Convex Cross-section Research Articles

ANALYSIS OF GEOMORPHOLOGICAL CHARACTERISTICS OF SKIING TRACKS FOR TOURISTIC POTENTIAL EVALUATION OF UKRAINIAN CARPATHIANS

The aim of the paper is to evaluate the quality of skiing tracks in the Ukrainian Carpathians. To do this we suppose to define a set of geomorphological characteristics of skiing tracks and determine theirs influence value on the tracks specialization and its suitability for skiing, also assess the touristic potential of the ski resorts of the Ukrainian Carpathians.
 Methods and approaches of research borrowed from a similar study on the avalanches danger estimation of other ski resorts. We obtained a number of geomorphological characteristics of the tracks and visually estimated the quality of its bed using created lengthwise and cross-section profiles of skiing slopes using a digital relief model. The visual analysis identified the areas for braking, as well as significant inequalities, protracted areas and track parts with inversed inclination which make worse the quality of the skiing and is danger the skiers.
 So the main research method is the cartographic modeling. We selected 7 ski resorts located in different parts of the Ukrainian Carpathians. The profiles were created using free Geographic Information System QGIS and open geospatial data of radar survey of the Earth's surface (SRTM and ASTER GDEM). We also compared received results with foreign similar studies. Scientific novelty. There are defined the set of geomorphological characteristics of a ski slope in the article. There are the length of the track (or its horizontal projection), the level difference and the derivative characteristic is the steepness of the slope (as well as its maximum and minimum values). This list was supplemented by cross-section profiles description (it may be convex, bent, flat or inclined). Altogether we compared 24 tracks of the Ukrainian Carpathians. There are created lengthwise and cross-section profiles for each of them and all results put into a table presented in the article.
 Practical results. We made a conclusion that the skiing slopes of the Ukrainian Carpathians have similar geomorphological characteristics in most cases. The average slope of the tracks is 9.5°. The maximum value is 13° and the minimum is about 3°. The length of the tracks varies from 1 to 4 km and the length of majority of them is not excites of 1.8 km. The height difference is from 50 m to 550 m, the average mean is 315 m, which is not quite long. The configurations of the most horizontal profiles are convex or even, which is not optimal for skiing. In addition, the presence of hills makes “blind zones” which limit the visibility of the track and can cause a collision of skiers. Most of skiing track beds has convex cross-section profiles or they are significantly declined, which is also not an advantage.
 Based on the received metric values we defined the weak and strong sides of the national resorts. The ski slopes haven’t many complexity categories and are interesting for amateur skiers. Therefore the national resorts give way to foreign ones even located in the Carpathians which have a greater variety and more levels of complexity of tracks. This circumstance can be an obstacle to maintenance of tracks and increase requirements for corresponding equipment. So national skiing resorts should focus on pricing policies and territorial accessibility.

Analytic description of nanowires II: morphing of regular cross sections for zincblende- and diamond-structures to match arbitrary shapes.

Setting out from our recent publication [König & Smith (2021). Acta Cryst. B77, 861], we extend our analytic description of the regular cross sections of zincblende- and diamond-structure nanowires (NWires) by introducing cross section morphing to arbitrary convex shapes featuring linear interfaces as encountered in experiment. To this end, we provide add-on terms to the existing number series with their respective running indices for zinc-blende- (zb-) and diamond-structure NWire cross sections. Such add-on terms to all variables yield the required flexibility for cross section morphing, with main variables presented by the number of NWire atoms NWire(dWire[i]), bonds between NWire atoms Nbnd(dWire[i]) and interface bonds NIF(dWire[i]). Other basic geometric variables, such as the specific length of interface facets, as well as widths, heights and total area of the cross section, are given as well. The cross sections refer to the six high-symmetry zb NWires with low-index faceting frequently occurring in the bottom-up and top-down approaches of NWire processing. The fundamental insights into NWire structures revealed here offer a universal gauge and thus enable major advancements in data interpretation and the understanding of all zb- and diamond-structure-based NWires with arbitrary convex cross sections. We corroborate this statement with an exact description of irregular Si NWire cross sections and irregular InGaAs/GaAs core-shell NWire cross sections, where a radially changing unit-cell parameter can be included.

Bending Stability of Corrugated Tubes With Anisotropic Frustum Shells

Abstract Thin-walled corrugated tubes that have a bending multistability, such as the bendy straw, allow for variable orientations over the tube length. Compared to the long history of corrugated tubes in practical applications, the mechanics of the bending stability and how it is affected by the cross sections and other geometric parameters remain unknown. To explore the geometry-driven bending stabilities, we used several tools, including a reduced-order simulation package, a simplified linkage model, and physical prototypes. We found the bending stability of a circular two-unit corrugated tube is dependent on the longitudinal geometry and the stiffness of the crease lines that connect separate frusta. Thinner shells, steeper cones, and weaker creases are required to achieve bending bi-stability. We then explored how the bending stability changes as the cross section becomes elongated or distorted with concavity. We found the bending bi-stability is favored by deep and convex cross sections, while wider cross sections with a large concavity remain mono-stable. The different geometries influence the amounts of stretching and bending energy associated with bending the tube. The stretching energy has a bi-stable profile and can allow for a stable bent configuration, but it is counteracted by the bending energy which increases monotonically. The findings from this work can enable informed design of corrugated tube systems with desired bending stability behavior.

Thermal analysis of moving porous fin wetted by hybrid nanofluid with trapezoidal, concave parabolic and convex cross sections

In this study, the thermal performance of moving porous fin wetted with hybrid nanofluid with different cross-sections in the presence of a magnetic field is investigated. As an innovation, three different cross-sections) trapezoidal, concave parabolic and convex (have been used. The Shape-factor effect of hybrid nanoparticles is also considered in the equations. After extracting the governing equations and converting the PDE equations to ODE by Similarity solution, the equations are solved by Akbari-Ganji's method. The boundary conditions are an insulated tip with a finite length, and thermal functions for heat transfer coefficient and conductivity have been assumed. The impacts of several characteristics on the dimensionless temperature are thoroughly investigated, including Peclet number, thermal conductivity parameter, emissivity parameter, heat transfer coefficient parameter, convective–conductive parameter, and radiative–conductive parameter. The results show that Akbari-Ganji's method has good accuracy in solving heat transfer equations related to moving porous fin. Also, increasing the Peclet number increases the dimensionless temperature, because increasing the Peclet number causes the fin to move faster.

Thermal Analysis of Moving Porous Fin Wetted by Hybrid Nanofluid with Trapezoidal, Concave Parabolic and Convex Cross Sections

Thermal Analysis of Moving Porous Fin Wetted by Hybrid Nanofluid with Trapezoidal, Concave Parabolic and Convex Cross Sections

Optimization of a Convex Rail Design for Electromagnetic Launchers

A rail geometry with a convex cross section instead of a rectangular one provides a higher contact area, uniform current density, and less transition on the contact surface, and it increases the performance in electromagnetic launchers. In addition, the design of convex rails should be considered together with armature structure, the distance between rails, rail length, and parasitic masses that all have an influence on the overall efficiency and armature/rail transition. A novel complete rail and launch package optimization method is presented in this article. In the first part of this article, the optimum convex rail cross sections for five different separation values are found to obtain uniform current density distribution on rail cross section. For this part, a transient finite element (FE) model in 2-D is developed to calculate the current density distribution and combined with a real-coded genetic algorithm (GA). Then, the armature and sabot petal masses are calculated for each optimized rail geometry and each separation values. In the second part, the efficiency of each optimum design with different separation values is evaluated by a transient 3-D FE model with transient solver taking the calculated armature and sabot petal masses into account. Finally, the length of the rails of the final design is investigated for the transition phenomena. It is observed that 48-mm rail separation with 12.9- and 21-mm elliptical cross-sectional parameters has the highest exit velocity (2355 m/s) for 400-g projectile with uniform current density at inner rail surfaces.

Investigation of Side-Dam Plate in Single-Wheel Caster for Casting Rods

The cross section of a thin rod cast by a single-wheel caster, for which the wheel cross section is an inverted trapezoidal groove, is concave. To make the cross section convex, an inner side-dam plate is proposed. A single-wheel caster with a flat wheel (without a groove) and rotating side-dam plates is also proposed. 5182 aluminum alloy rods with a convex or rectangular cross section can be cast. The area of the rod is smaller than 150 mm2. The diameter of the converted circle area is 15 mm.

Листовидные бифасы в комплексах начального верхнего палеолита Южной Сибири и севера Центральной Азии

An important component of the study of the complexes of the initial Upper Paleolithic (IUP) is the selection of marker tools – products with certain morphological properties and a specific chronological and territorial binding. One of the markers for the industries of the military-industrial conflict of Southern Siberia and the north of Central Asia are leaf-shaped and oval bifaces. These tools are flattened, have either a biconvex or a convex cross section, the elongated edges are characterized by bifacial, sometimes parallel retouch. Such products are have been documented in the early Upper Paleolithic industries throughout the region. Mostly they are represented by single single objects in the aeemblages. The largest collection of leaf-shaped bifaces was documented in the Derbinsky Bay of the Krasnoyarsk Reservoir (middle course of the Yenisei River). Most often, the leaf-shaped bifaces are combined with sharp pointed tools with the base of the trimming, tronki products and plates with a dulled edge.

Multi-metal 4D printing with a desktop electrochemical 3D printer

4D printing has the potential to create complex 3D geometries which are able to react to environmental stimuli opening new design possibilities. However, the vast majority of 4D printing approaches use polymer based materials, which limits the operational temperature. Here, we present a novel multi-metal electrochemical 3D printer which is able to fabricate bimetallic geometries and through the selective deposition of different metals, temperature responsive behaviour can thus be programmed into the printed structure. The concept is demonstrated through a meniscus confined electrochemical 3D printing approach with a multi-print head design with nickel and copper used as exemplar systems but this is transferable to other deposition solutions. Improvements in deposition speed (34% (Cu)–85% (Ni)) are demonstrated with an electrospun nanofibre nib compared to a sponge based approach as the medium for providing hydrostatic back pressure to balance surface tension in order to form a electrolyte meniscus stable. Scanning electron microscopy, X-ray computed tomography and energy dispersive X-ray spectroscopy shows that bimetallic structures with a tightly bound interface can be created, however convex cross sections are created due to uneven current density. Analysis of the thermo-mechanical properties of the printed strips shows that mechanical deformations can be generated in Cu-Ni strips at temperatures up to 300 °C which is due to the thermal expansion coefficient mismatch generating internal stresses in the printed structures. Electrical conductivity measurements show that the bimetallic structures have a conductivity between those of nanocrystalline copper (5.41 × 106 S.m−1) and nickel (8.2 × 105 S.m−1). The potential of this novel low-cost multi-metal 3D printing approach is demonstrated with the thermal actuation of an electrical circuit and a range of self-assembling structures.

Fabrication of Aluminum Alloy Rods Using a Single Wheel Caster with Rotating Side Dam Plates and Pool-Less Pouring

A single wheel caster equipped with rotating side dam plates was proposed and assessed in conjunction with a pool-less pouring method as a compact and economical system for producing metal rods. The diameter and width of the single wheel were 600 and 10 mm, respectively, while those of the rotating side dam plates were 200 and 15 mm. Both were made from mild steel and rotated at the same speed. This system was tested using 5182 aluminum alloy at a casting speed of 5 m/min, and it was determined that rods with convex cross-sections could be formed with cross-sectional areas ranging from 75 to 135 mm2.

A general approach to fast prototype the topology of braided structures

The braiding technique has been adapted to fabricate advanced composite structures. One of the most important advantages of braiding technique is that it can form a continuous and integrated part on complex shapes which is highly challenging by other composite manufacturing methods. However, the design and analysis methodologies of braided composites such as finite element analysis are limited even with computer aided tools due to the complexity of the realistic 3D representations of braided structures. The general strategy is to use multi-scale models to account for elastic constants at each hierarchy where material properties are homogenized. If one could directly use the topology of the braided structure in the finite element analysis, there is no need to perform multi-scale analysis on the part. In this paper, we propose a general method to generate 3D representations of braided structures using explicitly expressed formulas. Kinematics of braiding, discretization of an arbitrary centerline curve, and definition of convex cross-sections along the braiding directions are the foundations required to derive the 3D geometrical representation of a braided structure on complex shape mandrel presented in the proposed method. The topology of braided structure generated by the model is validated by the physical structures which are digitized into STL file by 3D laser scanning. A finite element model based on the topology is also performed to demonstrate the robustness of the model. The model is a computationally inexpensive and versatile applicable for any non-straight and non-concave shape mandrel given that it is braidable.

Effects of the thickness on the stability of axially moving viscoelastic rectangular plates

The differential quadrature method is employed to solve the differential equation governing the in-plane moving rectangular viscoelastic plate with concave or convex cross sections. The boundary conditions of the plate are specified as simply supported-free (SFSF) and clamped-simply supported (CSCS). Plots showing the influence of the cross section's form on the plate’s stability are presented and it is observed that the plate generally undergoes divergence instability but coupled mode instability also occurs for SFSF boundary conditions. Coupled mode instability appears when the cross-section is convex or varies linearly. Also, the increase of the thickness ratio plays an increasing role on the critical instability values of the moving speed.

Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method

A simple solution to propagation problem in open waveguides and dielectric fibers of arbitrary convex cross section is presented. The idea of the analysis is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. A complex root tracing algorithm is utilized to find the propagation coefficients of the investigated guides. Different convex shapes of the guides are analyzed, and the obtained results are compared with the alternative solutions to verify the validity of the proposed method.

Analysis and Design of a Polygonal Oblique Beam for the Butterfly Vibratory Gyroscope with Improved Robustness to Fabrication Imperfections.

This paper focuses on structural optimization of a Butterfly vibratory gyroscope (BFVG). An oblique suspension beam adopting polygonal cross-section is proposed in order to enhance the sensitivity and robustness. The operation principles of the BFVG are introduced. The suspension beam, which was found to be the key component, is selectively stressed. Varying cross sections of the suspension beam, including parallelogram, pentagon, hexagon, platform of pentagon, L-shaped and convex shapes are compared with each other. In particular, in order to show the advantages of the proposed polygonal cross-section, the convex cross-section is used as a reference. The influence of fabrication imperfections, which includes alignment error, silicon thickness error, etching depth error, upper width error, bottom width error and deep reactive-ion etching (DRIE) verticality error, on the oblique beam’s spindle azimuth angle of the two cross-sections is analyzed. Further, the quadrature error of two cross-sections with a fabrication defect is analyzed. The theoretical arithmetic results suggest that a polygonal cross-section beam is much more stable than a convex cross-section beam in most cases. The robustness of the fabrication imperfection is improved nine-fold and the quadrature error due to fabrication defect is reduced by 70 percent with a polygonal cross-section. It could be a better candidate for BFVG’s oblique beam, which would provide a gyroscope with good robustness and repeatability.

Core geometry for recriticality prevention against CDA in sodium-cooled fast reactor

In core disruptive accident (CDA) of sodium-cooled fast reactors (SFRs), fuel and steel can melt to form a molten pool. The objective of the present work is to investigate design measures for core of SFR to prevent recriticality. This paper studied core geometry of convex cross-section shape to increase neutron leakage from core surface in case of core compaction. In order to evaluate effective neutron multiplication factor, 70-group neutron diffusion calculations were performed by changing parameters related to the convex core geometry (i.e. ratio of inner height to inner diameter). Neutron diffusion code and nuclear data library employed in those calculations are CITATION and JENDL-3.3, respectively. By optimizing core configuration, the compaction reactivity of the convex shaped core showed drastic reduction from 2.07 % of reference cylindrical core (Japan Sodium-cooled Fast Reactor) to -3.28 %.

An automated procedure for the generation and conformal discretization of 3D woven composites RVEs

A generation tool is developed for complex three dimensional textile reinforced composites Representative Volume Elements (RVEs). This integrated methodology takes into account contact conditions between yarns with polygonal convex cross sections by means of an iterative geometry generation scheme. The tensioning of the yarns is applied in an implicit geometrical manner resulting in their movement leading to contacts between them. The non-circular shape of their cross sections requires the use of a rotational degree of freedom to describe their movement. This rotational degree of freedom is managed during the contact solving procedure. A level set-based post-processing is then used at the end of RVE the generation to automatically supress any residual interpenetration, that further enables controlling the volume fraction (Vyarn) of each family of yarns in the RVE. A thin clearance can also be inserted between yarns during the post processing phase in order to ease the subsequent conforming mesh generation. An implicit geometry-based meshing procedure is subsequently used to produce a high quality discretization of the obtained RVEs. This integrated procedure is used for various woven and 3D RVEs to illustrate its versatility, showing that the discretized RVEs can be used for parametric studies based on computational homogenisation.

Computing Ellipsoidal Robust Forward Invariant Tubes for Nonlinear MPC

Min-max differential inequalities (DIs) can be used to characterize robust forward invariant tubes with convex cross-section for a large class of nonlinear control systems. The advantage of using set-propagation over other existing approaches for tube MPC is that they avoid the discretization of control policies. Instead, the conservatism of min-max DIs in tube MPC arises from the discretization of sets in the state-space, while the control law is never discretized and remains defined implicitly via the solution of a min-max optimization problem. The contribution of this paper is the development of a practical implementation of min-max DIs for tube MPC using ellipsoidal-tube enclosures. We illustrate these developments with a spring-mass-damper system.

Korn inequalities for shells with zero Gaussian curvature

We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero principal longitudinal curvature and positive circumferential curvature, including, for example, cylindrical and conical shells with arbitrary convex cross sections. We prove that the best constant in the first Korn inequality scales like thickness to the power 3/2 for a wide range of boundary conditions at the thin edges of the shell. Our methodology is to prove, for each of the three mutually orthogonal two-dimensional cross-sections of the shell, a “first-and-a-half Korn inequality”—a hybrid between the classical first and second Korn inequalities. These three two-dimensional inequalities assemble into a three-dimensional one, which, in turn, implies the asymptotically sharp first Korn inequality for the shell. This work is a part of mathematically rigorous analysis of extreme sensitivity of the buckling load of axially compressed cylindrical shells to shape imperfections.

Inverse Design of Cooling Arrays of Micro Pin-Fins Subject to Specified Coolant Inlet Temperature and Hot Spot Temperature

ABSTRACTGiven a micro pin-fin array cooling scheme with these constraints: (a) given maximum allowable temperature of the material (the hot spot temperature), (b) given inlet cooling fluid temperature, (c) given total pressure loss (pumping power affordable), and (d) given overall thickness of the entire micro pin-fin cooling array, find the maximum possible average heat flux on the hot surface and find the maximum possible heat flux at the hot spot under the condition that the entire amount of the inputted heat is removed by the cooling fluid. The goal was to create an optimum performance map for a cooling micro array having specified inlet coolant temperature and maximum temperature. Fully 3D conjugate heat transfer analysis was performed on each of the randomly created candidate configurations. Response surfaces based on Radial Basis Functions were coupled with a genetic algorithm to arrive at a Pareto set of best trade-off solutions. These Pareto optimized configurations indicate the maximum physically possible heat fluxes for specified material and constraints. Detailed off-design performance maps of such Pareto-optimized cooling arrays of micro pin-fins were calculated that demonstrate superior on-design and off-design performance of pin-fins having symmetric convex cross sections as opposed to the commonly used circular cross sections.

Failure criteria for cohesive‐frictional materials based on Mohr–Coulomb failure function

SummaryThis study presents two three‐parameter failure criteria for cohesive‐frictional materials based on the Mohr–Coulomb failure function. One proposed failure criterion can be linked to Mogi's empirical formula and incorporates the well‐known Von‐Mises, Drucker–Prager, and Linear Mogi criteria as special cases. Another one with smooth and convex cross sections contains a general Lode dependence in the deviatoric plane and includes the Matsuoka–Nakai and Lade–Duncan Lode dependences as special cases. The effect of the intermediate principal stress on the strength of the material can be taken into account in both criteria. The proposed criteria are numerically calibrated against polyaxial data sets of many different types of rocks and concrete. The comparison results show that the performance of the proposed criteria is excellent, and the failure criterion with a general Lode dependence performs better than the other one for concrete. Copyright © 2015 John Wiley & Sons, Ltd.