On a Kind of Biharmonic Boundary Value Problems Related to Clamped Elastic Thin Plates

By using complex variable methods, the houndary value problem for biharmonic functions arisen from the theory of clamped elastic thin plate is shown to be equivalent to the first fundamental problem in plane elasticity which, as well-known,may be easily solved by reduction to a Fredholm integral equation. The case of circular plate is illustrated in detail,the solution of which is obtained in closed form.