Stress analysis in anisotropic functionally graded materials by the MLPG method

A meshless method based on the local Petrov-Galerkin approach is proposed for stress analysis in two-dimensional (2D), anisotropic and linear elastic/viscoelastic solids with continuously varying material properties. The correspondence principle is applied for non-homogeneous, anisotropic and linear viscoelastic solids where the relaxation moduli are separable in space and time. The inertial dynamic term in the governing equations is considered too. A unit step function is used as the test functions in the local weak-form. It leads to local boundary integral equations (LBIEs). 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. For time-dependent problems, the Laplace-transform technique is utilized. Several numerical examples are given to verify the accuracy and the efficiency of the proposed method.