Bending of Rectangular Cross‐Section Cantilever with Cylindrical Cutouts

Using a special class of basis functions, the Saint‐Venant flexure function suitable for the problem of bending of a rectangular bar with $\mathrm{4N}(N=1\text{,}2\text{,}3\text{,}••\text{.})$ circular‐cylindrical cavities is obtained. It is assumed that the load passes through the centroid of the symmetrical cross section of the beam. It is also assumed that all conditions needed for the Saint‐Venant solution of bending of prismatic bars are met. The linearly‐independent basis functions automatically satisfy a homogeneous outer‐boundary condition. They are generated by integrating the products of trigonometric functions and the Green's function for the solution of the Poisson equation with singularities symmetrically located in four quadrants. By shrinking the radius of the closed circular path of integration, and by certain limiting processes, the integrations are performed analytically, leading to the basis functions in the form of infinite series. The convergence of these series is accelerated by using an analytic function and its derivatives. The inner‐boundary conditions(s) is (are) satisfied with the point‐by‐point technique and method of least square error.