scholarly journals Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

2021 ◽  
Vol 6 (1) ◽  
pp. 1427-1439
Author(s):  
Onyeka Festus ◽  
Edozie Thompson Okeke
Keyword(s):  
Boundary Condition ◽  
Analytical Solution ◽  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Support Boundary Condition ◽  
Thick Rectangular Plate

A New First-Order Shear Deformation Theory for Free Vibrations of Rectangular Plate

2015 ◽  
Vol 07 (01) ◽  
pp. 1550008 ◽  
Author(s):  
Wei Xiang ◽  
Yufeng Xing
Keyword(s):  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Free Vibrations ◽  
Variable Theory ◽  
First Order ◽  
Geometrical Constraints

A new first-order shear deformation theory (FSDT) with pure bending deflection and shearing deflection as two independent variables is presented in this paper for free vibrations of rectangular plate. In this two-variable theory, the shearing deflection is regarded as the only fundamental variable by which the total deflection and bending deflection can be expressed explicitly. In contrast with the conventional three-variable first-order shear plate theory, present variationally consistent theory derived by using Hamiltonian variational principle can uniquely define the bending and the shearing deflections, and give two rotations by the differentiations of bending deflection. Due to more restrictive geometrical constraints on rotations and boundary conditions, the obtained natural frequencies are equal to or higher than those by conventional FSDT for the rectangular plate with at least one pair of opposite edges simply supported. This new theory is of considerable significance in theoretical sense for giving a simple two-variable FSDT which is variational consistent and involve rotary inertia and shear deformation. The relation and differences of present theory with conventional FSDT and other relative formulations are discussed in detail.

Time-Dependent Creep Analysis for Life Assessment of Cylindrical Vessels Using First Order Shear Deformation Theory

2017 ◽  
Vol 33 (4) ◽  
pp. 461-474 ◽  
Author(s):  
M. D. Kashkoli ◽  
Kh. N. Tahan ◽  
M. Z. Nejad
Keyword(s):  
Analytical Solution ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Pressure Vessels ◽  
Life Assessment ◽  
Time Dependent ◽  
Creep Life ◽  
Creep Response ◽  
First Order

AbstractIn the present study, assuming that the thermo-elastic creep response of the material is governed by Norton's law, an analytical solution has been developed for the purpose of time-dependent creep response for isotropic thick-walled cylindrical pressure vessels. To study the creep response, the first-order shear deformation theory (FSDT) is applied. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT for time-dependent creep response of cylindrical pressure vessels. The novelty of the present work is that it seeks to investigate creep life of the vessels made of 304L austenitic stainless steel (304L SS) using Larson-Miller Parameter (LMP) based on FSDT. Using this analytical solution, stress rates are calculated followed by an iterative method using initial thermo-elastic stresses at zero time. When the stress rates are known, the stresses at any time are obtained and then using LMP, creep life of the vessels are investigated. The Problem is also solved, using the finite element method (FEM), the result of which are compared with those of the analytical solution and good agreement was found. It is found that the temperature gradient distribution has significant influence on the creep life of the cylinder, so that the maximum creep life is located at the outer surface of the cylinder where the minimum value of temperature is located.

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