Determination of stress intensity factors for finite cracked bimaterial plates in bending

A finite element discretized symplectic method is presented for the determination of modes I and II stress intensity factors (SIFs) for cracked bimaterial plates subjected to bending loads using Kirchhoff’s theory and symplectic approach. The overall plate is meshed by conventional discrete Kirchhoff theory elements and is divided into two regions: a near field which contains the crack tip and is enhanced by the symplectic series expansion and a far field which is far away from the crack tip. Based on the analytical solutions of global displacement, numerous degrees of freedom are transformed to a small set of undetermined coefficients of the symplectic series through a displacement transformation, while those in the far field remain unchanged. The SIFs can be obtained directly from coefficients of eigensolution (Reμ<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu < 1$$\end{document}), and no post-processing or special singular element are required to develop for extracting the SIFs. Numerical examples are presented and compared with existing results to demonstrate the efficiency and accuracy of the method.