Natural boundary element method for plane problem and bending problem of the elastic circular plate

Abstract：Both the plane problem of the elastic thin plate with Airy stress function serving as its unknown variable, and the bending problem with deflection serving as its unknown variable can be reduced to the boundary value problem of bi-harmonic equation.From this point, they are similar.With the Poisson integral formula from the natural boundary reduction for the bi-harmonic problem of interior circular domain, the boundary integral formulas of the Airy stress function and the bending deflection in the circular plate are put forward.Through the integral formula, the analytic solutions to the simple boundary value problems can be obtained directly, and for the complicated boundary value problems, the numerical solutions of high precision can be acquired.

Keyword：circular plate;plane problem;bending problem;natural boundary element method;