Relaxation methods applied to engineering problems - Biharmonic analysis as applied to the flexure and extension of flat elastic plates

Abstract

By extension of technique described in earlier papers, biharmonic analysis and the solution of the equation V%> = W are brought within range of the relaxation method. Special attention is given to the problem of a fiat elastic plate which is either bent or stretched (the second case being that to which photo-elastic methods are commonly applied). In all, four cases are presented, since the edge conditions may specify either tractions or displacements both in the flexural and in the extensional problem: one example of each is treated. Mixed boundary conditions (tractions specified at some points, displacements at others) are not considered in this paper. It would seem that only slight modifications of method will be required to deal with acolo-tropic plates (which present much greater difficulties in an orthodox analysis).