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The MLPG Method for Crack Analysis in Anisotropic Functionally Graded Materials

J. Sladek1, V. Sladek, Ch.Zhang2

1 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia, email:
2 Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany, email:

Structural Durability & Health Monitoring 2005, 1(2), 131-144.


A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is adopted for approximating the physical quantities in the LBIEs. The accuracy of the present method for computing the mode-I stress intensity factors is discussed by comparison with available analytical or numerical solutions.


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Sladek, J., Sladek, V., , C. (2005). The MLPG Method for Crack Analysis in Anisotropic Functionally Graded Materials. Structural Durability & Health Monitoring, 1(2), 131–144.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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