A new meshless Local Boundary Integral Equation (LBIE) method for solving two-dimensional elastostatic problems is proposed. Randomly distributed points without any connectivity requirement cover the analyzed domain and Local
Radial Basis Functions (LRBFs) are employed for the meshless interpolation of displacements. For each point a circular support domain is centered and a local integral representation for displacements is considered. At the local circular boundaries tractions are eliminated with the aid of companion solution, while at the intersections
between the local domains and the global boundary displacements and
tractions are treated as independent variables avoiding thus derivatives of LRBFs.
Stresses are evaluated with high accuracy and without derivatives of LRBFs via a
LBIE valid for stresses. All the integrations are performed quickly and economically
and in a way that renders the extension of the method to three-dimensional
problems straightforward. Six representative numerical examples that demonstrate
the accuracy of the proposed methodology are provided.