Nonnodal Extended Finite-Element Method for Crack Modeling with Four-Node Quadrilateral Elements

Asareh, Iman; Song, Jeong‐Hoon

doi:10.1061/(asce)em.1943-7889.0001662

Cited by 10 publications

(2 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To effectively compare the benefits of the proposed method, the cracks were modeled using two approaches: (i) the standard XFEM with shifting enrichment functions (SX) and (ii) the NXFEM (NX). Moreover, three different mass matrices were used in the simulations: (i) the consistent mass matrix (CS), (ii) the proposed lumped mass matrix (PL), and (iii) the lumped mass matrix proposed by Menouillard et al (ML).…”

Section: Numerical Examplesmentioning

confidence: 99%

A general mass lumping scheme for the variants of the extended finite element method

Asareh

Song

Mullen

et al. 2020

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Summary A new strategy for the mass matrix lumping of enriched elements for explicit transient analysis is presented. It is shown that to satisfy the kinetic energy conservation, the use of zero or negative masses for enriched degrees of freedom of lumped mass matrix may be necessary. For a completely cracked element, by lumping the mass of each side of the interface into the finite element nodes located at the same side and assigning zero masses to the enriched degrees of freedom, the kinetic energy for rigid body translations is conserved without transferring spurious energy across the interface. The time integration is performed by adopting an explicit‐implicit technique, where the regular and enriched degrees of freedom are treated explicitly and implicitly, respectively. The proposed method can be viewed as a general mass lumping scheme for the variants of the extended finite element methods because it can be used irrespective of the enrichment method. It also preserves the optimal critical time step of an intact finite element by treating the enriched degrees of freedom implicitly. The accuracy and efficiency of the proposed mass matrix are validated with several benchmark examples.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

A general mass lumping scheme for the variants of the extended finite element method

Asareh

Song

Mullen

et al. 2020

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…To evaluate the fatigue life of cracked specimens in the presence of bimaterial interfaces, Jameel and Harmain [24] modified the standard finite element approximation by adding appropriate enrichment functions in order to consider the effect of these discontinuities present in the domain, and the level set method was used to track different discontinuities in the domain. Many other applications of XFEM to fracture and fatigue analyses can be found in the papers [25][26][27][28][29][30]. Besides these methods, the meshless method (or mesh-free method) and the numerical manifold method (NMM) were also used for analyzing crack problems.…”

Section: Introductionmentioning

confidence: 99%

Fracture and Fatigue Analyses of Cracked Structures Using the Iterative Method

Tian

Cheng

2021

Geofluids

View full text Add to dashboard Cite

It is a quite challenging subject to efficiently perform fracture and fatigue analyses for complex structures with cracks in engineering. To precisely and efficiently study crack problems in practical engineering, an iterative method is developed in this study. The overall structure which contains no crack is analyzed by the traditional finite element method (FEM), and the crack itself is analyzed using analytical solution or other numerical solutions which are effective and efficient for solving crack problems. An iteration is carried out between the two abovementioned solutions, and the original crack problem could be solved based on the superposition principle. Several typical crack problems are studied using the present method, showing very high precision and efficiency of this method when making fracture and fatigue analyses of structures.

show abstract

Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation

et al. 2020

View full text Add to dashboard Cite

Nonnodal Extended Finite-Element Method for Crack Modeling with Four-Node Quadrilateral Elements

Cited by 10 publications

References 43 publications

A general mass lumping scheme for the variants of the extended finite element method

A general mass lumping scheme for the variants of the extended finite element method

Fracture and Fatigue Analyses of Cracked Structures Using the Iterative Method

Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation

Contact Info

Product

Resources

About