Numerical Limit Analysis of Two Dimensional Structures by the MLPG Method with Natural Neighbour Interpolation
In most engineering applications, solutions derived from the lower bound theorem of limit analysis are particularly valuable because they provide a safe estimate of the load that will cause collapse. In this paper, the lower bound theorem is firstly implemented making use of the meshless local Petrov-Galerkin (MLPG) method with natural neighbour interpolation. In the present MLPG formulation, the natural neighbour interpolation is employed for constructing trial functions, while the three-node triangular FEM shape function is used as the test function over a local sub-domain. The self-equilibrium stress field is expressed by linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors can be generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these nonlinear programming sub-problems and determine the maximal load amplifier. The numerical results show that the present solution procedure for limit analysis is effective and accurate.
Wei Yang, Mamtimin Geni, Tiejun Wang and Zhuo Zhuang
S. S. Chen et al., "Numerical Limit Analysis of Two Dimensional Structures by the MLPG Method with Natural Neighbour Interpolation", Advanced Materials Research, Vols. 33-37, pp. 881-888, 2008