Existence of weak solutions in elasticity

Solvability and uniqueness of solutions to the problems of equilibrium, vibration and dynamics in a weak setup for classical and nonclassical models of linear elasticity are established in a unified framework sufficiently flexible to accommodate new elastic models.

[1]  Peter Schiavone,et al.  A clarification of the role of crack-tip conditions in linear elasticity with surface effects , 2013 .

[2]  Xi-Qiao Feng,et al.  Surface stress effect in mechanics of nanostructured materials , 2011 .

[3]  Morton E. Gurtin,et al.  A continuum theory of elastic material surfaces , 1975 .

[4]  Victor A. Eremeyev,et al.  On the existence of solution in the linear elasticity with surface stresses , 2010 .

[5]  G. Fichera Existence Theorems in Elasticity , 1973 .

[6]  Bhushan Lal Karihaloo,et al.  Theory of Elasticity at the Nanoscale , 2009 .

[7]  Peter Schiavone,et al.  Solvability of boundary value problems in a theory of plane-strain elasticity with boundary reinforcement , 2009 .

[8]  Leonid P. Lebedev,et al.  Functional analysis in mechanics , 2002 .

[9]  G. Gustafson,et al.  Boundary Value Problems of Mathematical Physics , 1998 .

[10]  S. L. Sobolev,et al.  Some Applications of Functional Analysis in Mathematical Physics , 1991 .

[11]  Peter Schiavone,et al.  Effect of surface elasticity on an interface crack in plane deformations , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[12]  Victor A. Eremeyev,et al.  On the spectrum and stiffness of an elastic body with surface stresses , 2011 .

[13]  Ray W. Ogden,et al.  Elastic surface—substrate interactions , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  A. Korn Solution générale du problème d'équilibre dans la théorie de l'élasticité, dans le cas ou les efforts sont donnés à la surface , 1908 .

[15]  S. L. Sobolev,et al.  Applications of functional analysis in mathematical physics , 1963 .

[16]  Paul Steinmann,et al.  Relationships between the admissible range of surface material parameters and stability of linearly elastic bodies , 2012 .

[17]  José Barros-Neto,et al.  Problèmes aux limites non homogènes , 1966 .

[18]  B. L. Karihaloo,et al.  Theory of Elasticity at the Nano-Scale , 2008 .

[19]  Paul Steinmann,et al.  On thermomechanical solids with boundary structures , 2010 .