scholarly journals The solution of certain loss of contact between a plate and unilateral supports

2007 ◽  
Vol 34 (4) ◽  
pp. 289-308
Author(s):  
Yos Sompornjaroensuk ◽  
Kiattikomol Kraiwood
Keyword(s):  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Free Edge ◽  
Hankel Transform ◽  
Middle Line ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Loss Of Contact ◽  
Finite Hankel Transform ◽  
Square Plate

This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson?s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson?s ratio.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution

1983 ◽  
Vol 126 ◽  
pp. 237-250 ◽  
Author(s):  
S. S. Sadhal ◽  
Robert E. Johnson
Keyword(s):  
Exact Solution ◽  
Liquid Drop ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Creeping Flow ◽  
Immiscible Fluid ◽  
Interfacial Tensions ◽  
Surfactant Film ◽  
Dual Series Equations ◽  
The Difference

In this investigation the creeping flow due to the motion of a liquid drop or a bubble in another immiscible fluid is examined when the interface is partially covered by a stagnant layer of surfactant. The associated boundary-value problem involves mixed boundary conditions at the interface, which lead to a set of dual series equations. An inversion of these equations yields the exact solution to the stagnant cap problem.Several useful results are obtained in closed form. Among these are the expressions for the drag force, the difference between the maximum and the minimum interfacial tensions, and the amount of adsorbed surfactant. A shifting of the centre of the internal vortex is observed.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

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