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A finite element method for extended KdV equations [PDF]
International Journal of Applied Mathematics and Computer Science, 2016 The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used.
Karczewska Anna +3 more
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The Extended Finite Element Method for Dynamic Fractures [PDF]
Shock and Vibration, 2005 A method for modelling arbitrary growth of dynamic cracks without remeshing is presented. The method is based on a local partition of unity. It is combined with level sets, so that the discontinuities can be represented entirely in terms of nodal data ...
Goangseup Zi +3 more
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Full thermo-mechanical coupling using eXtended finite element method in quasi-transient crack propagation [PDF]
Advanced Modeling and Simulation in Engineering Sciences, 2018 This work aims to present a complete full coupling eXtended finite element formulation of the thermo-mechanical problem of cracked bodies. The basic concept of the extended finite element method is discussed in the context of mechanical and thermal ...
Fakhreddine Habib +2 more
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Improvements for the solution of crack evolution using extended finite element method [PDF]
Scientific ReportsIt is demonstrated that the eXtended Finite Element Method (XFEM) is of remarkable efficiency in simulating crack evolution by eliminating the need for remeshing and refinement.
Yuxiao Wang +3 more
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An Abaqus implementation of the extended finite element method [PDF]
Engineering Fracture Mechanics, 2009 Abstract In this paper, we introduce an implementation of the extended finite element method for fracture problems within the finite element software ABAQUSTM. User subroutine ( UEL ) in Abaqus is used to enable the incorporation of extended finite element capabilities.
E. Giner +3 more
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High-order extended finite element method for cracked domains [PDF]
International Journal for Numerical Methods in Engineering, 2005 The aim of the paper is to study the capabilities of the Extended Finite Element Method (XFEM) to achieve accurate computations in non smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical finite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because ...
Laborde, Patrick +3 more
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The extended/generalized finite element method: An overview of the method and its applications
International Journal for Numerical Methods in Engineering, 2010 AbstractAn overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non‐smooth features within elements.
Fries, Thomas-Peter, Belytschko, Ted
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Extended group finite element method [PDF]
Applied Numerical Mathematics, 2021 Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation interpolates nonlinear terms onto the finite element approximation space, we propose the use of a separate approximation ...
Kevin Tolle, Nicole Marheineke
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Research on Crack Propagation Based on Smooth-extended Finite Element Method [PDF]
Zhengzhou Daxue xuebao. Gongxue ban, 2022 In order to study the crack propagation problem, the smooth finite element method (S-FEM) was combined with the extended finite element method (X-FEM) to form the smooth-extended finite element method (S-XFEM) algorithm and program.Firstly, based on ...
WANG Jianming, LI Zhaoquan, LI Bozhi
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Journal of Materials Research and Technology, 2022 Several numerical methods have developed into indispensable and effective tools for solving science-technology problems. The finite element method has particularly become a popular and effective technology, among others—a method that cannot be separated ...
Huu-Dien Nguyen, Shyh-Chour Huang
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