The Principle of Asymptotic Proportionality

1990 ◽  
Vol 57 (1) ◽  
pp. 225-231
Author(s):  
H. C. M. Chan
Keyword(s):  
Function Method ◽  
Equilibrium Problems ◽  
Field Variable ◽  
Far Field ◽  
Elastic Media ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Induced Stresses ◽  
Physical Phenomena ◽  
Physical Quantities

The Principle of Asymptotic Proportionality, which is based on the Green’s function method for equilibrium problems, is proposed. Using this principle, the induced far-field variable due to any distribution of applied physical quantities can be approximated. This principle has been verified by considering the induced stresses due to applied tractions and dislocations in two-dimensional linear elastic media, and has been shown to be applicable to other physical phenomena such as electrostatics, gravitation, and electromagnetism.

Solutions to some classical problems in linear elastostatics

2020 ◽  
pp. 145-212
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Cross Section ◽  
Function Method ◽  
Arbitrary Cross Section ◽  
Two Dimensional ◽  
Linear Elastic ◽  
Linear Elastostatics ◽  
Airy’S Stress Function ◽  
Elastic Fracture ◽  
Stress And Deformation ◽  
Stress Function Method

This chapter presents and discusses the solution of several classical problems in linear elastostatics, including thick-walled spheres and cylinders under external and internal pressure; bending and torsion of prismatic bars of arbitrary cross section; and the use of Airy’s stress function method to solve several two-dimensional plane strain and plane stress traction boundary value problems, including a demonstration of the extent of the Saint-Venant effect. The discussion also includes an analysis of the asymptotic stress and deformation fields near the tips of sharp cracks, and a discussion of stress intensity factors which are of importance in linear elastic fracture mechanics.

Teaching kinematics via arduino based STEM education material

2021 ◽  
Vol 57 (1) ◽  
pp. 015010
Author(s):  
Atakan Çoban ◽  
Mustafa Erol
Keyword(s):  
Time Dependence ◽  
Stem Education ◽  
Error Rate ◽  
Educational Environment ◽  
Two Dimensional ◽  
Education Material ◽  
Sample Application ◽  
And Mathematics ◽  
Engineering Physics ◽  
Physical Quantities

Abstract The present study reports an Arduino-based STEM education material that resolves the kinematics of a moving object, specifically focusing on two dimensional motion of the object. Throughout the work, a sample application that can be prepared in a classroom where students are active and including the acquisitions of Technology, Engineering, Physics and Mathematics in a single educational environment. In the study, instantaneous time dependence of the displacements, namely x(t) and y(t) components and the resultant R(t) component, are experimentally measured on a vehicle by using an Arduino UNO, distance sensors and Bluetooth sensor prepared within the scope of a STEM education approach. The ratios between those measured physical quantities and theoretical estimations are found to be %13.1 for the position, %1.4 for the velocity and %7.8 for the acceleration. The error rate of the data was accepted to be reasonable considering highly economical teaching materials.

Study on soliton solutions of the longitudinal wave equation and magneto-electro-elastic circular rod dynamical model

2021 ◽  
Vol 35 (13) ◽  
pp. 2150168
Author(s):  
Adel Darwish ◽  
Aly R. Seadawy ◽  
Hamdy M. Ahmed ◽  
A. L. Elbably ◽  
Mohammed F. Shehab ◽  
...  
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Physical Interpretation ◽  
Elliptic Function ◽  
Function Method ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
Jacobi Elliptic Function ◽  
Two Dimensional

In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.

Implementation of p and h-p Versions of the Finite Element Method

1992 ◽  
Author(s):  
Ye-Chen Lai ◽  
Timothy C. S. Liang ◽  
Zhenxue Jia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elastic Analysis ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Shape Functions ◽  
Linear Elastic ◽  
Finite Element Software ◽  
Analysis Process ◽  
Adaptive Analysis

Abstract Based on hierarchic shape functions and an effective convergence procedure, the p-version and h-p adaptive analysis capabilities were incorporated into a finite element software system, called COSMOS/M. The range of the polynomial orders can be varied from 1 to 10 for two dimensional linear elastic analysis. In the h-p adaptive analysis process, a refined mesh are first achieved via adaptive h-refinement. The p-refinement is then added on to the h-version designed mesh by uniformly increasing the degree of the polynomials. Some numerical results computed by COSMOS/M are presented to illustrate the performance of these p and h-p analysis capabilities.

scholarly journals Far-Field Focus and Dispersionless Anticrossing Bands in Two-Dimensional Photonic Crystals

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Xiaoshuang Chen ◽  
Renlong Zhou ◽  
Yong Zeng ◽  
Hongbo Chen ◽  
Wei Lu
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Surface Polaritons ◽  
Concave Lens ◽  
Bloch Mode ◽  
Two Dimensional Photonic Crystal ◽  
Photonic Band

We review the simulation work for the far-field focus and dispersionless anticrossing bands in two-dimensional (2D) photonic crystals. In a two-dimensional photonic-crystal-based concave lens, the far-field focus of a plane wave is given by the distance between the focusing point and the lens. Strong and good-quality far-field focusing of a transmitted wave, explicitly following the well-known wave-beam negative refraction law, can be achieved. The spatial frequency information of the Bloch mode in multiple Brillouin zones (BZs) is investigated in order to indicate the wave propagation in two different regions. When considering the photonic transmission in a 2D photonic crystal composed of a negative phase-velocity medium (NPVM), it is shown that the dispersionless anticrossing bands are generated by the couplings among the localized surface polaritons of the NPVM rods. The photonic band structures of the NPVM photonic crystals are characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands.

scholarly journals NEGATIVE REFRACTION AND SUBWAVELENGTH FOCUSING USING PHOTONIC CRYSTALS

2004 ◽  
Vol 18 (25) ◽  
pp. 1275-1291 ◽  
Author(s):  
EKMEL OZBAY ◽  
KAAN GUVEN ◽  
ERTUGRUL CUBUKCU ◽  
KORAY AYDIN ◽  
B. KAMIL ALICI
Keyword(s):  
Optical Properties ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Numerical Study ◽  
Effective Index ◽  
Index Of Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Flat Lens ◽  
Effective Index Of Refraction

In this article, we present an experimental and numerical study of novel optical properties of two-dimensional dielectric photonic crystals (PCs) which exhibit negative refraction. We investigate two mechanisms which utilize the band structure of the PC to generate a negative effective index of refraction (n eff <0) and demonstrate the negative refraction experimentally. To the isotropic extend of n eff , different PC slab structures are employed to focus the radiation of a point source. It is shown experimentally that the PC can generate an image of the source with subwavelength resolution in the vicinity of the PC interface. Using a different PC, one can also obtain a far field focusing. In the latter case, we explicitly show the flat lens behavior of the structure. These examples indicate that PC-based lenses can surpass limitations of conventional lenses and lead to novel optics applications.

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