BIHARMONIC PROBLEM IN A RECTANGLE

This paper addresses the fascinating long history of the classical two -dimensional biharmonic problem for a rectangular domain. Among variou s 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 velocit ies applied along its walls, an equilibrium of an elastic rectangle, a nd bending of a clamped thin rectangular elastic plate by a normal loa d. The object of this paper is bath to clarify some purely mathematica l questions connected with the solution of the infinite systems of lin ear algebraic equations and to provide a considerable simplification o f the numerical algorithm. The method is illustrated by several exampl es of steady Stokes flow in a square cavity.