Classical solutions of forced vibration of rectangular plate driven by displacement boundary conditions

2006 ◽  
Vol 291 (3-5) ◽  
pp. 1104-1121 ◽  
Author(s):  
S.R. Wu
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Forced Vibration ◽  
Classical Solutions ◽  
Displacement Boundary

Series Solution and Stress Analysis of Rectangular Plate With Mixed Boundary Conditions

2005 ◽  
Author(s):  
Jiemin Liu ◽  
Jintang Liu ◽  
Toshiyuki Sawa
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Size Factor ◽  
Singular Stress ◽  
Feature Size ◽  
Concentrated Force ◽  
Displacement Boundary

Stress functions expressed from Fourier series, suitable for arbitrary stress boundary conditions, were derived using method of variable separation. General displacement expressions containing the displacement of rigid body were also derived. A method of solving mixed boundary problems (in which external forces acting at a part of the whole boundaries are known and displacements at the rest boundaries are known) was presented. As an example, a rectangular plate, one side of which was fixed and objective side was subjected to a concentrated force, was analyzed. In addition, characteristics of stress distributions in the regions of stress concentration were questioned. It was found from the presented results of calculation that describing stress concentration with the singular stress at a point was unworkable. Describing stress concentration with the average stress in the feature size instead of the singular stress at a point was operative and reflected objectively practical stress and displacement boundary conditions. The concept of feature-size-factor was introduced.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Classical Solutions ◽  
Schauder Estimate ◽  
Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

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