Mixed plane problems in linearized solid mechanics: Exact solutions

A N Guz, Igor Guz

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2004


  • 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


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