A semi-analytical solution for forced vibrations response of rectangular orthotropic plates with various boundary conditions

2010 ◽  
Vol 24 (1) ◽  
pp. 357-364 ◽  
Author(s):  
Ahmad Rahbar Ranji ◽  
Hamidreza Rostami Hoseynabadi
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Forced Vibrations ◽  
Orthotropic Plates ◽  
Various Boundary Conditions

LINEAR BENDING ANALYSIS OF INHOMOGENEOUS VARIABLE-THICKNESS ORTHOTROPIC PLATES UNDER VARIOUS BOUNDARY CONDITIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 417-438 ◽  
Author(s):  
A. M. ZENKOUR ◽  
M. N. M. ALLAM ◽  
D. S. MASHAT
Keyword(s):  
Boundary Conditions ◽  
Variable Thickness ◽  
Flexural Rigidity ◽  
Approximate Solutions ◽  
Rectangular Plates ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Thickness Parameter ◽  
Space Concept

An exact solution to the bending of variable-thickness orthotropic plates is developed for a variety of boundary conditions. The procedure, based on a Lévy-type solution considered in conjunction with the state-space concept, is applicable to inhomogeneous variable-thickness rectangular plates with two opposite edges simply supported. The remaining ones are subjected to a combination of clamped, simply supported, and free boundary conditions, and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for inhomogeneous variable-thickness plates as for isotropic homogeneous plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Benchmark numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of inhomogeneity, aspect ratio, thickness parameter, and the degree of nonuniformity on the deflections and stresses are investigated.

A Reduction Method for Buckling Problems of Orthotropic Plates

1957 ◽  
Vol 8 (2) ◽  
pp. 145-156 ◽  
Author(s):  
P. Shuleshko
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Reduction Method ◽  
Isotropic Plate ◽  
Axial Loading ◽  
Orthotropic Plates ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Plate Buckling

SummarySeveral plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.

scholarly journals ANALYTICAL SOLUTION OF THE EQUATION OF CONDUCTIVITY FOR VARIOUS BOUNDARY CONDITIONS

2019 ◽  
Vol 2019 (4) ◽  
pp. 33-37
Author(s):  
Vadim Krys'ko ◽  
Olga Saltykova ◽  
Alexey Tebyakin
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Solution Method ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensional ◽  
Various Boundary Conditions ◽  
The Finite Difference Method

The aim of the work is to obtain an analytical solution of the heat equation for various boundary conditions in the case of a two-dimensional body. As a solution method, the method of variational iterations is used. In the work, both an analytical and a numerical solution of the problem are obtained for the boundary conditions of various types and taking into account the internal heat source. To obtain a numerical solution, the finite difference method was used. The results are compared and the conclusion is made on the reliability of the decisions.

Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates

1999 ◽  
Vol 67 (3) ◽  
pp. 558-567 ◽  
Author(s):  
S. S. Vel ◽  
R. C. Batra
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Laminated Plates ◽  
The Body ◽  
Rectangular Plates ◽  
Laminated Plate ◽  
Various Boundary Conditions ◽  
Linear Piezoelectricity ◽  
Piezoelectric Plates

Analytical solutions for the static three-dimensional deformations of multilayered piezoelectric rectangular plates are obtained by using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thicknesses. The equations of static, linear, piezoelectricity are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series; the continuity conditions at the interfaces and boundary conditions at the edges are used to determine the coefficients. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. Results are presented for thick piezoelectric plates with two opposite edges simply supported and the other two subjected to various boundary conditions. [S0021-8936(00)01803-1]

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