Numerical Simulations of Fracture Problems by Coupling the Fem and the Direct Method of Lines
نویسندگان
چکیده
In this paper, we propose a method for calculating stress intensity factors of plane fracture problems with cracks by coupling the ®nite element method (FEM) and the direct method of lines. We introduce polygonal arti®cial boundaries and divide the physical domain into two parts: a large domain without any crack tips and small polygonal domains surrounding the crack tips. We solve the problem de®ned in the small domains with crack tips by using the direct method of lines and design discrete nonlocal arti®cial boundary conditions on the polygonal arti®cial boundaries by imposing the continuity of displacement and normal stress. Then the original problem is reduced to a boundary value problem de®ned in a domain without any crack tips. The ®nite element approximation of the reduced problem is considered and we can prove that the ®nite element approximation is well posed. Numerical examples and results of a fracture problem with exact solution and two typical fracture problems demonstrate the eciency and accuracy of the present method.
منابع مشابه
Stiffeners Mechanical Effect Analysis by Numerical Coupling
Given any structure, we seek to find the solution of mechanical problem as precisely and efficiently as possible. Within this condition, the BEM is robust and promising development, standing out in the analysis of cases with occurrence of large stress gradients, as in problems of fracture mechanics. Moreover, in BEM the modeling of infinite means is performed naturally, without the use of appro...
متن کاملMixed Strong Form Representation Particle Method for Solids and Structures
In this paper, a generalized particle system (GPS) method, a general method to describe multiple strong form representation based particle methods is described. Gradient, divergence, and Laplacian operators used in various strong form based particle method such as moving particle semi-implicit (MPS) method, smooth particle hydrodynamics (SPH), and peridynamics, can be described by the GPS metho...
متن کاملCracking Elements Method for Simulating Complex Crack Growth
The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implic...
متن کاملاستفاده از روش غنی شده بدون شبکه گلرکین در تعیین پارامتر های شکست صفحات FGM
Stress-intensity factors (SIFs) are the most important parameters in fracture mechanics analysis of structures. These parameters are evaluated for a stationary crack in functionally graded plates of arbitrary geometry using a novel Galerkin based mesh-free method. The method involves an element-free Galerkin method (EFGM), where the material properties are smooth functions of spatial coordinate...
متن کاملNURBS-Based Isogeometric Analysis Method Application to Mixed-Mode Computational Fracture Mechanics
An interaction integral method for evaluating mixed-mode stress intensity factors (SIFs) for two dimensional crack problems using NURBS-based isogeometric analysis method is investigated. The interaction integral method is based on the path independent J-integral. By introducing a known auxiliary field solution, the mixed-mode SIFs are calculated simultaneously. Among features of B-spline basis...
متن کامل