The Refined Theory of Plane Problems for One-Dimensional Quasicrystalline Bodies

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Ad Hoc ◽  
Three Dimensional ◽  
Refined Theory ◽  
Shear Surface ◽  
Surface Loading ◽  
Thick Plates ◽  
One Dimensional ◽  
Nonhomogeneous Boundary ◽  
Deformation Regime ◽  
Nonhomogeneous Boundary Conditions

Without employing ad hoc assumptions, various equations and solutions for plane problems of one-dimensional quasicrystals are deduced systematically. A method for the exact solution of three-dimensional equations is presented under homogeneous and nonhomogeneous boundary conditions. The equations and solutions are used to construct the refined theory of thick plates for both an in-plane extensional deformation regime and a normal or shear surface loading. With this method, the refined theory can now be explicitly established from the general solution of quasicrystals and the Lur’e method. In two illustrative examples of infinite plates with a circular hole, it is shown that explicit expressions of analytical solutions can be obtained by using the refined theory.

The Refined Theory of One-Dimensional Quasi-Crystals in Thick Plate Structures

2011 ◽  
Vol 78 (3) ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Thick Plate ◽  
Ad Hoc ◽  
Plate Theory ◽  
Pure Shear ◽  
Refined Theory ◽  
Plate Structures ◽  
Thick Plates ◽  
Refined Plate Theory ◽  
One Dimensional ◽  
Quasi Crystals

For one-dimensional quasi-crystals, the refined theory of thick plates is explicitly established from the general solution of quasi-crystals and the Luré method without employing ad hoc stress or deformation assumptions. For a homogeneous plate, the exact equations and solutions are derived, which consist of three parts: the biharmonic part, the shear part, and the transcendental part. For a nonhomogeneous plate, the exact governing differential equations and solutions under pure normal loadings and pure shear loadings, respectively, are obtained directly from the refined plate theory. In an illustrative example, explicit expressions of analytical solutions are obtained for torsion of a rectangular quasi-crystal plate.

The Refined Theory of Axisymmetric Circular Cylinder in One-Dimensional Hexagonal Quasicrystals

2012 ◽  
Vol 217-219 ◽  
pp. 1421-1424 ◽  
Author(s):  
Bao Sheng Zhao ◽  
Di Wu
Keyword(s):  
General Solution ◽  
Circular Cylinder ◽  
Ad Hoc ◽  
Approximate Equation ◽  
Refined Theory ◽  
One Dimensional ◽  
Stress Components ◽  
Refined Equation ◽  
Independent Variable ◽  
1D Hexagonal Quasicrystals

A refined theory of axisymmetric cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs) is analyzed. Based on elastic theory with 1D hexagonal QCs, the refined theory of axisymmetric cylinder is derived by using general solution of 1D hexagonal QCs and Lur’e method without ad hoc assumptions. At first, expressions were obtained for all the phonon and phason displacements and stress components in term of the three functions with single independent variable. Based on the boundary conditions, the refined equation for the cylinder is derived directly. And the approximate equation is accurate up to the second-order terms with respect to radius of circular cylinder.

The Refined Analysis about Mechanical Behavior for Torsional Circular Shaft of Cubic Quasicrystal

2011 ◽  
Vol 213 ◽  
pp. 83-87
Author(s):  
Bao Sheng Zhao ◽  
Yang Gao ◽  
Ying Tao Zhao
Keyword(s):  
Harmonic Function ◽  
Ad Hoc ◽  
Reverse Direction ◽  
Refined Theory ◽  
Surface Loading ◽  
Circular Shaft ◽  
Cylindrical Coordinate ◽  
Higher Order Terms ◽  
Approximate Expressions ◽  
Classical Elasticity Theory

Cheng’s refined theory is extended to investigate torsional circular shaft of cubic quasicrystal, and Lur’e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The refined theory of torsional circular shaft of cubic quasicrystal under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal, and the refined theory provides the solutions about torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions are obtained for circular shaft from boundary conditions. Using Taylor series of the Bessel functions and then dropping all the terms associated with the higher-order terms, we obtain the approximate expressions for circular shaft of cubic quasicrystal under reverse direction surface. To illustrate the application of the theory developed, one example is examined.

The Exact Deformation Theory of Two-Dimensional Dodecagonal Quasicrystal Shaft

2011 ◽  
Vol 213 ◽  
pp. 276-280
Author(s):  
Bao Sheng Zhao ◽  
Ying Tao Zhao ◽  
Yang Gao
Keyword(s):  
Harmonic Function ◽  
Deformation Theory ◽  
Ad Hoc ◽  
Reverse Direction ◽  
Refined Theory ◽  
Two Dimensional ◽  
Surface Loading ◽  
Circular Shaft ◽  
Cylindrical Coordinate ◽  
Classical Elasticity Theory

Cheng’s refined theory is extended to investigate torsional circular shaft of two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs), and Lur’e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The exact deformation of torsional circular shaft of 2D dodecagonal QCs under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs, and the exact deformation theory provides the solutions about torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions are obtained for circular shaft from boundary conditions. Using Taylor series of the Bessel functions and then dropping all the terms associated with the higher-order terms, we obtain the approximate expressions for circular shaft of 2D dodecagonal QCs under reverse direction surface. To illustrate the application of the theory developed, one example is examined.

A Refined Theory of Axisymmetric Thermoelastic Circular Cylinder with Transversely Isotropic

2012 ◽  
Vol 622-623 ◽  
pp. 1611-1615
Author(s):  
Di Wu ◽  
Bao Sheng Zhao
Keyword(s):  
Circular Cylinder ◽  
Radial Direction ◽  
Ad Hoc ◽  
Transversely Isotropic ◽  
Approximate Solutions ◽  
Refined Theory ◽  
Surface Loading ◽  
Refined Equation ◽  
Exact Temperature ◽  
Approximate Equations

For analyzing the exact stress field, the exact displacement field and the exact temperature field in axisymmetric thermoelastic circular cylinder with transversely isotropic, the refined theory of an axisymmetric circular cylinder was researched. Without ad hoc assumptions, the refined equation of an axisymmetric thermoelastic circular cylinder with transversely isotropic was obtained, which yields Bessel's function and the solution of the cylinder directly from the general solution. By dropping terms of high order, the approximate solutions are derived for a circular cylinder under radial direction surface loading. At last, we study the approximate equations with the temperature effect.

scholarly journals THE REFINED THEORY OF ELASTIC PLATES AS ASYMPTOTIC APPROACH OF 3D PROBLEM

2018 ◽  
Vol 196 ◽  
pp. 02037
Author(s):  
Nelly Rogacheva
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Three Dimensional ◽  
Transverse Shear Deformation ◽  
Refined Theory ◽  
Elastic Plates ◽  
Asymptotic Approach ◽  
Thick Plates ◽  
Kirchhoff Theory ◽  
3D Problem

The refined theory of elastic thin and thick plates is constructed by the asymptotic method for reducing three-dimensional (3D) equations of linear elasticity to two-dimensional ones without the use of any assumptions. The resulting refined theory is much more complicated than the known classical Kirchhoff theory: the required values of the refined theory vary in thickness of the plate by more complex laws; the system of partial differential equations of the refined theory has a higher order than the system of equations of the classical theory. A comparison of the obtained theory with the popular refined theory of Timoshenko and E. Reissner, taking into account the transverse shear deformation is made. It is shown that the inclusion only of the transverse shear deformation is insufficient. In addition to the transverse shear deformation, many additional terms having the same order as the transverse shear deformation must be taken into account.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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