XRPIM versus XFEM

We present an extended radial point interpolation method (XRPIM) for modeling cracks and material interfaces in two-dimensional elasto-static problems. Therefore, partition of unity enrichment is incorporated into RPIM. We employ both step enrichment and crack tip enrichment for cracks. The studies are restricted to stationary cracks though the method can be extended easily to moving boundaries. We compare the results to the extended finite element method to show the superiority of our method. We show for two selected problems that the error is of magnitudes lower compared to XFEM simulations.

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A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems

International Journal of Computational Methods ◽

10.1142/s0219876220410029 ◽

2020 ◽

pp. 2041002

Author(s):

Wei Li ◽

Qifan Zhang ◽

Qiang Gui ◽

Yingbin Chai

Keyword(s):

Acoustic Radiation ◽

Interpolation Method ◽

Partition Of Unity ◽

Local Approximation ◽

Triangular Element ◽

Two Dimensional ◽

Shape Functions ◽

Radial Point Interpolation ◽

Point Interpolation Method ◽

Point Interpolation

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

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An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

Science and Technology Development Journal ◽

10.32508/stdj.v18i2.1079 ◽

2015 ◽

Vol 18 (2) ◽

pp. 106-113

Author(s):

Nha Thanh Nguyen ◽

Hien Thai Nguyen ◽

Minh Ngoc Nguyen ◽

Thien Tich Truong

Keyword(s):

Integral Method ◽

Interpolation Method ◽

Two Dimensional ◽

Radial Point Interpolation Method ◽

Interaction Integral ◽

Crack Problems ◽

Radial Point Interpolation ◽

T Stress ◽

Point Interpolation Method ◽

Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

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Comparative modelling of crack propagation in elastic–plastic materials using the meshfree local radial basis point interpolation method and eXtended finite-element method

Royal Society Open Science ◽

10.1098/rsos.190543 ◽

2019 ◽

Vol 6 (11) ◽

pp. 190543 ◽

Cited By ~ 1

Author(s):

Yazhe Li ◽

Nengxiong Xu ◽

Jinzhi Tu ◽

Gang Mei

Keyword(s):

Finite Element Method ◽

Crack Propagation ◽

Extended Finite Element Method ◽

Interpolation Method ◽

Extended Finite Element ◽

Elastic Plastic ◽

Plastic Materials ◽

Point Interpolation Method ◽

Point Interpolation ◽

Elastic Plastic Materials

The modelling and understanding of crack propagation for elastic–plastic materials is critical in various engineering applications, such as safety analysis of concrete structures and stability analysis of rock slopes. In this paper, the local radial basis point interpolation method (LRPIM) combined with elastic–plastic theory and fracture mechanics is employed to analyse crack propagation in elastic–plastic materials. Crack propagation in elastic–plastic materials is compared using the LRPIM and eXtended finite-element method (XFEM). The comparative investigation indicates that: (i) the LRPIM results are close to the model test results, which indicates that it is feasible for analysing the crack growth of elastic–plastic materials; (ii) compared with the LRPIM, the XFEM results are closer to the experimental results, showing that the XFEM has higher accuracy and computational efficiency; and (iii) compared with the XFEM, when the LRPIM method is used to analyse crack propagation, the propagation path is not smooth enough, which can be explained as the crack tip stress and strain not being accurate enough and still needing further improvement.

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