TY  - EJOU
AU  - Sladek, J.  
AU  - Sladek, V.  
AU  - Krivacek, J.  
AU  - Zhang, Ch.  

TI  - Meshless Local Petrov-Galerkin Method for Stress and Crack Analysis in 3-D Axisymmetric FGM Bodies
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2005
VL  - 8
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Meshless method
KW  -  local weak-form
KW  -  unit step function
KW  -  moving least-squares approximation
KW  -  Laplace-transform
KW  -  functionally graded materials (FGMs)
KW  -  transient elastodynamics
KW  -  crack problems

DO  - 10.3970/cmes.2005.008.259