Boundary element analysis of nonlinear transient heat conduction problems involving non-homogenous and nonlinear heat sources using time-dependent fundamental solutions

A Time-Stepping Drbem for Magneto-Thermo-Viscoelastic Interactions in a Rotating Nonhomogeneous Anisotropic Solid

“…This method was originally introduced by Brebbia and Nardini [1983] and details may be found in the monograph of Partridge et al [1992]; Gaul et al [2003]. The interested readers can find more details in the following references ( [Wrobel and Brebbia, 1987;Beer and Watson, 1992;Divo and Kassab, 2003;Ang et al, 2003;Fahmy, 2010;Mohammadi et al, 2010]). Due to the rapid development of computers, computational electromagnetics is becoming increasingly important in modern technology because it can replace many expensive experiments with less costly computer simulations.…”

The Effect of Rotation and Inhomogeneity on the Transient Magneto-Thermoviscoelastic Stresses in an Anisotropic Solid

“…Fahmy [9] used the boundary element method to obtain thermal stresses in a nonhomogeneous anisotropie solid. More extensive applications of boundary element methods may be found in Canelas and Sensale [10], Davi and Müazzo [11], Fahmy and ElShahat [12], Hou et al [13], Karlis et al [14], Matsumoto et al [15], Mohammadi et al [16] and Zhang et al [17]. A completely different approach to address dynamic problems utilizing static fundamental solutions is the so-called dual reciprocity boundary element method (DRBBM).…”

Optimal material distribution for heat conduction of FGM based on meshless weighted least-square method

“…In the majority of heat conduction problems, mesh generation of FEM is a far more time consuming and expensive task than the solution of the partial difference equations [4]. Mohammadi et al [3] presented a new method for the boundary element analysis of unsteady heat conduction problems. In their method, at each time step the temperature at boundary nodes and some internal grid points is computed and used as pseudo-initial values for the next time step.…”

“…Various numerical techniques, such as the finite difference method (FDM), finite element method (FEM) [1], boundary element method (BEM) [2,3] or more recently developed meshless methods, have been developed for analyzing the heat conduction problems because of the complexity of the corresponding governing equation, analytical solutions are usually difficult to obtain. Chareonsuk and Vessakosol [1] investigated numerical solutions for functionally graded solids under thermal and mechanical loads using a high-order control volume finite element method.…”