On the uniqueness of solutions for the Dirichlet boundary value problem of linear elastostatics in the circular domain |
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Authors: | A Rohe F Molenkamp W T Van Horssen |
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Affiliation: | (1) Geo-engineering Section, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands |
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Abstract: | Summary The uniqueness and mathematical stability of the Dirichlet boundary value problem of linear elastostatics is studied. The
problem is posed as a set of partial differential equations in terms of displacements and Dirichlet-type of boundary conditions
(displacements) for arbitrary bounded domains. Then for the circular interior domain the closed form analytical solution is
obtained, using an extended version of the method of separation of variables. This method with corresponding complete solution
allows for the derivation of a necessary and sufficient condition for uniqueness. The results are compared with existing energy
and uniqueness criteria. A parametric study of the elastic characteristics is performed to investigate the behaviour of the
displacement field and the strain energy distribution, and to examine the mathematical stability of the solution. It is found
that the solution for the circular element with hourglass-like boundary conditions will be unique for all v ≠ 0.5, 0.75, 1.0 and will be mathematically stable for all v ≠ 0.75. Locking of the circular element occurs for v = 0.75 as the energy tends to infinity. |
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