scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

Geological Field Sketches and Illustrations

2019 ◽  
Author(s):  
Matthew J. Genge
Keyword(s):  
Cross Sections ◽  
Earth Science ◽  
Three Dimensional ◽  
Worked Examples ◽  
Scientific Publications ◽  
Thin Sections ◽  
Geological Features ◽  
Different Types ◽  
The Subject

Drawings, illustrations, and field sketches play an important role in Earth Science since they are used to record field observations, develop interpretations, and communicate results in reports and scientific publications. Drawing geology in the field furthermore facilitates observation and maximizes the value of fieldwork. Every geologist, whether a student, academic, professional, or amateur enthusiast, will benefit from the ability to draw geological features accurately. This book describes how and what to draw in geology. Essential drawing techniques, together with practical advice in creating high quality diagrams, are described the opening chapters. How to draw different types of geology, including faults, folds, metamorphic rocks, sedimentary rocks, igneous rocks, and fossils, are the subjects of separate chapters, and include descriptions of what are the important features to draw and describe. Different types of sketch, such as drawings of three-dimensional outcrops, landscapes, thin-sections, and hand-specimens of rocks, crystals, and minerals, are discussed. The methods used to create technical diagrams such as geological maps and cross-sections are also covered. Finally, modern techniques in the acquisition and recording of field data, including photogrammetry and aerial surveys, and digital methods of illustration, are the subject of the final chapter of the book. Throughout, worked examples of field sketches and illustrations are provided as well as descriptions of the common mistakes to be avoided.

Torsion of Noncylindrical Shafts of Circular Cross Section

1950 ◽  
Vol 17 (3) ◽  
pp. 275-282
Author(s):  
H. J. Reissner ◽  
G. J. Wennagel
Keyword(s):  
Cross Sections ◽  
Inverse Method ◽  
Direct Method ◽  
Circular Cross Section ◽  
Theory Of Elasticity ◽  
Elementary Functions ◽  
Single Term ◽  
Circumferential Displacement ◽  
Basic Differential Equation ◽  
Technical Interest

Abstract The theory of torsion of noncylindrical bodies of revolution, initiated by J. H. Michell and A. Föppl, is stated by a basic differential equation of the circumferential displacement and by a boundary condition of the shear stress along the generator surface. The solution of these two equations by the “direct” method of first assuming the boundary shape has not lent itself to closed solutions in terms of elementary functions, so that only approximation, infinite series, and experimental methods have been applied. A semi-inverse method analogous to Saint Venant’s semi-inverse method for cylindrical bodies has the disadvantage of the restriction to special boundary shapes but the advantage of exact solutions by means of elementary functions. By this method, bodies of conical, ellipsoidal, and hyperbolic boundary shapes have been obtained in a simple analysis. One class of integrals leading to other boundary shapes seems not to have been analyzed up to now, namely, the integrals in the form of a product of two functions of, respectively, axial (z) and radial (r) co-ordinates. A first suggestion of this possibility was given in Love’s treatise on the mathematical theory of elasticity. In the present paper, the classes of boundary shapes, displacements, and stress distributions are investigated analytically and numerically. The extent of the numerical investigation contains only the results of single-term integrals for full and hollow cross sections of technical interest. The detailed analysis of the boundary shapes, following from series integrals, presents essential mathematical obstacles. Overcoming these difficulties might lead to a multitude of solutions of interesting boundary shapes, and stress and strain distribution.

Hydraulic characteristics and calculation of the innovative systems of surface runoff disposal

2021 ◽  
pp. 46-51
Author(s):  
Ю.В. Брянская ◽  
А.Э. Тен ◽  
Н.Т. Джумагулова ◽  
Г.Н. Громов
Keyword(s):  
Cross Sections ◽  
Surface Runoff ◽  
Experimental Studies ◽  
Drainage System ◽  
Anthropogenic Pollution ◽  
Hydraulic Characteristics ◽  
Regulatory Requirements ◽  
The Subject ◽  
Intensive Development ◽  
Selection Of

В условиях интенсивного развития новых отечественных и зарубежных технологий, материалов и оборудования, применяемых для защиты окружающей природной среды от загрязнений техногенного происхождения, особую актуальность приобретают разработки новых систем отвода и очистки поверхностных сточных вод. Эти системы позволяют использовать последние достижения отраслевой науки и оптимизировать алгоритм выполнения операций и практических приемов их гидравлического расчета. Примером является инновационная система отвода поверхностных сточных вод АСО Qmax, которая относится к открытой системе каналов (лотков) для сбора и отведения поверхностных сточных вод, формирующихся при выпадении атмосферных осадков. Однако широкому применению данного вида конструкций в России препятствует отсутствие методики их гидравлического расчета, в том числе таблиц для подбора сечений (диаметров) каналов, которая бы удовлетворяла требованиям российской нормативно-методической базы проектирования систем отведения поверхностных сточных вод. В этой связи предметом данной статьи явилась оценка гидравлических характеристик трубопроводов, каналов (лотков) системы водоотвода АСО Qmax. Приведены результаты теоретических и экспериментальных исследований гидравлических характеристик системы АСО Qmaxс учетом адаптации для российских условий и нормативных требований, а также обоснование рекомендуемых параметров для их использования. In the context of the intensive development of new domestic and foreign technologies, materials and equipment used to protect the environment from anthropogenic pollution, the development of advanced systems for surface runoff removal and treatment is of special actuality. These systems provide for using the latest achievements of the sectoral science and optimizing the algorithm for performing operations and practical methods for the hydraulic calculations. An example of the innovative surface runoff disposal system is ASO Qmax, that refers to an open system of channels for the collection and disposal of surface runoff formed during precipitation. However, the widespread use of these facilities in Russia is hampered by the lack of a method for the hydraulic calculations, including tables for the selection of cross-sections (diameters) of channels that meet the requirements of the Russian guidelines and regulations for the design of surface runoff disposal systems. In this regard, the subject of this paper is the estimation of the hydraulic characteristics of pipelines, channels of ASO Qmax drainage system. The results of theoretical and experimental studies of the hydraulic characteristics of ASO Qmax system with account of the adaptation for the Russian conditions and regulatory requirements, as well as the justification of the recommended parameters for their use are presented.

Spherical Symmetry in the Theory of Elasticity

1958 ◽  
Vol 25 (1) ◽  
pp. 136-140
Author(s):  
F. Goded
Keyword(s):  
General Solution ◽  
Stress Tensor ◽  
Axial Symmetry ◽  
Spherical Symmetry ◽  
Stress Function ◽  
Theory Of Elasticity ◽  
Plane Symmetry ◽  
The Subject ◽  
The Common

Abstract Part 1 of the paper presents a study of the common characteristics of both plane symmetry and axial symmetry in the theory of elasticity; viz., the form of the stress tensor and the existence of further analogous symmetries. In Part 2, the subject deals with the possibility of the existence of further analogous symmetries which are found to be possible only in some specific cases. In particular, spherical symmetry is treated. The method of obtaining the stress function of this new symmetry and the equation which this function must satisfy also are discussed, together with the stresses expressed by means of this stress function. The paper ends with a brief review of a general solution of the stress function and an example of the application of this stress function to a given problem.

scholarly journals Advances in Conjugated Polymer Lasers

Polymers ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 443 ◽  
Author(s):  
Hongyan Xia ◽  
Chang Hu ◽  
Tingkuo Chen ◽  
Dan Hu ◽  
Muru Zhang ◽  
...  
Keyword(s):  
Conjugated Polymers ◽  
Cross Sections ◽  
Conjugated Polymer ◽  
Low Cost ◽  
Research Direction ◽  
Stimulated Emission ◽  
Laser Materials ◽  
Radiation Mechanism ◽  
The Subject ◽  
Low Cost Manufacturing

This paper provides a review of advances in conjugated polymer lasers. High photoluminescence efficiencies and large stimulated emission cross-sections coupled with wavelength tunability and low-cost manufacturing processes make conjugated polymers ideal laser gain materials. In recent years, conjugated polymer lasers have become an attractive research direction in the field of organic lasers and numerous breakthroughs based on conjugated polymer lasers have been made in the last decade. This paper summarizes the recent progress of the subject of laser processes employing conjugated polymers, with a focus on the photoluminescence principle and excitation radiation mechanism of conjugated polymers. Furthermore, the effect of conjugated polymer structures on the laser threshold is discussed. The most common polymer laser materials are also introduced in detail. Apart from photo-pumped conjugated polymer lasers, a direction for the future development of electro-pumped conjugated polymer lasers is proposed.

scholarly journals Geometric modeling of surfaces dependent cross sections in the tasks of spinning and laying

2019 ◽  
Vol 110 ◽  
pp. 01057
Author(s):  
Yuri Deniskin ◽  
Pavel Miroshnichenko ◽  
Andrew Smolyaninov
Keyword(s):  
Composite Materials ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Solid Modeling ◽  
Uniform Method ◽  
Calculation Methods ◽  
Related Process

The article is devoted to the development of a geometric model of surfaces of dependent sections to solve the problems of winding by continuous fibers in the direction of the force and its related process of automated winding of composite materials. A uniform method for specifying the surfaces of dependent sections with a curvilinear generator and a method for solid modeling of the shell obtained by winding or calculation methods are described.

scholarly journals The torsion of a semi-infinite elastic solid by an elliptical stamp

1968 ◽  
Vol 9 (1) ◽  
pp. 36-45
Author(s):  
Mumtaz K. Kassir
Keyword(s):  
Field Equation ◽  
Classical Theory ◽  
Cross Sections ◽  
Plane Surface ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Circular Area

The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z ≧ 0) when a part of the boundary surface (z = 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11, and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.

Surface Reconstruction From Dexel Data for Virtual Sculpting

2004 ◽  
Author(s):  
Xiaobo Peng ◽  
Weihan Zhang ◽  
Sai-Gowthami Asam ◽  
Ming C. Leu
Keyword(s):  
Surface Reconstruction ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Ray Casting ◽  
Virtual Sculpting ◽  
Shortest Distance ◽  
Branching Problem ◽  
Volume Ray Casting ◽  
Swept Volume ◽  
Differential Equation Method

This paper presents a new method for surface reconstruction from dexel data for virtual sculpting. We are in the midst of developing a dexel model based sculpting system having the capability of interactive solid modeling with haptics interface. The geometric modeling of our sculpting system is based on the Sweep Differential Equation method to compute the boundary of the tool swept volume. Ray casting is used to perform Boolean operations between the tool swept volume and the virtual stock in dexel models to simulate the sculpting process. The dexel data are converted to a series of planar contours in parallel slices (i.e. cross sections). The overlapping ratio between two contour areas is used as the criterion for deciding on the corresponding contours in two adjacent slices. The tiling problem is tackled by using the rule of the shortest distance between points on two corresponding contours. The branching problem is solved by adding one line segment between two contours to form one composite contour. Examples are given to demonstrate the ability of the developed code to convert from dexel data to triangular meshes for the viewing of a sculpted model in different directions.

FREE VIBRATION OF AN ORTHOTROPIC HOLLOW BODY OF REVOLUTION

2005 ◽  
Vol 05 (02) ◽  
pp. 299-312
Author(s):  
D. REDEKOP
Keyword(s):  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Body Of Revolution ◽  
Orthotropic Cylinder ◽  
Dimensional Theory ◽  
Hollow Cylinders ◽  
Definition Of

A method is developed to determine the natural frequencies of vibration of an orthotropic hollow body of revolution of constant thickness but of arbitrary smooth meridian. Equations are derived using the linear three-dimensional theory of elasticity, and a numerical solution is obtained using the differential quadrature method. The geometric generality of the solution is attained by delaying definition of local geometric parameters until the solution stage. Validation is by comparison with previously published results, including results for a hollow orthotropic cylinder. Sample results are given for orthotropic hollow cylinders and spherical segments, and conclusions are drawn.

scholarly journals V. On the general theory of elastic stability

1914 ◽  
Vol 213 (497-508) ◽  
pp. 187-244 ◽  
Keyword(s):  
General Theory ◽  
Boundary Conditions ◽  
Radial Pressure ◽  
Elastic Stability ◽  
Circular Ring ◽  
Theory Of Elasticity ◽  
Comprehensive Theory ◽  
The Subject ◽  
The Stability ◽  
Straight Rod

Problems which deal with the stability of bodies in equilibrium under stress are so distinct from the ordinary applications of the theory of elasticity that it is legitimate to regard them as forming a special branch of the subject. In every other case we are concerned with the integration of certain differential equations, fundamentally the same for all problems, and the satisfaction of certain boundary conditions; and by a theorem due to Kiechiioff we are entitled to assume that any solution which we may discover is unique. In these problems we are confronted with the possibility of two or more configurations of equilibrium , and we have to determine the conditions which must be satisfied in order that the equilibrium of any given configuration may be stable. The development of both branches has proceeded upon similar lines. That is to say, the earliest discussions were concerned with the solution of isolated examples rather than with the formulation of general ideas. In the case of elastic stability, a comprehensive theory was not propounded until the problem of the straight strut had been investigated by Euler, that of the circular ring under radial pressure by M. Lévy and G. H. Halphen, and A. G. Greenhill had discussed the stability of a straight rod in equilibrium under its own weight, under twisting couples, and when rotating.

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