A new approach for the Modified Local Green’s Function Method applied to solid mechanics problems

The Modified Local Green’s Function Method (MLGFM) is an integral method that does not need a previous explicit fundamental solution or a Green’s function, since projections of Green’s functions, determined by Finite Element Method, are used as fundamental solution to solve problems. As demonstrated in previous works, the MLGFM presents good convergence for potential, displacements, boundary flux and tractions, although the obtaining of the Green’s function projections can require a high computational effort. This paper proposes an alternative formulation to the MLGFM that avoids the need to obtain these projections and consequently reduces the number of numerical operations. The new formulation presents the same accuracy as the previous one but with less computational effort, and it is applied to some problems in solid mechanics and compared with the standard Finite Element Method and the Boundary Element Method.