Eigenpairs for Two-Dimensional Elasticity

Zohar Yosibash

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


The two-dimensional elastic solution in the vicinity of a singular point has the same characteristics as presented for the heat conduction solution, namely, it can be expanded as a linear combination of eigenpairs and their coefficients: (formula presented) r and _ being the polar coordinates of a system located in the singular point, and ?i and s._/ are the eigenpairs; M is zero except for cases in which the boundary near the singular point is curved (see Appendix C), and logarithmic terms may be present J ¤ 0 only for special cases for which m multiple eigenvalues exist with fewer than m corresponding eigenvectors (the algebraic multiplicity is grater than the geometric multiplicity), or when inhomogeneous BCs are prescribed on the V- notch faces. This case is not rigorously discussed in this chapter, but several remarks are provided at the end of it and it is further addressed in the chapters that compute the eigenpairs numerically.

Original languageEnglish
Title of host publicationInterdisciplinary Applied Mathematics
PublisherSpringer Nature
Number of pages36
StatePublished - 1 Jan 2012

Publication series

NameInterdisciplinary Applied Mathematics
ISSN (Print)0939-6047
ISSN (Electronic)2196-9973


  • Complex Eigenvalue
  • Homogeneous Boundary Condition
  • Isotropic Material
  • Logarithmic Singularity
  • Singular Point

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Management Science and Operations Research


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