An advanced computational method for transient heat conduction analysis in 3-D axisymmetric continuously nonhomogeneous functionally graded materials (FGM) is proposed. The analysed domain is covered by small circular subdomains. On each subdomain local boundary integral equations for the transient heat conduction problem are derived in the Laplace transform domain. The meshless approximation based on the moving least-squares method is employed for the numerical implementation. The Stehfest algorithm is applied for the numerical Laplace inversion to obtain the temporal variation. Numerical results are presented for finite full and hollow cylinders with an exponential variation of material parameters with spatial coordinates.
SUMMARYA meshless local Petrov-Galerkin (MLPG) method is applied to solve static and dynamic problems of orthotropic plates described by the Reissner-Mindlin theory. Analysis of a thick orthotropic plate resting on the Winkler elastic foundation is given too. A weak formulation for the set of governing equations in the Reissner-Mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate. Nodal points are randomly spread on the surface of the plate and each node is surrounded by a circular subdomain to which local integral equations are applied. The meshless approximation based on the Moving Least-Squares (MLS) method is employed in the numerical implementation. The present computational method is applicable also to plates with varying thickness. Numerical results for simply supported and clamped plates are presented.
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