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Numerical simulation of temperature field in heterogeneous material with the XFEM

Yu T. T., Gong Z. W.

Archives of Civil and Mechanical Engineering

2013

Vol. 13, no. 2

199--208

The purpose of this paper is to focus on modeling temperature field in heterogeneous materials. The heat conductivity is adopted as the basic parameter for calculation. The extended finite element method (XFEM) is applied for simulation of temperature field. For one element that contains no material interface, the temperature function will be degenerated into that of the conventional finite element. For the element containing material interfaces, the standard temperature based approximation is enriched by incorporating level-set-based enrichment functions which model the interfaces. For unsteady temperature field, the improved precise integration method is adopted for the solution of the ordinary differential equations. The mesh generation can be considerably simplified and high-quality meshes are obtained; meanwhile the solution of good precision and stability can be achieved.

Improved implementation of the extended finite element method for stress analysis around cracks

Yu T. T., Liu P.

Archives of Civil and Mechanical Engineering

2011

Vol. 11, no 3

787-805

Although the extended finite element method (XFEM) allows for modelling arbitrary discontinuities, its low order elements often means that frequent improvements on accuracy are required. The generalized finite element method (GFEM), the extension of the conventional FEM, improves the approximation accuracy of the FEM by introducing generalized degrees of freedom and re-interpolating nodal degrees of freedom. This paper enhances the implementation of the XFEM for stress analysis around cracks by coupling the GFEM and XFEM. The generalized node shape functions are used in a cluster of nodes around the cracks, and the conventional finite element shape functions are adopted at nodes outside the cracks, thereby reducing costs and improving the accuracy of stresses in the vicinity of the cracks. Several numerical examples show that the proposed approach generates higher accuracy for stress intensity factor computations at affordable costs.

Pomimo że rozszerzona metoda elementów skończonych (XFEM) pozwala modelować przypadkowe nieciągłości, metoda ta wymaga poprawy dokładności. Można to uzyskać poprzez zastosowanie dodatkowych metod modelowania. W pracy przedstawiono zastosowanie połączonych metod GFEM i XFEM do analizy naprężeń wokół pęknięcia. Kilka numerycznych przykładów wykazało, że proponowane podejście pozwala uzyskać lepszą dokładność od metod dotychczas stosowanych.