An equivalent boundary integral formulation for bending problems of thin plates

For the bending problems of simply supported thin plates, the governing bi-harmonic equation can be decomposed into two independent Poisson equations based upon Kirchhoff theory. The conventional boundary integral formulations based on this decomposition technique have been proved to yield non-equivalent solutions compared with the boundary value problem. In this paper, a boundary integral formulation called an equivalent boundary integral equation has been deduced from Poisson equations, and it is also numerically shown that the problem of solution non-equivalence of the conventional boundary integral equation does not exist in the equivalent boundary integral equation.