Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids

Abstract

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.

Direct localized boundary-domain integro-differential formulations for physically nonlinear elasticity of inhomogeneous body

“…The last integral in the left hand side of (15) disappears if χ(x, y) is given by (14). If the point y is situated inside the localization domain ω(y) or on the intersection of the local and global boundaries, ∂ω(y) ∩ Ω, the coefficient c ω (y) in (15) is the same as c(y) in equation (12).…”

“…Note that the term with R ik ω disappears in the last integral of (21) if the parametrix P ik ω (x, x i ) is given by (14). On the other hand, if the cut-off function χ(x, x i ) and its normal derivative are equal zero at x on the boundary ∂ω(x i ), then the the third and fourth integrals along Ω ∩ ∂ω(x i ) disappear in (21).…”

“…Note also that the Green function of the plane Laplace equation was used in [14] as a parametrix for the axially symmetric problem of heat transfer with variable coefficients.…”

Numerical Solution Of Maxwell Equations Using Local Weak Form Meshless Techniques

“…Some special techniques have to be used to overcome the problem, for example, the Lagrange multiplier method and the penalty method [4]. For some works on the meshless LBIE method one can mention the papers of Zhu et al [1,5,6] in linear and non-linear acoustic and potential problems and the works of Sladek brothers [7,8] for heat conduction problems. The method has now been successfully extended to a wide range of problems in engineering.…”

Analysis of thick functionally graded plates by local integral equation method

“…The price which is to be paid in that approach is the loss of a pure boundary integral character of the formulation. Recently, meshless methods are becoming popular, and they have been successfully applied to 2-D and 3-D axisymmetric transient heat conduction analyses for isotropic and anisotropic FGMs [4][5][6][7][8] and in elasticity [9][10][11].…”