Meshless formulation for shear-locking free bending elements

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-defor mable beams with a high length over thickness ratio. Based upon Timoshenko' s theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the fie ld of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. Howev er in the numerical process to integrate strain energy, the second derivati ve of the standard Moving Least Square (MLS) shape functions must be evalua ted, thus requiring at least a C-1 continuity of MLS shape functions instea d of C-0 continuity in the conventional EFGM. Yet this hindrance is overcom e effortlessly by only using at least a C-1 weight function. One-dimensiona l quartic spline weight function with C-2 continuity is therefore adopted f or this purpose. Various numerical results in this work indicate that the m odified version of the EFGM does not exhibit transverse shear locking, redu ces stress oscillations, produces fast convergence, and provides a surprisi ngly high degree of accuracy even with coarse domain discretizations.