Stress and Mixed Boundary Conditions for Bending and Stretching of Transversely Isotropic Elastic Beams

2012 ◽  
Vol 16 (1) ◽  
pp. 372-376
Author(s):  
Yang Gao ◽  
Bai-Xiang Xu
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Transversely Isotropic ◽  
Mixed Boundary Conditions ◽  
Elastic Beams

Impedance Functions for Surface Rigid Rectangular Foundations on Transversely Isotropic Multilayer Half-Spaces

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Amirhossein Amiri-Hezaveh ◽  
Morteza Eskandari-Ghadi ◽  
Mohammad Rahimian ◽  
Amir K. Ghorbani-Tanha
Keyword(s):  
Boundary Conditions ◽  
Half Space ◽  
Mixed Boundary ◽  
Surface Displacement ◽  
Transversely Isotropic ◽  
Mixed Boundary Conditions ◽  
Integral Transforms ◽  
Material Symmetry ◽  
Time Harmonic ◽  
Impedance Functions

A horizontally multilayered Green elastic transversely isotropic half-space is considered as the domain of the boundary value problem involved in this paper, such that the axes of material symmetry of different layers are parallel to the axis of material symmetry of the lowest half-space, which is depthwise. The domain is assumed to be affected by an arbitrary time-harmonic forced vibration due to a rigid rectangular surface foundation. With the use of a potential function method and the Hankel integral transforms, the displacements and stresses Green's functions are determined in each layer. The unknown functions due to integrations in each layer are transformed to the unknown functions of the surface layer with the use of the concept of propagator matrix and the continuity conditions. The mixed boundary conditions at the surface of the whole domain are numerically satisfied with the assumption of piecewise constant distribution of tractions in the contact area. It is numerically shown that the surface displacement and stress boundary conditions are satisfied very well. The vertical and horizontal impedance functions of the rectangular foundation are determined, which may be used as lumped parameters in time-harmonic soil-structure interaction with transversely isotropic horizontally layered domain as the soil. It is shown that the impedance functions determined in this paper coincide with the same functions for the simpler case of isotropic homogeneous half-space as degenerations of this study.

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.

scholarly journals Casimir effect for a massive scalar field under mixed boundary conditions

2003 ◽  
Vol 33 (4) ◽  
pp. 860-866 ◽  
Author(s):  
A.C. Aguiar Pinto ◽  
T.M. Britto ◽  
R. Bunchaft ◽  
F. Pascoal ◽  
F.S.S. da Rosa
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massive Scalar ◽  
Massive Scalar Field
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