scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

Numerical study for the improvement of bead spreading architecture with modified nozzle geometries in additive manufacturing of polymers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Easir Arafat Papon ◽  
Anwarul Haque ◽  
Muhammad Ali Rob Sharif
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
3D Printing ◽  
Cross Section ◽  
Nozzle Exit ◽  
Cross Sectional ◽  
Content Type ◽  
The Cross ◽  
Viscous Polymer ◽  
Sectional Shape

Purpose This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles. Design/methodology/approach The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations. Findings The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces. Originality/value The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Erythrocyte Sedimentation Rates in Inclined Vessels

1973 ◽  
Vol 51 (9) ◽  
pp. 685-690 ◽  
Author(s):  
R. N. O'Brien ◽  
M. B. Hocking ◽  
P. McOrmond ◽  
K. R. Thornton
Keyword(s):  
Cross Section ◽  
Sedimentation Rates ◽  
Settling Rate ◽  
Cross Sectional ◽  
Erythrocyte Sedimentation ◽  
The Cross ◽  
Sectional Shape ◽  
Erythrocyte Sedimentation Rates ◽  
Test Rack ◽  
Settling Rates

The rates of erythrocyte settling have been investigated in round and square cross-section tubes, vertically; and at nine different angles; and with the square tubes flat and on edge, to a minimum of 15° from the horizontal. Apparent settling rates increased as the angle from the horizontal decreased. Real settling rates (vertical settling rates) increased sharply on decreasing the angle from the horizontal, to a maximum at about 60°, and then decreased less abruptly for the shallower angles. The cross-sectional shape of the tube did not significantly affect the settling rates of erythrocytes. Settling in inclined tubes proceeds fast enough to permit clinical erythrocyte settling rate (E.S.R.) tests to be carried out in 10 min in place of the usual 60 min. If the standard E.S.R. test rack deviates as little as 5° from the vertical it can cause the observed settling rates to double relative to readings obtained on a vertical rack.

Semicrystalline Structure and Mechanical Properties of Polyolefin-Based Materials

2012 ◽  
Vol 441 ◽  
pp. 713-716
Author(s):  
Mizue Kuriyagawa ◽  
Koh Hei Nitta
Keyword(s):  
Mechanical Properties ◽  
Cross Section ◽  
Draw Ratio ◽  
Structural Model ◽  
Point Of View ◽  
Cross Sectional ◽  
Molecular Weights ◽  
The Cross ◽  
Sectional Shape ◽  
Structural Point

The mechanical yielding and necking behaviors of metallocene-catalyzed high density polyethylenes were investigated from a structural point of view. In particular the natural draw ratio was investigated with different crosshead speeds, molecular weights, and the cross-section shapes of sample specimens. We proposed a structural model for explaining the necking formation in addition to the molecular weight and the cross-sectional shape dependences of the natural draw ratio.

scholarly journals ЩОДО ПИТАННЯ ПРО РАЦІОНАЛЬНУ ФОРМУ ПРЕСОВАНОГО БУЛЬБОКОСИНЦЯ

2020 ◽  
pp. 165-172
Author(s):  
А. Г. Дибир ◽  
А. А. Кирпикин ◽  
Н. И. Пекельный
Keyword(s):  
Service Life ◽  
Residual Stresses ◽  
Cross Section ◽  
Transverse Load ◽  
Shear Stresses ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape ◽  
Aircraft Panels ◽  
Better Than

In airplane building and helicopter engineering a bulb angle bar  an angle bar with a bulb at the end of a wall are widespread. They are better than a simple angle bar, since they have higher critical stresses under compression more than the proportionality limit. They are better than T bar, as T bar are fastened with two rows of rivets, which impairs tightness. Bulb angle bar are better than Z bar. The latter are higher, which reduces the structural height of the cross section and increases the load on the panel and usually have an excess cross-sectional area. Bulb angle bars are widely used in the structure of metal fuselages of airplanes and helicopters, in the tail boom of helicopters, in the wing and tail unit of light aircraft, in flaps, ailerons and rudders. However, modern the bulb angle bar have a significant drawback.When a bulb angle bar is loaded by a transverse load from the skin in the wing structure, tail unit, fuselage, except of normal stresses from bending of the stringer with attached skin, supported by ribs or frames, additional normal and shear torsional stresses arise. This torsion is caused by the fact that the lateral load is not applied at the center of the bend. Additional stresses reduce the service life and tightness of the structure in this place. An altered cross-sectional shape of the bulb is proposed for use in light aircraft panels to increase their strength and service life. The change in shape had a significant impact on the location of the center of the bend in the cross section. The determination of the position of the center of the bend in the balloncube was carried out using the Wagner model with walls not working for shear stresses. The modified cross-sectional shape of the bulbogon allowed to reduce the level of residual stresses after the panels were assembled, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly in the panels. It is recommended to drill holes for rivets in the stringer in the middle of the entire width of its shelf, taking into account the wall.A modified cross-sectional shape of a corner with bulb is proposed for use in light aircraft panels. The change in shape had a significant impact on the location of the center of the bend in the cross section. This made it possible to reduce the level of residual stresses after the assembly of the panels, to rationally transfer the load from the casing to the stringer and to improve the technology of their assembly.

Bounds on the Maximum Thermoelastic Stress and Deflection in a Beam and Plate

1966 ◽  
Vol 33 (4) ◽  
pp. 881-887 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Thermoelastic Stress ◽  
Cross Sectional ◽  
Special Cases ◽  
End Conditions ◽  
Instantaneous Temperature ◽  
The Cross ◽  
Sectional Shape

It is shown in this paper that the thermal stress in a beam or plate cannot exceed the value kαEΔT, where ΔT is the maximum instantaneous temperature excursion in a cross section, and k is a coefficient dependent on the shape of the cross section. A simple general formula for k is found, and results for several special cases of practical interest are given. For rectangular beams (suitably oriented) and for plates, for example, k = 4/3. For any section, k = 1 if the thermal moment is zero; simplifications also occur if the thermal force is zero. The corresponding results for beam deflections are also carried out: The maximum deflection cannot exceed the value kδ kδ′αLΔT, where kδ and kδ′ are coefficients depending respectively on the cross-sectional shape and on the end conditions. For example, for rectangular cross sections, kδ = 3/4; and for a simply supported beam, kδ′ = 1/8.

scholarly journals INFLUENCE OF UNDERGROUND MINE PARAMETERS ON THE VALUE OF DAYLIGHT SURFACE SETTLEMENT OF UNDERMINED TERRITORY

2020 ◽  
Vol 11 (2) ◽  
pp. 5-18
Author(s):  
O. A Bogomolova ◽  
A. V Zhidelev
Keyword(s):  
Elastic Modulus ◽  
Cross Section ◽  
Lateral Pressure ◽  
Pressure Coefficient ◽  
Underground Mine ◽  
Cross Sectional ◽  
Lateral Pressure Coefficient ◽  
Vertical Displacements ◽  
The Cross ◽  
Sectional Shape

The article presents the analysis results of influence of shape and dimensions of cross-section, laying depth of mine, cross-section shape and dimensions of underground mine on the daylight surface settlement of undermined territory depending on the different numerical values of the soil lateral pressure coefficient of the surrounding soil. The numerical solution was obtained in an elastic setting using the computer programs «FEA» and «Stability». In the calculations, the elastic modulus of the enclosing rocks is taken equal to the dimensionless constant E /γ H = 500 (where γ; H are the rocks volumetric weight and laying depth of mine), therefore, the numerical values of the vertical displacements gained as a result of the calculations are also dimensionless. This approach is convenient for both quantitative and qualitative analysis, because not only specific values of vertical displacements are considered, but also change patterns of their values depending on changes in the numerical values of the variables of the calculated parameters. Assuming that the displacements in the linear formulation of the problem are inversely proportional to the elastic modulus, their magnitudes can be determined for any other value of E . It was established the vertical displacements of earth’s surface points located above the mine, provided that the depth of its laying is more than 15.2 m and the dimensions of the cross section are greater than 4×4 m, significantly depend on the shape of the cross section and the lateral pressure coefficient of the surrounding rock. In addition, smaller vertical precipitation of the daylight surface corresponds to an underground mine having an exotic and «non-technological» cross section in the deltoid form. Therefore, the problem arises is to obtain such an optimal cross-sectional shape of the mine that would ensure the minimum precipitation of the earth's surface. The cross-sectional shape of the mine must be as “technological" as possible according to its advancement. The subject of further research is the solution of these problems.

scholarly journals Simulation of local head loss of drip-irrigation tape with integrated in-line emitters as a function of cross section

2020 ◽  
Vol 18 (4) ◽  
pp. e0210
Author(s):  
Yalin Wang ◽  
Xueliang Ju ◽  
Shijiang Zhu ◽  
Meng Li
Keyword(s):  
Cross Section ◽  
Drip Irrigation ◽  
Low Pressure ◽  
Head Loss ◽  
Three Gorges ◽  
Cross Sectional ◽  
Water Conservancy ◽  
The Cross ◽  
Sectional Shape ◽  
The Relationship

Aim of study: To investigate how the cross section of a drip-irrigation tape affects local head loss.Area of study: The work was carried out in the laboratory of Irrigation hydraulics, College of Water Conservancy and Environment, Three Gorges University, Yichang, Hubei province.Material and methods: Tapes with six different wall thicknesses were studied experimentally to determine the relationship between cross-section deformation, wall thickness, and pressure. Based on the experimental results, we determined the factors that influence local head loss in drip-irrigation tapes by numerical simulation and dimensional analysis.Main results: The cross-sectional shape of the drip-irrigation tape varied with pressure: under low pressure, the cross section was nearly elliptical. The cross-sectional shape of the tape strongly influenced the local head loss, which was inversely proportional to the 0.867th power of the flattening coefficient of the drip irrigation tape. We expressed the local head loss of a drip-irrigation tape equipped with integrated in-line emitters by considering the deformation of the cross section. Under the conditions used in this study, when the cross section is circular, the ratio of local head loss to frictional head loss was about 10% but, when the cross section is elliptical, this ratio increased to 15%.Research highlights: The shape of the cross section of a drip-irrigation tape is nearly elliptical under low pressure. Local head loss is inversely proportional to the 0.867th power of that is the flatting coefficient of the drip-irrigation tape. Local head loss is about 1.5 times for elliptical tape than circular tape.

Design of C-Frames Using Real-Coded Genetic Optimization Algorithms and NURBS

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Cross Section ◽  
Cross Sections ◽  
Design Parameters ◽  
Binary Representation ◽  
Cross Sectional ◽  
Search Spaces ◽  
The Cross ◽  
Sectional Shape ◽  
Real Coded Genetic Algorithms

Abstract C-frames constitute a large portion of machine tools that are currently used in industry. Examples of these frames include drilling machines, presses, punching and stamping machines, clamps, hooks, etc. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal and rectangular sections. This paper introduces a new methodology for designing the frame’s cross-section. The cross-sectional shape is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Real-coded genetic algorithms are known to outperform the simple binary representation genetic algorithms when dealing with continuous search spaces. The results showed that the optimal shape was a semi I/T-section with the material bulk related to the applied load.

Geometric Design of Rectangular Cross-Sectional Springs

2018 ◽  
Vol 920 ◽  
pp. 126-131
Author(s):  
Yeong Maw Hwang ◽  
D.S. Lin ◽  
Sheng Liang Lin
Keyword(s):  
Shear Stress ◽  
Cross Section ◽  
Maximum Shear Stress ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Rectangular Section ◽  
Cross Sectional ◽  
Short Side ◽  
The Cross ◽  
Sectional Shape

In order to study the influence of the cross-sectional shape on the stiffness of a spring, a finite element analysis software DEFORM is used to simulate and analyze the torsion of rectangular cross-section bars. The material of the bar is TS1800 SAE9254 and the cross-section of aspect ratio (w / h) is 1.5. From literature it is known that when the rectangular section bar is twisted, the shear stress at the four corners is zero, so elliptical corners can decrease the volume and increase the stiffness with the same volume. Five levels for the long side of the elliptical corner are set as 1 to 5 mm, and 3 levels are set for the short side. Torsion of the rectangular section bars under 15 kinds of geometric designs are simulated to find the preferred cross-sectional shape design by evaluating the cross-sectional area, load, and the maximum shear stress. The objective of the design is obtaining a uniform stress distribution with a larger spring stiffness and lighter weight. The optimal cross section of the bars is established as the spring geometry, and the pre-loading processing of the spring is simulated. The required load and the maximum shear stress data are obtained. The effects of load, cross-sectional area and maximum shear stress on the springs performance are investigated.

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