Multiple reciprocity method with two series of sequences of high-order fundamental solution for thin plate bending

Abstract

The boundary value problem of plate bending problem on two-parameter foundation was discussed. Using two series of the high-order fundamental solution sequences, namely, the fundamental solution sequences for the multi-harmonic operator and Laplace operator, applying the multiple reciprocity method (MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high-order fundamental solution sequences.