J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 477-490, 2004, DOI:10.3970/cmes.2004.006.477

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a pure contour character only in… More >

J. Sladek¹, V. Sladek¹, P. Solek²

CMES-Computer Modeling in Engineering & Sciences, Vol.43, No.3, pp. 223-252, 2009, DOI:10.3970/cmes.2009.043.223

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in 3-D continuously non-homogeneous anisotropic bodies. Functionally graded materials (FGM) are multi-phase materials with the phase volume fractions varying gradually in space, in a pre-determined profile. The Heaviside step function is used as the test functions in the local weak form resulting into the derived local integral equations (LIEs). For transient elastodynamic problems either the Laplace transform or the time difference techniques are applied. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical… More >

J. Sladek¹, V. Sladek¹, C.L. Tan², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 161-174, 2008, DOI:10.3970/cmes.2008.032.161

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non-homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are randomly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdomain to which… More >