Uniformly loaded plate supported by an array of circular posts

An infinite, uniformly loaded thin plate is supported by an infinite two-dimensional array of circular posts. The moment, shear and deflections are determined by collocation methods. As the post radii b shrink to zero, asymptotic analysis shows the maximum moment increases as |ln b| and the maximum shear increases as b−1. The triangular array is found to incur much lower stresses and deformations than the square array.