An analytical singular element for interface cracks in bi-material Kirchhoff plate bending

By introducing appropriate transformations, a circular sector Kirchhoff plate bending composed of dissimilar materials with both straight sides free is led into symplectic duality system in this paper. The problem is solved by using the symplectic eigenfunction expansion method, and analytical expressions of symplectic eigenvalues and eigensolutions are derived. Using the symplectic eigensolutions as a displacement model, an analytical singular element is developed for the interface crack. Bending stress intensity factors can be determined directly from the expansion coefficients of the eigensolution. Numerical results show that the present method has a high accuracy in the calculation of stress intensity factors.