Limit Analysis Of Axisymmetric Structures Based On The Natural Element Method

Limit analysis is one of the most important branches of the plasticity,and provides the necessary theoretical basis for determining the safety of structures.Up to now,numerical methods for limit analysis is by means of the traditional mesh-base method.In recent years,the meshless method has also shown its good potential for the structural plastic limit analysis.Natural element method(NEM)not only has simple shape function construction,but also can exactly impose the essential boundary condition,which overcomes the difficulty of imposing essential boundary condition in traditional meshless methods.In other words,NEM is a newly numerical method which has advantage of both finite element method and meshless method.In order to exploit the advantage of the NEM,this paper utilizes the NEM to implement the limit analysis of axisymmetric structures.A numerical method is developed for the upper bound limit analysis of axisymmetric structures by using the NEM.A solution procedure for upper bound limit analysis of axisymmetric structures is presented based on the upper bound theorem of limit analysis.The displacement field of the axisymmetric structure is constructed by the Sibson natural neighbor interpolation.The penalty function method is employed to deal with the plastic incompressibility condition of the axisymmetric structure.The mathematical programming formulation of the upper bound limit analysis is established,and the direct iterative algorithm is used to solve it.In order to overcome the difficulty of dealing with the non-smoothing of the objective function,the rigid zone is distinguished from the plastic zone generally and they are dealt with differently in each iteration.Classical numerical examples show that the proposed method is effective and feasibility.Numerical methods are proposed for lower-bound limit analysis making use of NEM.In order to deal with the dimensional obstacle problem in the lower bound limit analysis,the reduced-basis technique is adopted to reduce the whole solution process of lower bound limit analysis to a series of subproblems.In each non-linear programming subproblem,the selfequilibrium stress basis vectors are generated by the equilibrium iteration procedure during elasto-plastic incremental analysis.Then the self-equilibrium stress field is simulated by linear combination of several self-equilibrium stress basis vectors.The complex method is used to solve these non-linear programming problems.Numerical examples show that the proposed method has high accuracy and good numerical stability.