Abstract
The general formulations presented in Part 1 of this paper are applied to some boundary value problems of structural mechanics. The bending problems of an elastic beam with the Bernoulli-Euler assumption are selected as the fundamental ones and are analyzed numerically. The numerical results are illustrated by the linear bending of beam with the four cases on boundary conditions and the nonlinear deflection of horizontal cantilever subjected to a vertical point load or a uniformly distributed load. The results are compared with exact ones for linear ceses and Ritz's solutions for nonlinear cases, respectively. It is shown that our integral equation approach, especially a canonical formulation, produces the better results by means of fundamental solutions with a comparatively simple structure. Although the problems treated in this paper are restricted to a beam theory governed by an ordinary differential equation, our approach is also applicable to shell problems governed by a system of partial differential equations as previously reported in an another paper.
