scholarly journals Construction of Unknotted and Knotted Symmetric Developable Bands

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 431
Author(s):  
Johannes Schönke ◽  
Michael Grunwald ◽  
Eliot Fried
Keyword(s):  
Rotational Symmetry ◽  
Machine Design ◽  
Circular Cylinders ◽  
Structural Elements ◽  
Bending Energy ◽  
Torus Knots ◽  
Practical Applications ◽  
Maximum Value ◽  
Rectangular Strip ◽  
Conveyor Belts

We describe a method for constructing developable bands with N ≥ 3 half twists. Each band is formed by threading a flat rectangular strip through a scaffold made from identical circular cylinders and smoothly connecting its short ends. The N cylinders in a scaffold are arranged with N-fold rotational symmetry. The number of half twists in a band is equal to the number N of cylinders in its scaffold and each band inherits the symmetry of its scaffold. Each scaffold admits a family of bands of the same length but variable width up to a maximum value determined by the features of the scaffold. Apart from orientable and nonorientable unknots, our method allows for the construction of bands with the topology of torus knots. We detail the geometric properties of the construction, discuss certain fundamental restrictions that must be met to ensure constructability, and calculate the elastic bending energy of each band. The rotational symmetry underlying the construction is essential for obtaining the presented bands, as the general non-symmetric problem is even more complex and has not yet been investigated. The bands and their corresponding scaffolds can be used as structural elements in practical applications, one of which we describe and analyze. The construction serves as a basis for a general framework for building a large variety of scaffolds and the corresponding unstretchable bands. Together, these assemblies can be used in architectural, interior, and machine design. They also open new avenues for the layout of conveyor belts in factories, airports, and other settings.

Design Under Arctic Conditions: A Summary of the Arctic Materials Project Guideline

2018 ◽  
Author(s):  
Agnes Marie Horn ◽  
Erling Østby ◽  
Odd Akselsen ◽  
Mons Hauge
Keyword(s):  
Cost Effective ◽  
Offshore Structures ◽  
International Standards ◽  
Hydrocarbon Exploration ◽  
Thickness Effect ◽  
The Arctic ◽  
Structural Elements ◽  
Practical Applications ◽  
Arctic Materials ◽  
Offshore Industry

The main goal of the 10 years Arctic Materials KMB project run by SINTEF (2008–2017) and supported by the industry is to establish criteria and solutions for safe and cost-effective application of materials for hydrocarbon exploration and production in arctic regions. The objective of the arctic materials project guideline (PG) is to assist designers to ensure safe and robust, yet cost-effective, design of offshore structures and structural elements in arctic areas through adequate material testing and requirements to material toughness. It is well known that when the temperature decreases, steel becomes more brittle. To prevent brittle fracture in the Arctic, the structure needs adequate toughness for the loading seen at low temperatures. None of the common offshore design codes today consistently address low temperature applications. In this respect, arctic areas are defined as minimum design temperatures below what current international standards have considered per today, i.e. −10 °C to −14°C. For practical applications, the PG defines arctic areas as minimum design temperature lower than −10 °C. It is acknowledging that design standards to a certain degree are based on operational and qualitative experiences gained by the offshore industry since the 1970’s. However, for arctic offshore facilities, limited operational experiences are gained by the industry. The basis of the guideline is that safe and robust design of structures and structural elements are ensured by combining standard industry practice today with learnings and findings from the 10 years Arctic Materials project. This paper is concerned with the rationale behind the material and test requirements provided in the arctic material guideline. The material requirements will be discussed in detail with emphasis on toughness requirement, constraint effect, thickness effect, acceptance criteria and material qualification criteria.

scholarly journals Advances of Italian Machine Design

Machines ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 61 ◽  
Author(s):  
Ceccarelli ◽  
Carbone
Keyword(s):  
Machine Design ◽  
Special Issue ◽  
Practical Applications ◽  
International Collaborations ◽  
Recent Developments ◽  
Italian Community

This Special Issue is aimed to promote and circulate recent developments and achievements in the field of Mechanism and Machine Science coming from the Italian community with international collaborations and ranging from theoretical contributions to experimental and practical applications [...]

Integrated Thermal Conduction and Hardenability Laboratory Activity

2013 ◽  
Author(s):  
Natasha L. Smith ◽  
Brandon S. Field
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Machine Design ◽  
Engineering Curriculum ◽  
Laboratory Activity ◽  
One Dimensional ◽  
Practical Applications ◽  
Transformation Curve ◽  
Transient Thermal ◽  
Quench Test

This paper describes an integrated laboratory project between separate heat transfer and machine design courses. The project was structured around a Jominy end quench hardenability test. Most of the students participating were simultaneously enrolled in both classes. In the heat transfer class, students were required to model one-dimensional, transient thermal conduction for an end quench geometry of 4140 steel. In machine design, students applied their theoretical temperature profiles to a continuous cooling transformation curve (CCT) of 4140 steel to predict microstructure and matched the theoretical cooling rates with hardenability curves from literature to predict hardness. In laboratory, students then performed an end quench test in accordance with ASTM A255 on four steel rods. By combining activities across the two courses, students developed an appreciation for the interconnectivity of material within the engineering curriculum, and learned that practical applications typically require they employ knowledge from a variety of sources.

scholarly journals Finite element modeling of bearing elements technological machines and equipment

2018 ◽  
Vol 226 ◽  
pp. 04010
Author(s):  
Sergey I. Yevtushenko ◽  
Sergey A. Alekseev ◽  
Igor A. Petrov ◽  
Vladimir E. Fedorchuk
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Bearing Capacity ◽  
Front Axle ◽  
Structural Elements ◽  
Conveyor Belts ◽  
Technical Production ◽  
Combine Harvester ◽  
And Performance ◽  
Plastic Containers

The paper considers the examples of technical production tests to determine the bearing capacity of the structural elements of technological machines and equipment used in various industries and agriculture: the bearing beam of the front axle of the combine harvester, fixed support plates of the apparatus for the production of plastic containers, bearing profiles of the thermal press designed to connect the ends of conveyor belts of various sizes, etc. The nature of stress distribution and deformations in the elements of the existing variants of technological machines and equipment allowed to identify shortcomings in their design. Analysis of calculations in ANSYS environment allowed to recommend variants of models of technological machines and equipment with better indicators of bearing capacity. This will greatly improve their reliability and performance.

Bending Stability of Corrugated Tubes with Anisotropic Frustum Shells

2021 ◽  
pp. 1-18
Author(s):  
Zhongyuan Wo ◽  
Evgueni Filipov
Keyword(s):  
Cross Sections ◽  
Tube Length ◽  
Bending Energy ◽  
Reduced Order ◽  
Stability Behavior ◽  
Practical Applications ◽  
Corrugated Tube ◽  
History Of ◽  
The Cross ◽  
Linkage Model

Abstract Thin-walled corrugated tubes that have a bending multi-stability, 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.

Stress Distribution in Bonded Dissimilar Materials With Cracks

1965 ◽  
Vol 32 (2) ◽  
pp. 403-410 ◽  
Author(s):  
F. Erdogan
Keyword(s):  
Mixed Boundary ◽  
Dissimilar Materials ◽  
Relative Displacement ◽  
Concentrated Load ◽  
Temperature Changes ◽  
Practical Applications ◽  
Maximum Value ◽  
Peculiar Characteristic ◽  
Arbitrary Location ◽  
External Loads

The problem of two bonded dissimilar semi-infinite planes containing cracks along the bond is reconsidered. The external loads considered include the tractions on the crack surfaces, in-plane moments, residual stresses due to temperature changes, concentrated load and couple acting at an arbitrary location in the plane, and one-sided wedge loading of the crack. The stresses along the bonds are calculated and shown in graphs. In the example of wedge loading, the stress state and displacements in the vicinity of the crack tip are more closely studied; and the bonding stress σ and the relative displacement v1 − v2 along the crack are plotted as functions of log(r/a). It was found that, even though the stresses and displacements oscillate as r approaches zero, for the example of glass-steel bond the first zero of σ occurs around (r/a) = 10−10.63, and at a distance (r/a) = 10−10 the stress-concentration factor has already exceeded 104. Similarly, the region within which relative displacements oscillate is 0 < (r/a) < 10−7, and the maximum value of interference becomes v2 − v1 = P10−9.7, P (lb/in.) being the wedge load. It was concluded that, considering the magnitudes of distances and stresses involved, in practical applications the phenomenon of stress oscillation, which seems to be a peculiar characteristic of mixed-boundary-value problems of linear infinitesimal elastostatics, may be ignored.

An Overview of Synchronization Methods of Grid Fundamental Signal

2014 ◽  
Vol 494-495 ◽  
pp. 1779-1783
Author(s):  
Zhi Xia Zhang ◽  
Jiu Long Wang ◽  
Chang Liang Liu
Keyword(s):  
Filter Method ◽  
Fundamental Wave ◽  
Transform Method ◽  
Large Power ◽  
Zero Crossing ◽  
Practical Applications ◽  
Maximum Value ◽  
The Fourier Transform ◽  
Grid Interconnection ◽  
System Power

The synchronization signals of the grid fundamental wave are applied to various fields, such as power protection system, power quality system, and large power grid interconnection. As new problems emerging during the development of the grid, the synchronization methods keep continuous improved. These methods appeared in accordance with the time sequence are zero crossing detection method, the maximum value algorithm, the Fourier transform method, filter method, and phase locked loop method. In this paper, the typical methods are studied and made analysis of their characteristics, which can be used as reference in the practical applications.

Study on Mechanical Property of Conch Powder Reinforced Polyethylene Composite

2012 ◽  
Vol 557-559 ◽  
pp. 286-290
Author(s):  
Zhi Hong Guo ◽  
Jia Wei Shi ◽  
Qun Shao ◽  
Pei Jie Lin ◽  
Yan Ping Wang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Mechanical Property ◽  
Tensile Strength ◽  
High Tensile Strength ◽  
Frictional Loss ◽  
Practical Applications ◽  
Impact Performance ◽  
Polyethylene Composite ◽  
Maximum Value ◽  
The Impact

The impact performance of PE can be greatly enhanced by the use of functionalized conch powder, while maintaining high tensile strength thus giving this study high potentiality for its practical applications. The conch powder was treated by titanate coupling agent NDZ-201 before use and the influence of different proportions of conch powder on the mechanical properties of PE/conch powder composite is discussed in this article. The impact strength has a maximum value of 63.4kJ/m2 and the frictional loss records a minimum of 4.27×10-1mm3/(Nm)-1 and 42.2% lower than that of pure PE.

Hartmann flow in annular channels. Part 2. Numerical solutions for low to moderate Hartmann numbers

1969 ◽  
Vol 37 (2) ◽  
pp. 209-229 ◽  
Author(s):  
C. J. Apelt
Keyword(s):  
Flow Rate ◽  
Current Flow ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Annular Channel ◽  
Circular Cylinders ◽  
Induced Current ◽  
Annular Channels ◽  
Eccentric Cylinders ◽  
Maximum Value

Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.

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