Responses of multilayered two-dimensional decagonal quasicrystal circular nanoplates with initial stresses and nanoscale interactions

2021 ◽  
Vol 87 ◽  
pp. 104216
Author(s):  
Yunzhi Huang ◽  
Jian Chen ◽  
Min Zhao ◽  
Miaolin Feng
Keyword(s):  
Initial Stresses ◽  
Two Dimensional ◽  
Decagonal Quasicrystal ◽  
Nanoscale Interactions

scholarly journals Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

2021 ◽  
Author(s):  
Tuoya Sun ◽  
Junhong Guo ◽  
E. Pan
Keyword(s):  
Elastic Medium ◽  
Vibration Frequency ◽  
Surrounding Medium ◽  
Nonlocal Parameter ◽  
Buckling Load ◽  
Width Ratio ◽  
Two Dimensional ◽  
Coating Materials ◽  
Decagonal Quasicrystal ◽  
Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

A TWO-DIMENSIONAL STATIC DEFORMATION OF AN IRREGULAR INITIALLY STRESSED MEDIUM

2008 ◽  
Vol 22 (20) ◽  
pp. 3473-3485
Author(s):  
M. M. SELIM
Keyword(s):  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Static Deformation ◽  
Initial Stresses ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Notable Effect ◽  
Approach Method

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.

Thermal mechanical coupling analysis of two-dimensional decagonal quasicrystals with elastic elliptical inclusion

2021 ◽  
pp. 108128652110387
Author(s):  
Yuan-Yuan Ma ◽  
Xue-Fen Zhao ◽  
Ting Zhai ◽  
Sheng-Hu Ding
Keyword(s):  
Flow Direction ◽  
Elastic Field ◽  
Cauchy Type ◽  
Two Dimensional ◽  
Elliptic Inclusion ◽  
Riemann Boundary Value Problem ◽  
Decagonal Quasicrystal ◽  
Riemann Boundary ◽  
Linear Temperature ◽  
Mechanical Coupling

In this paper, the thermal mechanical coupling problem of an infinite two-dimensional decagonal quasicrystal matrix containing elastic elliptic inclusion is studied under remote uniform loading and linear temperature variation. Combining with the theory of the sectional holomorphic function, conformal transformation, singularity analysis, Cauchy-type integral and Riemann boundary value problem, the analytic relations among the sectional functions are obtained, and the problem is transformed into a basic complex potential function equation. The closed form solutions of the temperature field and thermo-elastic field in the matrix and inclusion are obtained. The solutions demonstrate that the uniform temperature and remote uniform stresses will induce an internal uniform stress field. Numerical examples show the effects of the thermal conductivity coefficient ratio, the heat flow direction angle and the elastic modulus on the interface stresses. The results provide a valuable reference for the design and application of reinforced quasicrystal materials.

Synchrotron X-ray studies of diffuse scattering in an Al–Cu–Co two-dimensional decagonal quasicrystal

1992 ◽  
Vol 66 (5) ◽  
pp. 241-251 ◽  
Author(s):  
Y. He ◽  
X. Yan ◽  
T. Egami ◽  
S. J. Poon ◽  
G. J. Shiflet
Keyword(s):  
Diffuse Scattering ◽  
Two Dimensional ◽  
Decagonal Quasicrystal ◽  
X Ray

Electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal circular plates with simply supported or clamped boundary conditions

2021 ◽  
pp. 108128652098161
Author(s):  
Yunzhi Huang ◽  
Min Zhao ◽  
Miaolin Feng
Keyword(s):  
Boundary Conditions ◽  
Electric Fields ◽  
Radial Coordinate ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
Circular Plates ◽  
State Equations ◽  
Element Analysis ◽  
Decagonal Quasicrystal ◽  
Simply Supported

A three-dimensional (3D) electric–elastic analysis of multilayered two-dimensional decagonal quasicrystal (QC) circular plates with simply supported or clamped boundary conditions is presented through a state vector approach. Both perfect and imperfect bonds between the layers are considered by adjusting the parameter sets in the model. Governing equations for the plates subjected to electric or elastic load on the bottom surfaces are derived using the state equations and the propagator matrix method. We explicitly obtain the analytical solution by writing the physical variables as Bessel series expansions and polynomial functions with respect to the radial coordinate. The solution is validated by comparing the numerical results with the 3D finite element analysis. The basic physical quantities of the plates in the phonon, phason, and electric fields are computed in the numerical examples. Result shows that the QC layers as coatings decrease the deflection in the phonon and phason fields of plates. The phonon–phason coupling elastic modulus and piezoelectric constant produce positive and negative effects on the magnitudes of stresses. Besides, compliance coefficients of the weak interface in the phonon field contribute more to the variations than those in the phason field.

STUDY ON ELASTIC ANALYSIS OF CRACK PROBLEM OF TWO-DIMENSIONAL DECAGONAL QUASICRYSTALS OF POINT GROUP 10, $\overline {10}$

2009 ◽  
Vol 23 (16) ◽  
pp. 1989-1999 ◽  
Author(s):  
WU LI ◽  
TIAN YOU FAN
Keyword(s):  
Complex Variable ◽  
Point Group ◽  
Crack Problem ◽  
Plane Elasticity ◽  
Two Dimensional ◽  
Partial Differential ◽  
Decagonal Quasicrystal ◽  
Complex Variable Function ◽  
Variable Function ◽  
Group 10

By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, [Formula: see text] to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.

scholarly journals An exact solution for a multilayered two-dimensional decagonal quasicrystal plate

2014 ◽  
Vol 51 (9) ◽  
pp. 1737-1749 ◽  
Author(s):  
Lian-Zhi Yang ◽  
Yang Gao ◽  
Ernian Pan ◽  
Natalie Waksmanski
Keyword(s):  
Exact Solution ◽  
Two Dimensional ◽  
Decagonal Quasicrystal
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