Analysis of shear flexible beams, using the Meshless Local Petrov-Galerkin Method based on Locking-Free formulation

초록

In this paper, the problems of shear flexible beams are analyzed by the MLPG method based on a locking free weak formulation. For a locking free weak formulation, the numerical characteristics of variational functional of shear flexible beam in the thin beam limit are discussed. Based on the observation, a locking free local symmetric weak from is derived by changing the dependent-variables in governing equations from the pair of displacement and rotation to the pair of displacement and rotation to the pair of displacement and transverse shear strain. For the interpolation of the dependent-variables (i.e. displacement and transverse shear strain) in the locking-free local symmetric weak form, the recently proposed generalized moving least squares(GMLS) interpolation scheme is utilized to introduce the slope of displacement as another nodal degree of freedom independent of nodal displacement. Numerical tests are carried out to identify the locking-free nature of the proposed method for the problems of shear flexible beams in the thick beam limit and in the thin beam limit. The numerical results are compared with analytical solutions.