A modified Kirchhoff theory for boundary element analysis of thin plates resting on two-parameter foundation

This paper introduces a boundary element analysis of thin plates resting on a two-parameter elastic foundation, based on a modified Kirchhoff theory in which the transverse normal stress is considered. The boundary integral equations are derived with three degrees-of-freedom per boundary node, thus avoiding the generation of unknown corner terms for plates with nonsmooth boundaries. Explicit expressions of kernel functions are provided in terms of complex Bessel functions. Additional boundary element derivations for plates with free-edge conditions are presented, and reduction of loading domain integral terms for cases with concentrated loads and moments, and uniformly- or linearly-distributed loading is included. Several case studies have been analysed and the results were compared with the corresponding analytical solutions, It is clear that the three degrees-of-freedom approach has led to very accurate results for plates with corners. The transverse normal stress has a minor effect on plate deflection, but it has some effect on stresses and moments, which increases with the thickness of the plate.