scholarly journals Effects of Boundary Conditions on the Critical Spanning Probability

1998 ◽  
Vol 09 (04) ◽  
pp. 643-647 ◽  
Author(s):  
Muktish Acharyya ◽  
Dietrich Stauffer

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find pc=0.311605(5) in the cubic lattice.

1999 ◽  
Vol 10 (01) ◽  
pp. 183-188 ◽  
Author(s):  
MATT FORD ◽  
D. L. HUNTER ◽  
NAEEM JAN

We use the Hoshen–Kopelman algorithm with the Nakanashi method of recycling redundant labels to measure the fraction of spanning configurations, R(pc), at and near pc, for random site percolation in two and three dimensions with different boundary conditions. For the square and cubic lattices we find that R(pc) is 0.50 and 0.28 for free edges and 0.64 (2-d) and 0.56 (3-d) for both helical and periodic boundary conditions. The error bars are of the order of ±0.01 for these results.


Author(s):  
Mosfequr Rahman ◽  
F. N. U. Aktaruzzaman ◽  
Saheem Absar ◽  
Aniruddha Mitra ◽  
Awlad Hossain

Depending on the type of matrix materials, composites can be broadly divided into three different major classifications: Organic-matrix composites (OMC), metal-matrix composites (MMC), and ceramic-matrix composites (CMC). OMC can be further sub-classified into polymer-matrix composites (PMC) and carbon-matrix composites or carbon-carbon composites. In this paper the main objective is to focus on polyurethane based PMC composites. Polyurethane is one of the widely used polymer matrix materials. It has diversified applications, easily available and cheap. In this computational study a composite shaft with a core made of matrix material completely wrapped around by a woven fiber cloth with a very strong bonding between core and fibers is considered. Three different types of woven fibers: fiber glass, Kevlar 49, and carbon fibers, are considered. A woven fabric is the interlocking or weaving of two unidirectional fibers. This configuration is often used to produce curve surfaces because of the ease with which it could be placed on and conform to curved surfaces. Authors had fabricated these three composites in their in-house laboratory. They had also experimentally measured the mechanical properties of these composites using 3-point bending test which already been published. In this current study finite element analyses has been performed for the modeling of the static response of these three different polyurethane based composite shafts as fiber glass reinforced polyurethane epoxy, carbon fiber reinforced polyurethane epoxy, and Kevlar fibers reinforced polyurethane epoxy for three different boundary conditions. These three boundary conditions are simply supported, cantilever, both end fixed types with bending loads applied at the middle for simply supported case and distributed load along the length of the shaft for the last two types of boundary conditions. A three dimensional model of the composite beam has been implemented in this study using SolidWorks. A finite element commercial software ANSYS is used to investigate the stress response and deformation behavior of the model geometry for these three polyurethane based composite shafts for these three boundary conditions. A twenty node three dimensional element has been implemented for the finite element formulation of the modeled geometry such that it is applicable for the analysis of a layered composite structure, while providing support for linear, large rotation, and large strain nonlinear loading conditions. Convergence has also been ensured for various mash configurations in this work.


2019 ◽  
Vol 25 (19-20) ◽  
pp. 2567-2579 ◽  
Author(s):  
Siamak Mohajel Sadeghi ◽  
Akbar Alibeigloo

In this research based on theory of elasticity, free vibration behavior of a viscoelastic cylindrical shell with different boundary conditions is studied. A constitutive equation for viscoelastic material is assumed to obey the Boltzmann model and Poisson's ratio is held to be constant. Moreover, the Prony series is used to model time dependent modulus of elasticity. Governing equations of motions for simply-supported edges conditions are solved analytically using the state-space technique along the radial coordinate and the Fourier series method along the axial and circumferential directions. In the case of other edges condition a semi-analytical solution is employed by using the differential quadrature method instead of Fourier series solutions. It is worthy to note before solving the problem, that the Laplace transform is employed to convert governing differential equations from the time-domain into the Laplace domain. Then, validation of the present formulation is performed by comparing the numerical results with those published in the literature. Finally, effect of viscoelastic properties, boundary conditions, the thickness-to-radius ratio and length-to-radius ratio on the frequency behavior are studied.


Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.


2003 ◽  
Vol 14 (10) ◽  
pp. 1405-1412 ◽  
Author(s):  
YURIY YU. TARASEVICH ◽  
ELENA N. MANZHOSOVA

We consider site percolation on a correlated bi-colored simple cubic lattice. The correlated medium is constructed from a strongly alternating bi-colored simple cubic lattice due to anti-site disordering. The percolation threshold is estimated. The cluster size distribution is obtained. A possible application to the double 1:1 perovskites is discussed.


Author(s):  
Y. Wang ◽  
B. Q. Zhang

The SIMPLE (for Semi-Implicit Method for Pressure-Linked Equations) is successfully used in predicting three-dimensional flows in a double-recirculating combustor. Effects of different boundary conditions and turbulence models on the flow are examined. Compared with experiment results, the numerical predictions are satisfactory.


2009 ◽  
Vol 20 (02) ◽  
pp. 267-272 ◽  
Author(s):  
OLIVIER SCHOLDER

This paper presents an algorithm, which computes the number of anti-red bonds in a simple cubic lattice (site percolation) for different sizes and densities. Our interest was the fractal dimension of anti-red bonds at the percolation threshold. The value is found to be 1.18 ± 0.01. Two different theories proposed by Conigilio resp. Gouyet suggested a fractal dimension of 1.25 resp. 0.9. Thus, we can exclude the theory of Gouyet and are consistent with the one by Coniglio.


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