Application of the Meshless Local Petrov-Galerkin Method in the Elasto-Plastic Fracture Problem of Moderately Thick Plate

Abstract:

A meshless local Petrov-Galerkin method for the analysis of the elasto-plastic fracture problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. An incremental Newton-Raphson iterative algorithm is employed to solve incremental nonlinear local Petrov-Galerkin equations. Numerical results show that the present method possesses not only feasibility, but also rapid convergence for the elasto-plastic fracture problem of the moderately thick plate.

• Periodical: Applied Mechanics and Materials (Volumes 155-156)
• Pages: 485-490
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.155-156.485
• Online since: February 2012
• Authors: Ping Xia, Ke Xiang Wei
• Keywords: Elasto-Plastic Problem, Incremental Newton-Raphson Iterative Algorithm, Local Petrov-Galerkin Method, Meshless Method, Moderately Thick Plate

References

[1] Atluri S.N., Zhu T.: A new meshless local Petrov-Galerkin approach in computational mechanics. Computational Mechanics, 1998, 22(2): 117–127.

DOI: 10.1007/s004660050346

[2] Long S.Y., Atluri S.N.: A meshless local Petrov-Galerkin formulation for solving the bending problem of a thin plate. Computer Modeling in Engineering & Sciences, 2002, 3(1): 53–63.

[3] Long S.Y., Liu K.Y., Hu D.A.: A new meshless method based on MLPG for elastic dynamic problems. Engineering Analysis with Boundary Elements 2006, 30(1): 43–48.

DOI: 10.1016/j.enganabound.2005.09.001

[4] Ching H.K., Batra R.C.: Determination of crack tip fields in linear elastostatics by the meshless local Petrov-Galerkin method. Computer Modeling in Engineering & Sciences, 2001, 2, 273–290.

[5] Sun J.D., Zhang W.X., Tong L.W.: Modal analysis of moderately thick plates by element-free method, China Civil Engineering Journal, 2006, 39(10): 29–33.

[6] Xia P., Long S.Y., Wei K.X.: An analysis for the elasto-plastic problem of the moderately thick plate using the meshless local Petrov-Galerkin method. Engineering Analysis with Boundary Elements, 2011, 35 (7): 908–914.

DOI: 10.1016/j.enganabound.2011.02.006