scholarly journals A Superellipse with Deformation and Its Application in Describing the Cross-Sectional Shapes of a Square Bamboo

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2073
Author(s):  
Weiwei Huang ◽  
Yueyi Li ◽  
Karl J. Niklas ◽  
Johan Gielis ◽  
Yongyan Ding ◽  
...  
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Deformation Parameter ◽  
Rotational Symmetry ◽  
Cross Sectional ◽  
Future Studies ◽  
Initial Application ◽  
Stem Development ◽  
The Cross ◽  
The Difference

Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry.

CALCULATION OF NON-STANDARD SINGLE CARGO HOOK

2021 ◽  
pp. 148-155
Author(s):  
В.И. Сероштан ◽  
П.В. Витчук ◽  
В.Ю. Анцев ◽  
Н.А. Витчук
Keyword(s):  
Cross Sections ◽  
Hot Stamping ◽  
Cross Sectional Area ◽  
Design Stage ◽  
Sectional Area ◽  
Current Standard ◽  
Cross Sectional ◽  
The Cross ◽  
The Difference ◽  
Positive Effect

Oднорогие грузовые крюки грузоподъемных кранов изготавливают способом горячей штамповки и свободной ковки. Действующим стандартом предусмотрено 26 типоразмеров заготовок грузовых крюков. Очевидно, что номенклатура стандартных однорогих грузовых крюков ограничена и не может удовлетворить всего многообразия требований при создании специальных грузоподъемных машин для конкретных условий. В случае применения нестандартных крюков или при нестандартной грузоподъемности крана проводится поверочный расчет крюка. В существующем упрощенном методе расчета однорогих грузовых крюков сечения крюка заменяют правильной трапецией без учета скруглений. Поэтому предложен уточненный метод расчета нестандартных однорогих крюков грузоподъемных кранов. Осуществлена проверка предлагаемого метода при помощи SolidWorks, доказана его точность. Проведен сравнительный анализ результатов вычислений по предлагаемому и существующему упрощенному методам. Сравнение расчетных площадей сечений грузовых крюков, полученных предлагаемым и упрощенным методами, показывает, что разница между ними для стандартных крюков колеблется в пределах 6-10%. В среднем площадь сечения крюка, полученная по предлагаемому уточненному расчету, меньше, чем по упрощенному на 8%. Результаты расчета точной площади поперечного сечения грузового крюка и полученные на их основе значения напряжений в опасных сечениях позволяют на стадии проектирования достичь оптимальной формы грузового крюка. Это позволит в процессе производства получить наименьшее значение металлоемкости грузового крюка, что положительно скажется на его себестоимости Load single-hooks for cranes are made by hot stamping and free forging. The current standard provides for 26 standard sizes of cargo hook blanks. Obviously, the range of standard single-horned cargo hooks is limited and cannot satisfy the whole variety of requirements when creating special lifting machines for specific conditions. In the case of using non-standard hooks or with non-standard crane lifting capacity, a verification calculation of the hook is carried out. In the existing simplified method for calculating one-horned load hooks, the cross-sections of the hook are replaced with a regular trapezoid without taking into account the fillets. Therefore, we propose a refined method for calculating non-standard single-horned hooks of hoisting cranes. We tested the method using SolidWorks and proved its accuracy. We carried out a comparative analysis of the results of calculations by the proposed and existing simplified methods. Comparison of the calculated cross-sectional areas of cargo hooks obtained by the proposed and simplified methods shows that the difference between them for standard hooks ranges from 6-10%. On average, the cross-sectional area ofthe hook, obtained according to the proposed refined calculation, is less than the simplified one by 8%. The results of calculating the exact cross-sectional area of the load hook and the values of stresses in dangerous sections obtained on their basis allow one at the design stage to achieve the optimal shape of the load hook. This will allow one in the production process to obtain the smallest value of the metal consumption of the cargo hook, which will have a positive effect on its cost

Comparison of the Cross Sectional Area, the Loss in Volume and the Mechanical Properties of LAE442 and MgCa0.8 as Resorbable Magnesium Alloy Implants after 12 Months Implantation Duration

2010 ◽  
Vol 638-642 ◽  
pp. 675-680 ◽  
Author(s):  
Martina Thomann ◽  
Nina von der Höh ◽  
Dirk Bormann ◽  
Dina Rittershaus ◽  
C. Krause ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Cross Sections ◽  
Degradation Process ◽  
Cross Sectional Area ◽  
Bending Test ◽  
Sectional Area ◽  
Cross Sectional ◽  
Initial Strength ◽  
Three Point Bending ◽  
The Cross

Current research focuses on magnesium based alloys in the course of searching a resorbable osteosynthetic material which provides sufficient mechanical properties besides a good biocompatibility. Previous studies reported on a favorable biocompatibility of the alloys LAE442 and MgCa0.8. The present study compared the degradation process of cylindrical LAE442 and MgCa0.8 implants after 12 months implantation duration. Therefore, 10 extruded implants (2.5 x 25 mm, cross sectional area 4.9 mm²) of both alloys were implanted into the medullary cavity of both tibiae of rabbits for 12 months. After euthanization, the right bone-implant-compound was scanned in a µ-computed tomograph (µCT80, ScancoMedical) and nine uniformly distributed cross-sections of each implant were used to determine the residual implants´ cross sectional area (Software AxioVisionRelease 4.5, Zeiss). Left implants were taken out of the bone carefully. After weighing, a three-point bending test was carried out. LAE442 implants degraded obviously slower and more homogeneously than MgCa0.8. The mean residual cross sectional area of LAE442 implants was 4.7 ± 0.07 mm². MgCa0.8 showed an area of only 2.18 ± 1.03 mm². In contrast, the loss in volume of LAE442 pins was more obvious. They lost 64 % of their initial weight. The volume of MgCa0.8 reduced clearly to 54.4 % which corresponds to the cross sectional area results. Three point bending tests revealed that LAE442 showed a loss in strength of 71.2 % while MgCa0.8 lost 85.6 % of its initial strength. All results indicated that LAE442 implants degraded slowly, probably due to the formation of a very obvious degradation layer. Degradation of MgCa0.8 implants was far advanced.

Simulation of Flow Field on a Large Scale Wind Turbine

2008 ◽  
Author(s):  
I. Janajreh ◽  
C. Ghenai
Keyword(s):  
Flow Field ◽  
Wind Energy ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Cross Sections ◽  
Large Scale ◽  
Wind Farms ◽  
Operating Characteristics ◽  
Cross Sectional ◽  
Capital Costs

Large scale wind turbines and wind farms continue to evolve mounting 94.1GW of the electrical grid capacity in 2007 and expected to reach 160.0GW in 2010 according to World Wind Energy Association. They commence to play a vital role in the quest for renewable and sustainable energy. They are impressive structures of human responsiveness to, and awareness of, the depleting fossil fuel resources. Early generation wind turbines (windmills) were used as kinetic energy transformers and today generate 1/5 of the Denmark’s electricity and planned to double the current German grid capacity by reaching 12.5% by year 2010. Wind energy is plentiful (72 TW is estimated to be commercially viable) and clean while their intensive capital costs and maintenance fees still bar their widespread deployment in the developing world. Additionally, there are technological challenges in the rotor operating characteristics, fatigue load, and noise in meeting reliability and safety standards. Newer inventions, e.g., downstream wind turbines and flapping rotor blades, are sought to absorb a larger portion of the cost attributable to unrestrained lower cost yaw mechanisms, reduction in the moving parts, and noise reduction thereby reducing maintenance. In this work, numerical analysis of the downstream wind turbine blade is conducted. In particular, the interaction between the tower and the rotor passage is investigated. Circular cross sectional tower and aerofoil shapes are considered in a staggered configuration and under cross-stream motion. The resulting blade static pressure and aerodynamic forces are investigated at different incident wind angles and wind speeds. Comparison of the flow field results against the conventional upstream wind turbine is also conducted. The wind flow is considered to be transient, incompressible, viscous Navier-Stokes and turbulent. The k-ε model is utilized as the turbulence closure. The passage of the rotor blade is governed by ALE and is represented numerically as a sliding mesh against the upstream fixed tower domain. Both the blade and tower cross sections are padded with a boundary layer mesh to accurately capture the viscous forces while several levels of refinement were implemented throughout the domain to assess and avoid the mesh dependence.

scholarly journals Supplemental Material: Plate boundary trench retreat and dextral shear drive intracontinental fault-slip histories: Neogene dextral faulting across the Gabbs Valley and Gillis Ranges, Central Walker Lane, Nevada

2020 ◽  
Author(s):  
J. Lee ◽  
et al.
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Plate Boundary ◽  
Fault Slip ◽  
Cross Sectional ◽  
Walker Lane ◽  
Dextral Shear ◽  
The Cross

<div>Figure 6. Interpretative cross sections illustrating the cross-sectional geometry of several paleovalleys. See Figure 3 for location of all cross sections and Figure 8 for location of cross section CCʹ. Cross sections AAʹ and BBʹ are plotted at the same scale, and cross section CCʹ is plotted at a smaller scale. Figure 6 is intended to be viewed at a width of 45.1 cm.</div>

scholarly journals Mechanical Behavior of Damaged H-Section Steel Structure

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xibing Hu ◽  
Rui Chen ◽  
Yuxuan Xiang ◽  
Yafang Chen ◽  
Qingshan Li
Keyword(s):  
Cross Sections ◽  
Elastic Moduli ◽  
Mechanical Test ◽  
Steel Structure ◽  
Steel Structures ◽  
Computational Accuracy ◽  
Cross Sectional ◽  
Steel Columns ◽  
Steel Members ◽  
The Cross

Steel structures are usually damaged by disasters. According to the influence law of the damage on the elastic modulus of steel obtained by the mechanical test of damaged steel, the average elastic moduli of H-section steel members were analyzed. The equations for calculating the average elastic moduli of damaged H-section steel members at different damage degrees were obtained. By using the analytical cross-sectional method, the cross-sectional M-Φ-P relationships and the dimensionless parameter equations of the H-sections in the full-sectional elastic distribution, single-sided plastic distribution, and double-sided plastic distribution were derived. On the basis of the cross-sectional M-Φ-P relationships and dimensionless parameters of actual steel members, the approximate calculation equations for the damaged cross sections were obtained. The Newmark method was used to analyze the deformation of damaged steel columns. Analytical results show good agreement with the test results. The equations and methods proposed in this study have high computational accuracy, and these can be applied to the cross-sectional M-Φ-P relationships and deformation calculation of damaged steel members.

The Optimization Design of the Cross-Sectional Layout of an Umbilical Based on the Hybrid Genetic Algorithm

2021 ◽  
Author(s):  
Xu Yin ◽  
Zhixun Yang ◽  
Dongyan Shi ◽  
Jun Yan ◽  
Lifu Wang ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Cross Sections ◽  
Optimization Design ◽  
Mechanical Performance ◽  
Fitness Function ◽  
Hybrid Genetic Algorithm ◽  
Optimization Strategy ◽  
Cross Sectional ◽  
Great Probability ◽  
The Cross

Abstract The umbilical which consists of hydraulic tubes, electrical cables and optical cables is a key equipment in the subsea production system. Each components perform different physical properties, so different cross-sections will present different geometrical characteristic, carrying capacities, the cost and the ease of manufacture. Therefore, the cross-sectional layout design of the umbilical is a typical multi-objective optimization problem. A mathematical model of the cross-sectional layout considering geometric and mechanical properties is proposed, and the genetic algorithm is introduced to copy with the optimization model in this paper. A steepest descent operator is embedded into the basic genetic algorithm, while the appropriate fitness function and the selection operator are advanced. The optimization strategy of the cross-sectional layout based on the hybrid genetic algorithm is proposed with the fast convergence and the great probability for global optimization. Finally, the cross-section of an umbilical case is performed to obtain the optimal the cross-sectional layout. The geometric and mechanical performance of results are compared with the initial design, which verify the feasibility of the proposed algorithm.

Computational Investigation on the Dispersive Transport of Angiographic Contrast Injected Antegradely Into Flow in a Tube

2007 ◽  
Author(s):  
Qing Hao ◽  
Baruch B. Lieber
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Single Molecule ◽  
Molecular Diffusion ◽  
Local Concentration ◽  
Dispersive Transport ◽  
Cross Sectional ◽  
Advection Dispersion ◽  
The Cross ◽  
The Difference

When a solute such as angiographic contrast is introduced into a solvent such as blood analog fluid flowing in a straight circular tube, it spreads under the combined action of molecule diffusion and the variation of velocity over the cross-section [8]. If two molecules are being carried in the flow, for example, one in the center and one near the wall, the rate of separation caused by the difference in bulk velocity will greatly exceed that caused by molecule motion. Given enough time, any single molecule would wander randomly throughout the cross section of the pipe because of molecular diffusion, and would sample at random all the advective velocities [4]. Therefore, Taylor [8] adopted the Lagrangian approach to the problem, casting the equations in a coordinate system that moves with the average velocity of the flow and replacing the molecular diffusion coefficient with a dispersion coefficient, and the local concentration with the cross sectional mean concentration. Recasting Taylor’s equation in an inertial coordinate system one obtained the so called advection-dispersion equation.

The effect of crown position and tree age on resin-canal density in Scots pine (Pinus sylvestris L.) needles

2001 ◽  
Vol 79 (11) ◽  
pp. 1257-1261 ◽  
Author(s):  
Jinxing Lin ◽  
D A Sampson ◽  
R Ceulemans
Keyword(s):  
Pinus Sylvestris ◽  
Scots Pine ◽  
Cross Sections ◽  
Resin Canal ◽  
Tree Age ◽  
Needle Length ◽  
Cross Sectional ◽  
Crown Position ◽  
The Cross ◽  
Resin Canals

Resin canals are an important taxonomic characteristic in conifers. In this paper we examined within- and between-needle variation of the cross-sectional number of resin canals in Scots pine (Pinus sylvestris L.). Variation within needles was determined from 12 free-hand sections taken along the whole length of foliage collected from a common crown position. The effect of crown location and tree age on resin-canal density was also examined from the midpoint cross sections of 450 Scots pine needles collected from interior and exterior locations from the top, middle, and bottom of 25 crowns of trees ranging in age from 8 to 70 years. Within-needle resin-canal density varied with needle length. Two resin canals were typical for the basal and the terminal needle cross sections. There were 3.2 and 8.6 resin canals for cross sections taken from 10 and 30% of the needle length from the basal sheath, respectively. Resin-canal density was largest, and relatively constant, between 30 and 80% of the needle length. We found significant differences in the cross-sectional number of needle resin canals, as influenced by crown positions and tree age. Resin-canal density increased with foliage height. Foliage from the top one-third of crowns had significantly more resin canals than foliage from the bottom. Foliage collected from the crown interior (proximal to the stem) had fewer resin canals than samples from the crown edge. Resin-canal density increased from 7.1 to 10.3 as tree age increased from 8 to 70 years. These results suggest that crown position and tree age need to be incorporated into the sampling protocols used to establish species standards in resin-canal density, at least for Scots pine, if meaningful comparisons are to be made.Key words: resin canal, needle age, crown position, needle anatomy, Pinus sylvestris.

A Method of Form Selection for Large Scale Structures

2002 ◽  
Author(s):  
Damiano Pasini ◽  
S. C. Burgess ◽  
D. J. Smith
Keyword(s):  
Cross Sections ◽  
Large Scale ◽  
Design Parameters ◽  
Cross Sectional ◽  
Geometrical Properties ◽  
Large Scale Structures ◽  
Shape Selection ◽  
Efficiency Parameter ◽  
Sectional Shape ◽  
Selection Of

This paper presents a new method for modelling the efficiency of large-scale structural forms. Parametric equations, which include all design parameters and also the effect of buckling, are developed. Shape transformers, envelope efficiency parameter and scaling factor are introduced to describe the geometrical properties of cross-sections and to allow interaction between form and cross-sectional shape selection. Design charts provide insight and understanding and assist the selection of different structural concepts at the preliminary stage of design.

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