An application of non-singularity BEM to plate bending, buckling and natural vibration problems

In this paper the fundamental solution of the singular governing equation of plate static bending is taken as the Green's function, which can satisfy the governing equation precisely in the plate region. Based on the principle of superposition, let the function values on the plate boundary, induced by a set of the Green's function sources (including the known sources in the plate region and the unknown sources in the fictitious region), satisfy the prescribed conditions on specially chosen boundary matching points, and the corresponding semi-analytical and semi-numerical solution can be obtained, which is free from the restraint of boundary forms and boundary conditions. The more matching points there are on the boundary, the better the accuracy of results is. Finally, in static bending problems a set of linear algebraic equations has to be computed; in buckling problems the minimum value of buckling eigenvalue equation has to be found; in natural vibration problems the eigenvalues of the frequency equation have to be calculated. Numerical examples are given and the results are compared with those by the analytical method and other methods. It can be seen that they are very close to each other.