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Computation of corner singularities in linear elasticity. (English) Zbl 0822.35040

Costabel, Martin (ed.) et al., Boundary value problems and integral equations in nonsmooth domains. Proceedings of the conference, held at the CIRM, Luminy, France, May 3-7, 1993. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 167, 59-68 (1995).
It is well known that elliptic boundary value problems admit non-regular solutions when the domain has corners on its boundary and these singular solutions are determined by an eigenvalue problem of a (system of) ordinary differential equations on an interval. In this paper, the authors give an explicit construction for solution basis of such (system of) equations in the most general case. Together with boundary conditions imposed one can easily compute the exponents of the singularities from a given analytic function. The authors describe this construction for \(2\times 2\) systems of order 2, and give the solution basis and the resulting explicit method for the computation of the exponents of the singularities in the case of orthotropic elasticity. They also present some of the numerical results so obtained.
For the entire collection see [Zbl 0810.00016].
Reviewer: H.Ding (Beijing)

MSC:

35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35A20 Analyticity in context of PDEs
74B05 Classical linear elasticity
35Q72 Other PDE from mechanics (MSC2000)
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