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Function theoretic solutions to problems of orthotropic elasticity

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Abstract

The plane strain problem for a two dimensional orthotropic elastic body is investigated. In particular analytic representations for the solution of the displacement boundary value problem and the stress boundary value problems are found. To this end, the Navier equations are reduced by means of composite transformations to normal form. These are the so-called equations for bianalytic function of the type (λk). The generalized Cauchy integral formula for this function theory is used to obtain representation formulae. A simplified method to solve these problems by bianalytic function theory is given for certain situations of plane strain for an orthotropic elastic body. AMS (MOS): 35A20, 35CO5, 35G15, 35J55.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Delaware, 19711, Newark, DE, USA

    Robert P. Gilbert

  2. Zhongshan University, Guangzhou, People's Republic of China

    Lin Wei

Authors
  1. Robert P. Gilbert
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  2. Lin Wei
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Additional information

Applied Mathematics Institute Technical Report No. 140A, July 1983.

The work of this author was supported in part by grant no. DE-AC01-81ER-10967 from the Department of Energy.

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Gilbert, R.P., Wei, L. Function theoretic solutions to problems of orthotropic elasticity. J Elasticity 15, 143–154 (1985). https://doi.org/10.1007/BF00041989

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  • DOI: https://doi.org/10.1007/BF00041989

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