Biharmonic Problem in a Rectangle |
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Authors: | VV Meleshko |
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Institution: | (1) Fluid Dynamics Laboratory, Department of Technical Physics, Eindhoven University of Technology, p.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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Abstract: | This paper addresses the fascinating long history of the classical two-dimensional biharmonic problem for a rectangular domain. Among various mathematical and engineering approaches, the method of superposition is effective for solving mechanical problems concerning creeping flow of viscous fluid set up in a rectangular cavity by tangential velocities applied along its walls, an equilibrium of an elastic rectangle, and bending of a clamped thin rectangular elastic plate by a normal load. The object of this paper is both to clarify some purely mathematical questions connected with the solution of the infinite systems of linear algebraic equations and to provide a considerable simplification of the numerical algorithm. The method is illustrated by several examples of steady Stokes flow in a square cavity. |
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Keywords: | biharmonic equation rectangle method of superposition creeping Stokes flows |
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