مهندسی عمران شریف (Nov 2018)
CRACK GROWTH SIMULATION USING COLLOCATION DISCRETE LEAST SQUARES, COHESIVE CRACK, AND DIFFRACTION METHODS
Abstract
During recent years, many researches have been conducted on the numerical methods for solving the governing differential equations. FEM is one of the strongest and most useful of these methods. However, this method encounters some difficulties when deals with the problems involving moving boundaries, crack propagation or extremely large deformation due to the need of renewing the mesh of the elements. One of the solutions is the elimination of the need for the mesh. Therefore, the meshfree methods have been developed. In the present study, Collocation Discrete Least Squares Meshless method (CDLSM) is formulated for predicting the crack growth phenomenon in the two-dimensional elastic solid problems. For simulating the crack initiation and growth, the cohesive crack concept has been implemented. CDLSM is a true meshless method which is developed based on the minimization of the sum of the squares of the errors in the nodal points in the domain and on the boundaries and does not use any kinds of background mesh for approximating the response function or for discretizing the developed system of equations. These errors in this study have been defined as the differences between the computed response from the proposed method in the nodal points and their corresponding exact responses within the domain and on the boundaries. Based on the concept of the cohesive crack, the crack initiation is modeled by controlling the existed applied vertical stresses on the crack faces. When these stresses reach a certain value, specifically in this study, the tensile strength of the concrete, the crack initiation is assumed to be occurred. After cracking, depending on the value of the opening crack displacement, (COD), applied stresses are enforced to reduce to zero for completely opened crack. For incorporating the discontinuity arising from the crack into the continuum shape function formulations of the proposed meshless method, the diffraction technique has been used.
Keywords
