Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function

2009 ◽  
Vol 47 (1) ◽  
pp. 82-88 ◽  
Author(s):  
E. Jomehzadeh ◽  
A.R. Saidi
Keyword(s):  
Boundary Layer ◽  
Analytical Solution ◽  
Free Vibration ◽  
Transversely Isotropic ◽  
Layer Function ◽  
Boundary Layer Function

Bending Analysis of Thick Laminated Rectangular Plates Using a Boundary Layer Function

2010 ◽  
Vol 224 (10) ◽  
pp. 2073-2081 ◽  
Author(s):  
A R Saidi ◽  
S R Atashipour ◽  
H Keshavarzi
Keyword(s):  
Boundary Layer ◽  
Shear Deformation Theory ◽  
Transversely Isotropic ◽  
Rectangular Plates ◽  
Governing Equations ◽  
Third Order ◽  
Transversely Isotropic Plate ◽  
Reissner Theory ◽  
Layer Function ◽  
Boundary Layer Function

In this article, the governing bending equations of thick laminated transversely isotropic rectangular plates are derived based on third-order shear deformation theory (TSDT). Using a new function, called the boundary layer function, the three coupled governing equations are converted to two decoupled equations. These equations are in terms of the deflection of the plate and the mentioned boundary layer function, which are written in invariant form. By solving the decoupled equations, a Levy-type analytical solution is presented for bending of a transversely isotropic plate. Finally, numerical results are presented for boundary layer phenomenon and its effects in TSDT. It is shown that all of the boundary layer effects in Mindlin—Reissner theory appear in this theory. However, it is shown that the intensity of the boundary layer effects in TSDT exceeds that of the Mindlin—Reissner theory.

Effective Approximation for Elliptic Partial Differential Equation with Periodical Boundary Value Problem

2010 ◽  
Vol 29-32 ◽  
pp. 1294-1300
Author(s):  
Xin Cai
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Partial Differential ◽  
Layer Function ◽  
Smooth Component ◽  
Boundary Layer Function

Elliptic partial differential equation with periodical boundary value problem was considered. The equation would degenerate to parabolic partial differential equation when small parameter tends to zero. This is a multi-scale problem. Firstly, the property of boundary layer was discussed. Secondly, the boundary layer function was presented. The smooth component was constructed according to the boundary layer function. Thirdly, finite difference scheme for the smooth component is proposed according to transition point in time direction. Finally, experiment was proposed to illustrate that our presented method is an effective computational method.

scholarly journals Singularly perturbed parabolic problem with oscillating initial condition

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1323-1327
Author(s):  
Asan Omuraliev ◽  
Ella Abylaeva
Keyword(s):  
Boundary Layer ◽  
Parabolic Problem ◽  
Singularly Perturbed ◽  
Initial Condition ◽  
Parabolic Boundary ◽  
Layer Function ◽  
Angular Boundary ◽  
Singularly Perturbed Parabolic Problem ◽  
Boundary Layer Function ◽  
Regularized Asymptotics

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularized asymptotics of the solution of the problem is constructed.

GENERALIZED METHOD OF BOUNDARY LAYER FUNCTION FOR BISINGULARLY PERTURBED DIFFERENTIAL COLE EQUATION

2017 ◽  
Vol 101 (3) ◽  
pp. 507-516 ◽  
Author(s):  
Keldibay Alymkulov ◽  
Dilmurat Adbillajanovich Tursunov ◽  
Bektur Abdrahmonovich Azimov
Keyword(s):  
Boundary Layer ◽  
Layer Function ◽  
Boundary Layer Function

On the Stress Singularities and Boundary Layer in Moderately Thick Functionally Graded Sectorial Plates

2010 ◽  
Author(s):  
A. R. Saidi ◽  
F. Hejripour ◽  
E. Jomehzadeh
Keyword(s):  
Boundary Layer ◽  
Plate Theory ◽  
Functionally Graded ◽  
Stress Singularities ◽  
Equilibrium Equations ◽  
Arbitrary Boundary ◽  
Edge Zone ◽  
Layer Function ◽  
Sector Plate ◽  
Boundary Layer Function

In this paper, the stress analysis of moderately thick functionally graded (FG) sector plate is developed for studying the singularities in vicinity of the vertex. Based on the first-order shear deformation plate theory, the governing partial differential equations are obtained. Using an analytical method and defining some new functions, the stretching and bending equilibrium equations are decoupled. Also, introducing a function, called boundary layer function, the three bending equations are converted into two decoupled equations called edge-zone and interior equations. These equations are solved analytically for the sector plate with the simply supported radial edges and arbitrary boundary condition along the circular edge. The singularities of shear force and moment resultants are discussed for both salient and re-entrant sectorial plates. Also, the effects of power of the FGM, thickness to length ratio on the stress singularities of the FG sector plates are investigated.

Abstract linear second order differential equations with two small parameters and depending on time operators

2017 ◽  
Vol 33 (2) ◽  
pp. 233-246
Author(s):  
ANDREI PERJAN ◽  
◽  
GALINA RUSU ◽  
Keyword(s):  
Boundary Layer ◽  
A Priori Estimates ◽  
Real Hilbert Space ◽  
A Priori ◽  
Estimates Of Solutions ◽  
Layer Function ◽  
Priori Estimates ◽  
Unperturbed Problem ◽  
Small Parameters ◽  
Boundary Layer Function

In a real Hilbert space H consider the following singularly perturbed Cauchy problem. We study the behavior of solutions uεδ to this problem in two different cases: ε → 0 and δ ≥ δ0 > 0; ε → 0 and δ → 0, relative to solution to the corresponding unperturbed problem. We obtain some a priori estimates of solutions to the perturbed problem, which are uniform with respect to parameters, and a relationship between solutions to both problems. We establish that the solution to the perturbed problem has a singular behavior, relative to the parameters, in the neighbourhood of t = 0. We show the boundary layer and boundary layer function in both cases.

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