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.

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 Decomposed Theorem of Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystal

2011 ◽  
Vol 341-342 ◽  
pp. 1-5 ◽  
Author(s):  
Bao Sheng Zhao ◽  
Ying Tao Zhao ◽  
Yang Gao
Keyword(s):  
Boundary Conditions ◽  
Ad Hoc ◽  
Isotropic Plate ◽  
Refined Theory ◽  
Two Dimensional ◽  
Classical Elasticity ◽  
Circular Shaft ◽  
Cylindrical Coordinate ◽  
Stress Components ◽  
Classical Elasticity Theory

Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft for two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs)with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The decomposed theorem of torsional circular shaft of 2D dodecagonal QCs with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on 2D dodecagonal QCs without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations.

The General Solution for Torsional Circular Shaft of Cubic Quasicrystal

2011 ◽  
Vol 213 ◽  
pp. 206-210
Author(s):  
Bao Sheng Zhao ◽  
Jia Lian Shi ◽  
Ying Tao Zhao ◽  
Yang Gao
Keyword(s):  
General Solution ◽  
Boundary Conditions ◽  
Ad Hoc ◽  
Isotropic Plate ◽  
Refined Theory ◽  
Classical Elasticity ◽  
Circular Shaft ◽  
Cylindrical Coordinate ◽  
Stress Components ◽  
Classical Elasticity Theory

Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft of cubic quasicrystal with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The general solution of torsional circular shaft on cubic quasicrystal with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on cubic quasicrystal without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations. Using basic mathematic method and the general solutions, an 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.

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 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.

scholarly journals Modeling and Numerical Simulation of the Turbulent Two-Phase Jet Confined in the Cylindrical Channel

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Turbulent Mixing ◽  
Cylindrical Channel ◽  
Stationary Flow ◽  
Important Class ◽  
Two Dimensional ◽  
Mixing Processes ◽  
Two Phase ◽  
Immiscible Liquids ◽  
Cylindrical Coordinate ◽  
Ground Part

Mixing processes in the turbulent two-phase jet confined at some distance from the nozzle aremodeled and examined. Many natural and technical phenomena deal with the turbulent mixing and heattransfer in the jet of mutually immiscible liquids, which represent an important class of the modern multiphasesystems dynamics. The differential equations for axially symmetrical two-dimensional stationary flow and theintegral correlations in a cylindrical coordinate system are considered for the free heterogeneous jet confined atits initial or ground part in the cylindrical channel. Algorithm and the results obtained may be of interest for theresearch and industrial tasks, where the calculations of the turbulent mixing and heat transfer in multiphase jetdevices are of importance.

A refined theory of torsional deformation of a circular shaft

2008 ◽  
Vol 207 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Bao-sheng Zhao ◽  
Yang Gao ◽  
Xiu-E Wu
Keyword(s):  
Refined Theory ◽  
Torsional Deformation ◽  
Circular Shaft
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