Green’s functions for the bending of thin plates under various boundary conditions and applications: a review

Hasebe, Norio; Wang, X.

doi:10.1016/s0263-8231(02)00015-0

Cited by 6 publications

(1 citation statement)

References 32 publications

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“…The function theory in that case becomes significantly easier with the solutions for Φ ( ζ ) and Ψ ( ζ ) also being rational functions. But then the approach we have demonstrated here reduces to ideas that are already well known in solid mechanics; see, for example, the review on the bending of thin plates using the so-called ‘rational function method’ by Hasebe & Wang [ 29 ]. What we have shown here is that if one wants to extend the rational function method to multiply connected regions, then the natural mathematical generalization is to consider the class of multiply connected quadrature domains; the boundaries of those domains can be parametrized by so-called automorphic functions [, 23 , 24 , 26 ] (i.e.…”

Section: Discussionmentioning

confidence: 99%

Stress fields around two pores in an elastic body: exact quadrature domain solutions

Crowdy

2015

Proc. R. Soc. A.

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Analytical solutions are given for the stress fields, in both compression and far-field shear, in a twodimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the SchottkyKlein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

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