Regularized boundary integral equation formulations for thin elastic plate bending analysis

The boundary integral equations conventionally used for thin elastic plate bending analysis have the singularities of the Cauchy principal value order for which special care must be taken in numerical evaluation when the boundary is discretized by using the higher-order elements. In the present paper, the boundary integral equations are regularized up to an integrable order by using the subtracting and adding back technique. The obtained boundary integral equations both for deflection and rotation are weakly singular, and their discretized forms can be integrated accurately by the standard Gaussian quadrature formula. Numerical implementation of the resulting regularized integral equations is presented, and effectiveness of the proposed method is discussed through some numerical demonstrations.