Mixed plane problems in linearized solid mechanics

Exact solutions

A N Guz, Igor Guz

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann-Hilbert methods and Keldysh-Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin.

Original languageEnglish
Pages (from-to)1-29
Number of pages30
JournalInternational Applied Mechanics
Volume40
Issue number1
DOIs
Publication statusPublished - 2004

Keywords

  • mixed plane problems
  • exact solution
  • linearized solid mechanics
  • universal form of solutions
  • complex representations
  • 2 prestressed materials
  • initial stresses
  • dynamic problems
  • brittle-fracture
  • interface cracks
  • contact problems
  • elastic bodies
  • unequal roots
  • equal roots
  • compressible bodies

Cite this

Mixed plane problems in linearized solid mechanics : Exact solutions. / Guz, A N; Guz, Igor.

In: International Applied Mechanics, Vol. 40, No. 1, 2004, p. 1-29.

Research output: Contribution to journalArticle

@article{6a7cb39e4de542109a4896cd978f0806,
title = "Mixed plane problems in linearized solid mechanics: Exact solutions",
abstract = "The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann-Hilbert methods and Keldysh-Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin.",
keywords = "mixed plane problems, exact solution, linearized solid mechanics, universal form of solutions, complex representations, 2 prestressed materials, initial stresses, dynamic problems, brittle-fracture, interface cracks, contact problems, elastic bodies, unequal roots, equal roots, compressible bodies",
author = "Guz, {A N} and Igor Guz",
year = "2004",
doi = "10.1023/B:INAM.0000023808.08859.48",
language = "English",
volume = "40",
pages = "1--29",
journal = "International Applied Mechanics",
issn = "1063-7095",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Mixed plane problems in linearized solid mechanics

T2 - Exact solutions

AU - Guz, A N

AU - Guz, Igor

PY - 2004

Y1 - 2004

N2 - The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann-Hilbert methods and Keldysh-Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin.

AB - The paper analyzes the exact solutions to mixed plane problems of linearized solid mechanics in cases of statics, dynamics, stability, and fracture. The exact solutions have a universal form for compressible and incompressible, elastic and plastic bodies and account for stresses and displacements expressed in terms of analytical functions of complex variables. To obtain these solutions, the use is made of complex variable theory, in particular, the Riemann-Hilbert methods and Keldysh-Sedov formula. When the initial (residual) stresses tend to zero, the exact solutions go over into the corresponding exact solutions of classical linear solid mechanics, which are based on the complex representations due to Muskhelishvili, Lekhnitskii, and Galin.

KW - mixed plane problems

KW - exact solution

KW - linearized solid mechanics

KW - universal form of solutions

KW - complex representations

KW - 2 prestressed materials

KW - initial stresses

KW - dynamic problems

KW - brittle-fracture

KW - interface cracks

KW - contact problems

KW - elastic bodies

KW - unequal roots

KW - equal roots

KW - compressible bodies

U2 - 10.1023/B:INAM.0000023808.08859.48

DO - 10.1023/B:INAM.0000023808.08859.48

M3 - Article

VL - 40

SP - 1

EP - 29

JO - International Applied Mechanics

JF - International Applied Mechanics

SN - 1063-7095

IS - 1

ER -