Analysis of local singular fields near the corner of a quarter-plane with mixed boundary conditions in finite plane elastostatics

We investigate a partially debonded circular elastic inclusion embedded in a particular class of harmonic materials by using the complex variable method under finite plane-strain deformations. A complete (or full-field) solution is derived. It is observed that the stresses in general exhibit oscillatory singularities near the two tips of the arc shaped interface crack. Particularly the traditional inverse square root singularity for stresses is observed when the asymptotic behavior of the harmonic materials obeys a constitutive restriction proposed by Knowles and Sternberg (1975, “On the Singularity Induced by Certain Mixed Boundary Conditions in Linearized and Nonlinear Elastostatics,” Int. J. Solids Struct., 11, pp. 1173–1201). It is also found that the number of admissible states under finite plane deformations for given external loads can be two, one, or even zero.

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POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS

Acta Mathematica Scientia ◽

10.1016/s0252-9602(18)30162-0 ◽

1992 ◽

Vol 12 (3) ◽

pp. 292-303

Author(s):

Ruying Xue

Keyword(s):

Boundary Conditions ◽

Positive Solutions ◽

Elliptic Equations ◽

Mixed Boundary ◽

Nonlinear Elliptic Equations ◽

Mixed Boundary Conditions ◽

Nonlinear Elliptic

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Effects of transverse shear on large deflection random response of symmetric composite laminates with mixed boundary conditions

10.2514/6.1989-1356 ◽

1989 ◽

Cited By ~ 3

Author(s):

C. PRASAD ◽

CHUH MEI

Keyword(s):

Boundary Conditions ◽

Transverse Shear ◽

Composite Laminates ◽

Large Deflection ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Random Response

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

Journal of High Energy Physics ◽

10.1007/jhep01(2021)039 ◽

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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