scholarly journals A new partition of unity finite element free from the linear dependence problem and possessing the delta property

2010 ◽  
Vol 199 (17-20) ◽  
pp. 1036-1043 ◽  
Author(s):  
Yongchang Cai ◽  
Xiaoying Zhuang ◽  
Charles Augarde
Keyword(s):  
Finite Element ◽  
Linear Dependence ◽  
Partition Of Unity ◽  
Dependence Problem ◽  
Element Free

Composite Patch Repair of Structural Member by Coupled FE-EFG Approach

2016 ◽  
Vol 829 ◽  
pp. 78-82
Author(s):  
Himanshu Pathak ◽  
Akhilendra Singh ◽  
Indra Vir Singh
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Partition Of Unity ◽  
Patch Repair ◽  
Integral Approach ◽  
Fe Method ◽  
Material Interface ◽  
Composite Patch ◽  
Geometric Discontinuities ◽  
Element Free

This paper presents a simple and efficient coupled finite element-element free Galekrin (FE-EFG) approach to simulate three-dimensional composite patch repair problem. In coupled FE-EFG approach, extended element free Galerkin (XEFG) is used near the crack surface as it can accurately model the discontinuities while the rest of domain is approximated by standard finite element (FE) method. The transition between FE and XEFG was modelled by a ramp function. The geometric discontinuities like crack and material interface are modeled by adding enrichment functions in EFG displacement approximation through partition of unity (PU). The location of geometrical discontinuity is traced by vector level set method. A domain based J-integral approach is used for the evaluation of stress intensity factors.

Application of Extended Finite Element Method (XFEM) to Stress Intensity Factor Calculations

2015 ◽  
Author(s):  
Do-Jun Shim ◽  
Mohammed Uddin ◽  
Sureshkumar Kalyanam ◽  
Frederick Brust ◽  
Bruce Young
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Degrees Of Freedom ◽  
Extended Finite Element Method ◽  
Partition Of Unity ◽  
Extended Finite Element ◽  
Element Method

The extended finite element method (XFEM) is an extension of the conventional finite element method based on the concept of partition of unity. In this method, the presence of a crack is ensured by the special enriched functions in conjunction with additional degrees of freedom. This approach also removes the requirement for explicitly defining the crack front or specifying the virtual crack extension direction when evaluating the contour integral. In this paper, stress intensity factors (SIF) for various crack types in plates and pipes were calculated using the XFEM embedded in ABAQUS. These results were compared against handbook solutions, results from conventional finite element method, and results obtained from finite element alternating method (FEAM). Based on these results, applicability of the ABAQUS XFEM to stress intensity factor calculations was investigated. Discussions are provided on the advantages and limitations of the XFEM.

Finite element free vibration of eccentrically stiffened plates

1988 ◽  
Vol 30 (6) ◽  
pp. 1303-1317 ◽  
Author(s):  
Abhijit Mukherjee ◽  
Madhujit Mukhopadhyay
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Stiffened Plates ◽  
Element Free

A parallel partition of unity method for the unsteady Stokes equations

2017 ◽  
Vol 27 (9) ◽  
pp. 2105-2114
Author(s):  
Xiaoying Zhao ◽  
Yanren Hou ◽  
Guangzhi Du
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Partition Of Unity ◽  
Time Dependent ◽  
The Finite Element Method ◽  
Partition Of Unity Method ◽  
Content Type ◽  
Standard Galerkin Method ◽  
Unsteady Stokes Equations

Purpose The purpose of this paper is to propose a parallel partition of unity method to solve the time-dependent Stokes problems. Design/methodology/approach This paper solved the time-dependent Stokes equations using the finite element method and the partition of unity method. Findings The proposed method in this paper obtained the same accuracy as the standard Galerkin method, but it, in general, saves time. Originality/value Based on a combination of the partition of unity method and the finite element method, the authors, in this paper, propose a new parallel partition of unity method to solve the unsteady Stokes equations. The idea is that, at each time step, one need to only solve a series of independent local sub-problems in parallel instead of one global problem. Numerical tests show that the proposed method not only reaches the same convergence orders as the fully discrete standard Galerkin method but also saves ample computing time.

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