Upper-bound limit analysis based on the natural element method

作者：Zhou Shu Tao; Liu Ying Hua

来源：Acta Mechanica Sinica, 2012, 28(5): 1398-1415.

DOI：10.1007/s10409-012-0149-9

• Upper bound limit analysis
• Meshless method
• Natural neighbour interpolation
• Natural element method
• Mathematical programming
• Iteration algorithm

The natural element method (NEM) is a newly-developed numerical method based on Voronoi diagram and Delaunay triangulation of scattered points, which adopts natural neighbour interpolation to construct trial functions in the framework of Galerkin method. Owing to its distinctive advantages, the NEM is used widely in many problems of computational mechanics. Utilizing the NEM, this paper deals with numerical limit analysis of structures made up of perfectly rigid-plastic material. According to kinematic theorem of plastic limit analysis, a mathematical programming natural element formulation is established for determining the upper bound multiplier of plane problems, and a direct iteration algorithm is proposed accordingly to solve it. In this algorithm, the plastic incompressibility condition is handled by two different treatments, and the nonlinearity and nonsmoothness of the goal function are overcome by distinguishing the rigid zones from the plastic zones at each iteration. The procedure implementation of iterative process is quite simple and effective because each iteration is equivalent to solving an associated elastic problem. The obtained limit load multiplier is proved to monotonically converge to the upper bound of true solution. Several benchmark examples are investigated to validate the significant performance of the NEM in the application field of limit analysis.

• 出版日期2012-10
• 单位清华大学