Meshless approach and its application in engineering problems

In this chapter, a meshless method is introduced for analyzing heat conduction, non-linear Poisson-type problems, thin plate bending on an elastic foundation, and functionally graded materials (FGM). In the meshless algorithm, the analog equation method (AEM) is used to obtain the equivalent homogeneous system to the original governing equation. After which MFS and RBF interpolation are used to construct the corresponding approximated particular part and complementary part, respectively. Finally, all unknowns are determined by satisfying boundary conditions and the governing equations in terms of potential, plate deflection, or displacement components at certain points, depending on the problem to be solved. Numerical examples are considered for square plate on a Winkler elastic foundation, different 2D structures made of FGM, and 2D standard Poisson equations. The numerical results are presented for each of the problems mentioned and comparison is made with those from other methods.