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The generalized-strain mesh-free (GSMF) local method, is derived through a weighted-residual formulation that leads to the work theorem of structures theory. In a local region, the work theorem establishes an energy relationship between a statically-admissible stress field and an independent kinematically-admissible strain field.

In the formulation of the GSMF, the kinematically-admissible strain field is chosen as the one corresponding to an arbitrary rigid-body displacement; as a consequence, the domain term is canceled out and the work theorem is reduced to regular local boundary terms only. The Moving Least Squares (MLS) approximation of the elastic field is used to construct the trial function in this local meshless formulation. GSMF has a highly computational efficiency leading to accurate numerical results in two-dimensional elasticity problems.

This paper is concerned with the size effect of the configuration parameters of the local support domain and the local weighted-residual domain on GSMF. It presents a comparison of the deflections and the error in energy for five different regular nodal distribution to solve the Timoshenko cantilever beam problem and the infinite plate with circular hole. The results are compared with the exact solution and optimal parameters have been determined.

Generalized-Strain Mesh-Free (GSMF), work theorem, Moving Least Squares (MLS), local support domain, local weighted-residual domain.