@Article{cmes.2005.008.259,
AUTHOR = {J.  Sladek, V.  Sladek, J.  Krivacek, Ch.  Zhang},
TITLE = {Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {8},
YEAR = {2005},
NUMBER = {3},
PAGES = {259--270},
URL = {http://www.techscience.com/CMES/v8n3/29749},
ISSN = {1526-1506},
ABSTRACT = {A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary value problem into a 2-d problem. The geometry of subdomains is selected as a toroid with a circular cross section in the considered (<i>x<sub>1</sub> ,x<sub>3</sub></i>)-plane. The final form of the local integral equations has a pure contour-integral character only in elastostatic problems. In elastodynamics an additional domain-integral is involved due to inertia terms. The moving least-squares (MLS) method is used for the approximation of physical quantities in LBIEs.},
DOI = {10.3970/cmes.2005.008.259}
}