| In this dissertation, the Boundary Integral Equation (BIE) method is developed for plates on elastic foundation.; In Part I, two versions of Green's identity for the operator ((DEL)('4) + (kappa)('2)) which governs the deflection of thin plates, resting on an elastic foundation, are established. They are used to derive two integral representations for the deflection of the plate and the corresponding sets of boundary integral equations. In the first version, the boundary terms do not have direct physical meaning, whereas, in the second version they have physical significance. The existence of the boundary integrals is proven and their discontinuity is evaluated. Moreover, an elegant procedure is presented for the evaluation of the influence fields for the deflections, slopes, bending and twisting moments and shearing forces. The influence fields are obtained as the deflection surfaces due to appropriate generalized loads, using a generalized form of the reciprocal theorem.; In Part II, a procedure for the numerical solution of the coupled singular boundary integral equations for clamped and simply supported plates is presented. The boundary integral equations are approximated by a system of simultaneous linear algebraic equations by dividing the boundary of the plate into a finite number of elements on which the unknown boundary quantities are assumed to vary according to a chosen law. Moreover, a procedure is developed for the numerical evaluation of double integrals having a logarithmic or a Caucy-type singularity.; In Part III, numerical results are presented for clamped and simply supported plates. The results are in excellent agreement with those obtained from existing analytical solutions. For small values of the constant of the elastic foundation, the results differ negligibly from those of plates which do not rest on an elastic foundation. The influence coefficients for the deflections and the stress resultants at some points of clamped and simply supported circular and rectangular plates are tabulated for certain values of appropriately chosen dimensionless parameters. |
