Fracture mechanics analysis of geometrically nonlinear thin plates by FEM /Hamid Taheri - Hamid, Taheri (2013)
In this study, general introduction and methodology of fracture mechanics analysis of plate are developed. The geometrical nonlinearities are due to large deformation or rotation. Two major theories in the analysis of plates consist of Kirchhoff and Reissner- Mindlin plate theories which former is suited for thin plates and latter for thicker plates. In order to perform geometrically nonlinear plate analysis, bending problems includes the interaction of plate out of plane bending and in-plane loadings. Different methods for the crack tip calculations of stress intensity factor were proposed which among them crack tip displacement method were found to be more convenient and straight forward for implementation based on specifically formed elements at the crack tip. During the implementation of ANSYS® codes, it was noticed that by applying modified Newton- Raphson method with carefully selected numbers of iterations and sub-steps both accuracy and time are served. Two different finite element method simulations of geometrically nonlinear plate structures were performed. A square and a rectangular plate possessing a center crack were subjected to different boundary conditions of clamped and simply supported edges separately. In both examples, the range of bending stress intensity factors was higher than the membrane stress intensity factor. By having aspect ratios of width divided by length of the geometry, b l , upper than 1, the bending stress intensity factor after a certain number of load increments is increasing significantly while the membrane stress intensity factor is not having any considerable changes for the clamped edges condition but has comparable amount for the simply supported edges.