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The approximation of the exact boundary conditions at an artificial boundary for linear elastic equations and its application. (English) Zbl 0754.35008

Equations of linear elasticity for plane unbounded domains are solved. The applied method is to introduce an artificial boundary to cut off the unbounded part of the domain and set up an artificial boundary condition at the artificial boundary of the remaining bounded domain. A sequence of approximations to the exact boundary condition at the artificial boundary is given and the original exterior problem is reduced to an equivalent boundary value problem on a bounded domain. The approximate boundary value problem on the bounded domain is solved by the finite element method. An optimal error estimate of the finite element solution is given.
A numerical example shows the presented method to be very effective. In the numerical example the unbounded domain is the exterior domain of square and the linear finite element approximation is used for computations.

MSC:

35A35 Theoretical approximation in context of PDEs
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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