A Finite Difference Energy Method to Arbitrary Grids Applied the Plate Bending Problems

Resumo

The finite difference energy method (FDEM), although already used in several structural problems
so far, including dynamic and nonlinear analysis, has always been applied to regular grids, making it limited to
applications with geometries formed by (or mapped to) rectangles. In order to make it competitive with other
methods, such as finite elements and meshless, it is necessary to generalize the FDEM to arbitrary domains and
boundaries, endowing it with ability to manipulate arbitrary grids. Thus, this paper presents a FDEM formulation
for regular and irregular grids applied to the thin plate bending problem. The coefficients were obtained at each
point of the arbitrary grid by expanding the Taylor series. The results show that using the proper choice of points
for the stencils we can keep the order of approximation of the case regular, but now allowing the generalization of
the use of the method that was only applied to rectangular grids.