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.

On the buckling analysis of isotropic, transversely isotropic, and laminated rectangular plates via Reddy plate theory: an exact closed-form procedure

2011 ◽  
Vol 226 (5) ◽  
pp. 1210-1224 ◽  
Author(s):  
Sh Hosseini-Hashemi ◽  
S R Atashipour ◽  
M Fadaee
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Transversely Isotropic ◽  
Form Solution ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Third Order ◽  
Solution Methods

Based on Reddy's third-order shear deformation theory, an exact closed-form solution is proposed to describe linear buckling of transversely isotropic laminated rectangular plates under either mono- or bi-axial compressive in-plane loads. To this end, the coupled governing equations are exactly converted to two sets of uncoupled equations for in-plane and transverse deformations of symmetric laminated plates. The new uncoupled equations are analytically solved by applying both Navier and Lévy-type solution methods. The validity and high accuracy of the current exact solution are evaluated by comparing the present results with their counterparts reported in literature.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

scholarly journals Higher-Order Thermo-Elastic Analysis of FG-CNTRC Cylindrical Vessels Surrounded by a Pasternak Foundation

Nanomaterials ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 79 ◽  
Author(s):  
Masoud Mohammadi ◽  
Mohammad Arefi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Deformation Theory ◽  
Volume Fraction ◽  
Effective Properties ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Elastic Response ◽  
Governing Equations ◽  
Third Order ◽  
Reinforced Composite

This study analyses the two-dimensional thermo-elastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) cylindrical pressure vessels, by applying the third-order shear deformation theory (TSDT). The effective properties of FG-CNTRC cylindrical pressure vessels are computed for different patterns of reinforcement, according to the rule of mixture. The governing equations of the problem are derived from the principle of virtual works and are solved as a classical eigenproblem under the assumption of clamped supported boundary conditions. A large parametric investigation aims at showing the influence of some meaningful parameters on the thermo-elastic response, such as the type of pattern, the volume fraction of CNTs, and the Pasternak coefficients related to the elastic foundation.

On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates

2014 ◽  
Vol 14 (07) ◽  
pp. 1450020 ◽  
Author(s):  
Atteshamuddin S. Sayyad ◽  
Yuwaraj M. Ghugal
Keyword(s):  
Boundary Conditions ◽  
Elasticity Theory ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Transversely Isotropic ◽  
Buckling Analysis ◽  
Transverse Shear Strain ◽  
Rectangular Plates

This paper presents the uniaxial and biaxial buckling analysis of rectangular plates based on new trigonometric shear and normal deformation theory. The theory accounts for the cosine distribution of the transverse shear strain through the plate thickness and on the free boundary conditions on the plate surfaces without using the shear correction factor. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The Navier type solutions for the buckling analysis of simply supported isotropic, transversely isotropic, orthotropic and symmetric cross-ply laminated composite rectangular plates subjected to uniaxial and biaxial compressions are presented. The effects of variations in the degree of orthotropy of the individual layers, side-to-thickness ratio and aspect ratio of the plate are examined on the buckling characteristics of composite plates. The present results are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT) and exact three-dimensional (3D) elasticity theory wherever applicable. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity 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.

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