideal anisotropic etch. The resulting devices have, consequently, non-rectangular cross-sections, which can affect their electrical behavior. This work addresses the dependence of fin width non-uniformity on the occurrence of short-channel effects through comparative analysis, based on threedimensional numeric simulation of non-rectangular cross-section devices. The influence of the fin crosssection shape on electrical parameters showed to be dependent on channel length, becoming more sensible to the fin shape as the channel length is reduced, with better DC performance present on devices with bottom fin width smaller than top fin width due to the higher transconductance and lower output conductance, resulting on higher intrinsic voltage gain. For opposite fin shapes the total gate capacitance present higher values, beneficiating AC analog parameters, such as unit gain frequency.

A study on full interaction of water waves with moored rectangular floating breakwater by applying 2DV scaled boundary finite element method

The problem of interaction between water wave and moored rectangular floating breakwater is studied using the semi-analytical Scaled Boundary Finite Element Method (SBFEM) in a two-dimensional vertical plane. The current study applies a generalized solution process by locating the scaling center within the bounded sub-domains instead of the body of structure, resulting in a homogeneous SBFEM equation. In spite of the merits of such choice for the scaling center that makes possible the analysis of non-rectangular objects, the method is changed to numerical-analytical one with its consequences. Such numerical solution in the problem of water wave radiation and diffraction is validated by comparing the results with previous reported studies. The generality and robustness of the current SBFEM-based model is also examined for non-rectangular cross-sections of the floating breakwater. Focusing on the proposed SBFEM-based model, the full wave-rigid body interaction is analyzed for a moored rectangular floating structure. Moreover, in order to make the linear numerical modeling accurate, taking into account the nonlinear aspects of the interaction problem, the artificial damping coefficients are quantified, and the relevant formula is derived.

Generation of 3D Microparticles in Microchannels with Non-rectangular Cross Sections

Flow lithography in a conventional rectangular microchannel is limited to fabrication of particles for which only the shapes of top perimeters are controlled. We present a flow lithography technique for fabrication of microparticles of diverse 3D shapes and multiple layers using non-rectangular microchannels with designed cross sections that allow the creation of complex shapes and diverse cross-sectional shapes. Variations in cross-sectional shape allow high-throughput, on-demand production of microparticles in unconventional shapes such as tetrahedrons and pyramids. Multilayered 3D particles were generated in an enlarging triangular channel combined with on-chip PDMS valves, which allow particle alignment and fluid exchange. These 3D microparticles are expected to further expand the wide variety of applications of microparticles, especially in drug delivery and tissue engineering fields.

Performance and implementation of centrifugal serpentine micromixers with non-rectangular cross-section

The fluid flow and mixing characteristics of planar serpentine microchannels consisting of repeating S-shaped units was characterized both computationally and experimentally for Reynolds numbers Re < 100. In particular, it was found that using non-rectangular cross-sections with changing orientation for the geometrical units greatly enhances their mixing performance relative to standard rectangular profile serpentine channels. The optimization of the cross-section enables efficient mixing of two-fluid components at Reynolds numbers as low as 20, making these designs practical for chemical reaction engineering and biological assays platforms. A computational analysis of the cross-sectional flow structures present in this type of channels indicates that their enhanced performance is correlated with the formation of secondary transversal vortexes. In the optimal designs, their presence increases the mass transfer in the microchannel by both stretching the interface between the fluid components to be mixed, as well as by promoting chaotic advection.

Mixing Enhancement in Serpentine Micromixers with a Non-Rectangular Cross-Section.

In this numerical study, a new type of serpentine micromixer involving mixing units with a non-rectangular cross-section is investigated. Similar to other serpentine/spiral shaped micromixers, the design exploits the formation of transversal vortices (Dean flows) in pressure-driven systems, associated with the centrifugal forces experienced by the fluid as it is confined to move along curved geometries. In contrast with other previous designs, though, the use of non-rectangular cross-sections that change orientation between mixing units is exploited to control the center of rotation of the transversal flows formed. The associated extensional flows that thus develop between the mixing segments complement the existent rotational flows, leading to a more complex fluid motion. The fluid flow characteristics and associated mixing are determined numerically from computational solutions to Navier–Stokes equations and the concentration-diffusion equation. It is found that the performance of the investigated mixers exceeds that of simple serpentine channels with a more consistent behavior at low and high Reynolds numbers. An analysis of the mixing quality using an entropic mixing index indicates that maximum mixing can be achieved at Reynolds numbers as small as 20 in less than four serpentine mixing units.

Extreme block and boulder transport along a cliffed coastline (Calicoan Island, Philippines) during Super Typhoon Haiyan

This paper presents data and analysis for block and boulder transport during Super Typhoon Haiyan along a 4.5km long, low (5–12m) cliffed coastline in Calicoan Island, Eastern Samar, Philippines. Wave runup exceeding 15.2m elevation above mean sea level drove large limestone clasts, with volumes up to ~83m3, up to ~280m inland. A few very large clasts with volumes 65–132m3 were not transported by the waves. When combined with recent transport reported in May et al. (2015), Cox et al. (2016), and other literature, it is becoming increasingly clear that the largest blocks transported by storms overlie much of the tsunami transport range, increasing the difficulty in attributing the transport source without additional evidence. Comparison of present results with a global database of storm boulder transport shows a mass-elevation envelope outside of which no transport is observed.Initiation of motion criteria were extended to include non-rectangular cross-sections, which significantly reduces inferred velocities, particularly for overturning motion. These new relations were applied to the largest observed sliding and overturning boulders while considering coefficient uncertainties, and resulting velocity uncertainty was large enough that direct inference of wave heights would be problematic. Estimates of initiation velocities for cliff-edge boulders computed using lifting/joint-bounded relations were unreasonably large when compared to those for sliding and overturning boulders, suggesting that processes other than Bernoulli lift forces dominated at cliff edges.

Analytical Solution of Laplace and Poisson Equations Using Conformal Mapping and Kronecker Products

In this paper, using the eigenvalues and eigenvectors of symmetric block diagonal matrices with infinite dimension and numerical method of finite difference, a closed-form solution for exact solution of Laplace equation is presented. The method of this paper has applications in different states of boundary conditions like Neumann, Dirichlet, and other mixed boundary conditions. Using the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part of this paper, examples, like water seepage problem through the soil and torsion of prismatic bars, are presented. Finally, a method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross-sections utilizing conformal mapping.

Gravity currents produced by constant and time varying inflow in a circular cross-section channel: Experiments and theory

We investigate high-Reynolds number gravity currents (GC) in a horizontal channel of circular cross-section. We focus on GC sustained by constant or time varying inflow (volume of injected fluid ∝ tα, with α=1 and α > 1). The novelty of our work is in the type of the gravity currents: produced by influx/outflux boundary conditions, and propagation in circular (or semi-circular) channel. The objective is to elucidate the main propagation features and correlate them to the governing dimensionless parameters; to this end, we use experimental observations guided by shallow-water (SW) theoretical models. The system is of Boussinesq type with the denser fluid (salt water) injected into the ambient fluid (tap water) at one end section of a circular tube of 19 cm diameter and 605 cm long. The ambient fluid fills the channel of radius r* up to a given height H*=βr* (0 < β < 2) where it is open to the atmosphere. This fluid is displaced by the intruding current and outflows either at the same or at the opposite end-side of the channel. The two different configurations (with return and no-return flow) allow to analyze the impact of the motion of the ambient fluid on the front speed of the intruding current. For Q larger than some threshold value, the current is expected theoretically to undergo a choking process which limits the speed/thickness of propagation. Two series of experiments were conducted with constant and time varying inflow. The choking effect was observed, qualitatively, in both series. The theory correctly predicts the qualitative behavior, but systematically overestimates the front speed of the current (consistent with previously-published data concerning rectangular and non-rectangular cross-sections), with larger discrepancies for the no-return flow case. These discrepancies are mainly due to: (i) the variations of the free-surface of the ambient fluid with respect to its nominal value (the theoretical model assumes a fixed free-slip top of the ambient fluid), and (ii) mixing/entrainment effects, as shown by specific measurements of the open interface level and velocity profiles.

An extended finite element model for structural analysis of cracked beam-columns with arbitrary cross-section

In this paper, an efficient finite element model for the structural analysis of cracked beam-columns with arbitrary cross-sections is presented. For this propose the combination of a planar beam element with only displacement degrees of freedom and extended finite element method (XFEM) is used. This element is highly capable in modeling the effect of edge cracks on the structural behavior of beams under various loading and boundary conditions. The method is able to solve the problem related to cracked beams with non-rectangular cross-sections with much less computational efforts compared to the available extended finite element models. Numerical examples are given to demonstrate the accuracy and the efficiency of the present method. There is a good agreement between the results obtained by the proposed method and those obtained by ABAQUS XFEM.

Optimal control of flood diversion in watershed using nonlinear optimization

This study aims to develop a simulation-based optimization model applicable to mitigate hazardous floods in storm events in a watershed which consists of a complex channel network and irregular topography. A well-established model, CCHE1D, is used as the simulation model to predict water stages and discharges of unsteady flood flows in a channel network, in which irregular (i.e. non-rectangular and non-prismatic) cross-sections are taken into account. Based on the variational principle, the adjoint equations are derived from the nonlinear hydrodynamic equations of CCHE1D, which are to establish a unique relationship between flood control variables and hydrodynamic variables. The internal conditions at the confluence in channel network for solving the adjoint equations in a watershed are obtained. An implicit numerical scheme (i.e. Preissman’s scheme) is implemented for discretizing and solving the adjoint equations with the derived internal conditions and boundary conditions. The applicability of this integrated optimization model is demonstrated by searching for the optimal diversion hydrographs for withdrawing flood waters through a single floodgate and multiple floodgates into detention basins. Numerical optimization results show that this integrated model is efficient and robust. It is found that the single-floodgate control leads to an unfavorable speed-up in river flow which may create extra erosions in the channel bed; and multiple-floodgates diversion control diverts less flood waters, therefore can be a cost-effective control action. This simulation-based optimization model is capable of determining the optimal schedules of diversion discharge, optimal floodgate locations, minimum capacities of flood water detention basins in rivers and watersheds.

Shear Capacity of the Flange-Web Intersections of Brick Masonry Nonrectangular Sections

The monolithic structural action of various types of walls of flanged cross section and walls with engaged stiffeners or returns (nonrectangular sections) is critically dependent on the shear capacity of the interface between the components making up the section. An assessment of the shear capacity of the interface may also be required as part of the elastic or inelastic analysis of structural elements. Observation of past earthquake events has confirmed that effectively connected flanges also directly influence the seismic performance of nonrectangular sections by providing a more robust and seismically resistant structural element. To analyze the significance of the parameters that influence the vertical shear resistance of interfaces of flanged sections of masonry obtained using different types of bonding and bonding patterns (header units, shear connectors, and wire ties), a series of specimens with H-shaped cross sections was tested. The vertical shear capacity of the interface at the flange-web intersection was assessed in each case and compared to predicted code capacities. Considerable strength reserves and shear ductility were observed in almost all cases. Following the experimental study, a numerical investigation was carried out using a simplified micromodeling finite element approach. It showed that both the size of the specimen as well as the boundary and applied loading conditions on the flanges can significantly influence the observed vertical shear resistance of the interfaces of specimens with the same bonding pattern. Using the results of the numerical investigation, the critical parameters for a test to determine the vertical shear capacity of brick masonry nonrectangular cross sections are assessed and the governing parameters for a suitable shear test suggested.

An analysis on the dependence on cross section geometry of galloping stability of two-dimensional bodies having either biconvex or rhomboidal cross sections

Galloping is a well-known type of aeroelastic instability, but still difficult to predict as the relevant experimental data must first be obtained. Available information on non-rectangular cross-sections is scarce and non-systematic. The purpose of the present paper is to add new information gathered through static wind tunnel experiments. The effects of cross-sectional shape on the transverse galloping stability (according to the Glauert–Den Hartog criterion for galloping instability) of biconvex and rhomboidal cross-section bodies have been systematically analyzed. Measuring the aerodynamic coefficients and the pressure distributions along the body surfaces permits a better understanding of the galloping phenomenon and how the aerodynamic characteristics of the bodies evolve when changing parametrically the cross-section geometry from the known-case of the flat plate to the also known square or circular prisms. As a result of these investigations the potential unstable zones in the angle of attack – cross-section aspect ratio plane ( α , t / c ) are identified.

Archipelago strait exchange processes?an overview

Archipelagos consist of a set of islands forming a collection of basins interconnected by straits, and are typically characterized by widely varying spatial and temporal scales regarding geometry and forcing conditions. Focusing on the strait exchange parameterization, we describe an archipelago water exchange model in which the archipelago is subdivided into a network of discrete basins and interconnecting straits and where the time integration assumes a series of quasi-steady states. We propose an algorithm that should be sufficiently flexible to provide reasonable strait exchange estimates under the variety of forcing conditions encountered in the Stockholm archipelago. We start from the functional formulation of two-layer hydraulic theory, which allows numerical schemes to be designed that, given the forcing conditions at the ends of a given strait, distinguish between maximal and sub-maximal flow cases and solve the flow accordingly. We relax the assumption of two homogeneous layers when necessary, using an approximate method based on a self-similarity assumption and with the sea-level difference over the strait as an explicit part of the problem. This method allows exchange flows with two groups of layers to be solved for the same set of geometries that the pure two-layer theory can handle, including sill–contraction combinations and non-rectangular cross-sections. We further show how aspiration of dense water from below the sill crest can be quantified with hydraulic theory, and be included in the method for stratified strait exchange. Rotational control in wide straits and in parallel straits connecting the same two basins is treated with a simple but robust scheme. We evaluate the calculations with data from the Oxdjupet strait in the Stockholm archipelago. Simulations with a three-dimensional, non-hydrostatic numerical model are performed to compensate for sparsity in data.

Archipelago strait exchange processes—an overview

Archipelagos consist of a set of islands forming a collection of basins interconnected by straits, and are typically characterized by widely varying spatial and temporal scales regarding geometry and forcing conditions. Focusing on the strait exchange parameterization, we describe an archipelago water exchange model in which the archipelago is subdivided into a network of discrete basins and interconnecting straits and where the time integration assumes a series of quasi-steady states. We propose an algorithm that should be sufficiently flexible to provide reasonable strait exchange estimates under the variety of forcing conditions encountered in the Stockholm archipelago. We start from the functional formulation of two-layer hydraulic theory, which allows numerical schemes to be designed that, given the forcing conditions at the ends of a given strait, distinguish between maximal and sub-maximal flow cases and solve the flow accordingly. We relax the assumption of two homogeneous layers when necessary, using an approximate method based on a self-similarity assumption and with the sea-level difference over the strait as an explicit part of the problem. This method allows exchange flows with two groups of layers to be solved for the same set of geometries that the pure two-layer theory can handle, including sill-contraction combinations and non-rectangular cross-sections. We further show how aspiration of dense water from below the sill crest can be quantified with hydraulic theory, and be included in the method for stratified strait exchange. Rotational control in wide straits and in parallel straits connecting the same two basins is treated with a simple but robust scheme. We evaluate the calculations with data from the Oxdjupet strait in the Stockholm archipelago. Simulations with a three-dimensional, non-hydrostatic numerical model are performed to compensate for sparsity in data.

Nonlinear analysis and tests of steel-fiber concrete beams in torsion

An analytical approach for the prediction of the behaviour of steel-fiber reinforced concrete beams subjected to torsion is described. The analysis method employs a special stress-strain model with a non-linear post cracking branch for the material behaviour in tension. Predictions of this model for the behaviour of steel-fiber concrete in direct tension are also presented and compared with results from tests conducted for this reason. Further in this work, the validation of the proposed torsional analysis by providing comparisons between experimental curves and analytical predictions, is attempted. For this purpose a series of 10 steel-fiber concrete beams with various cross-sections and steel-fiber volume fractions tested in pure torsion, are reported here. Furthermore, experimental information compiled from works around the world are also used in an attempt to establish the validity of the described approach based on test results of a broad range of studies. From these comparisons it is demonstrated that the proposed analysis describes well the behaviour of steel-fiber concrete in pure torsion even in the case of elements with non-rectangular cross-sections.

Straight, Single‐Tapered Composite I‐Beams of Orthotropic Materials

Design methods for tapered members of multiple materials with nonrectangular cross sections are not available. This finite-element study of straight, single-tapered I-beams was conducted to aid in developing a rational design method for nonprismatic, I-shaped structural members of layered orthotropic materials. Particular emphasis is placed on wood composites. Taper geometry (O≤\Nθ\N≤\N6.3°) is considered in concert with the elastic constants of the web substrate. Comparisons of the stresses and deflections in a prismatic beam and a tapered beam of the same average depth and having the same elastic properties for the web are used to identify potential design considerations. The bending, vertical, and shear stress maximums are greater in the tapered beam than in the prismatic beam. In addition, the stresses are distributed differently if the beam is tapered rather than prismatic. For example, the maximum shear stress is not necessarily in the web. Deflection of the tapered member is 19% greater and occurs at 0.43\IL\N rather than at midspan.

Maximal Exchange in Channels with Nonrectangular Cross Sections

Abstract The functional formalism of Gill and Dalziel is extended for two-layer flows in nonrectangular cross sections. Exchange flow through channels with a range of different cross sections is investigated in detail. Hydraulic transitions are found to play the same role in controlling the flow as in channels with rectangular cross sections. The response of the flow to different alongchannel geometries and net flow rates is qualitatively similar to that for rectangular cross sections but exhibits a number of novel features. In a channel of constant center line depth, the two hydraulic transitions do not coincide at the narrowest point unless the channel is symmetric about its middepth plane. For flow over a sill, the location of the virtual control is found to be a discontinuous function of the net flow rate, undergoing one or two jumps in position (depending on the precise geometry) as the net flow is altered. In the absence of friction and instabilities, it is not possible to eliminate the lower layer ...