Extended-finite element method as analysis model for Gauss point density topology optimization method

2015 ◽  
Vol 29 (4) ◽  
pp. 1341-1348 ◽  
Author(s):  
Dongkyu Lee ◽  
Soomi Shin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Extended Finite Element Method ◽  
Optimization Method ◽  
Analysis Model ◽  
Extended Finite Element ◽  
Gauss Point ◽  
Point Density ◽  
Topology Optimization Method

scholarly journals Enriched degree of freedom locking in crack analysis using the extended finite element method

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985979
Author(s):  
Han-Soo Kim ◽  
Geon-Hyeong Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Degree Of Freedom ◽  
Analysis Model ◽  
Extended Finite Element ◽  
Simple Method ◽  
Numerical Examples ◽  
Crack Analysis ◽  
Element Method

In this article, the enriched degree of freedom locking that can occur in a crack analysis with the extended finite element method is described. The discontinuous displacement field formulated by the enriched degree of freedom in the extended finite element method does not activate due to the enriched degree of freedom locking. Using the phantom node method, the occurrence of locking when two adjacent elements are simultaneously cracked in a loading step was verified. Two adjacent cracks can be determined to have developed simultaneously when an analysis model reveals a relatively uniform stress distribution on two adjacent elements. Numerical examples of a simply tensioned bar and a reinforced concrete beam are presented to demonstrate the erroneous analysis result due to the enriched degree of freedom locking. As a simple method to circumvent the enriched degree of freedom locking, the tensile strength of the neighboring elements was slightly increased in the numerical examples, and the effectiveness of the method was demonstrated. The proposed method is simple and easy for practicing engineers, and it can be easily applied to the three-dimensional crack propagation analysis.

scholarly journals A mesh-independent framework for crack tracking in elastodamaging materials through the regularized extended finite element method

2021 ◽  
Author(s):  
Elena Benvenuti ◽  
Nicola Orlando
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Damage Evolution ◽  
Extended Finite Element Method ◽  
Mesh Adaptivity ◽  
Extended Finite Element ◽  
Evolution Law ◽  
Crack Paths ◽  
Original Crack ◽  
Element Method

AbstractWe propose a formulation for tracking general crack paths in elastodamaging materials without mesh adaptivity and broadening of the damage band. The idea is to treat in a unified way both the damaging process and the development of displacement discontinuities by means of the regularized finite element method. With respect to previous authors’ contributions, a novel damage evolution law and an original crack tracking framework are proposed. We face the issue of mesh objectivity through several two-dimensional tests, obtaining smooth crack paths and reliable structural results.

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