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Series expansions of biharmonic functions around a slit

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1121)

Keywords

  • Stress Intensity Factor
  • Normal Derivative
  • Biharmonic Equation
  • Biharmonic Function
  • Angular Point

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References

  • Blum, H. and Rannacher, R. (1980). On the boundary value problem of the biharmonic operator on domains with angular corners. Math. Meth. in Appl. Sci. 2, pp.556–581.

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  • Grisvard, P. (1976). Behaviour of the solutions of an elliptic boundary value problem in a polygonal or polyhedral domain. Numerical solution of partial differential equations. III. B. Hubbard, editor. Academic Press, pp.207–274.

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  • Kondratev, V.A. (1967). Boundary problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc. 16, pp.227–313.

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  • Melzer, H. and Rannacher, R. (1980). Spannungskonzentrationen in Eckpunkten der Kirchhoffschen Platte. Bauingenieur, 55, pp. 181–184.

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  • Poritzki, H. (1946). Application of analytic functions to two-dimensional biharmonic analysis. Trans. A.M.S., vol.59, pp.248–279.

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  • Steinberg, J. (1980, 1982). The symmetry principle for biharmonic functions and its application to a problem in fracture mechanics. Technion preprint series No.MT-492, and No.MT-563.

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  • Williams, M.L. (1957). On the stress distribution at the base of a stationary crack. J. Appl. Mech.24, pp.109–114.

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© 1985 Springer-Verlag

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Steinberg, J. (1985). Series expansions of biharmonic functions around a slit. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076277

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  • DOI: https://doi.org/10.1007/BFb0076277

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15219-4

  • Online ISBN: 978-3-540-39377-1

  • eBook Packages: Springer Book Archive