A Study Of Numerical Methods For Limit And Shakedown Analyses Of Structures And Their Engineering Applications

At present an important subject on the limit and shakedown analyses is to study the strategies of applications, search for efficient and feasible computational methods so that the limit and shakedown theories can find their applications in engineering practice. In this paper, the numerical theo- ries and computational methods for limit and shakedown analyses of struc- tures are systematically studied and applied to the safety assessment of the pressure vessels with volume defects. A numerical method is developed for the upper bound limit analysis of 3-D structures. Based on the theories of the convex analysis and the nonsmooth analysis, the penalty-duality method is used to deal with the plastic incompressibility condition. The limit analysis of 3-D structures is formulated as a discrete nonlinear mathematical programming problem with equality constraints by means of finite element technique. An optimal direct iterative algorithm is given to solve this formulation. A finite element technique using the definition of the P-norm is devel- oped for calculating lower bounds of the limit load multiplier for axisymmetric structures which obey the von Mises yield criterion. Based on the lower bound limit theorem, a finite element mathematical programming formulation is established by applying the stress function method to con- struct the equilibrated stress field, and solved by the modified Newton-Raphson iterative algorithm. For two relaxed kinematic shakedown criteria, the corresponding 3-D numerical kinematic formulations are established and the respective solution approaches are presented. Based on the convex analysis and duality theorem, a kinematic shakedown formulation for 3-D problems is derived. A finite el- ement discretization of the kinematic extremum problem is considered. A di- rect iterative algorithm is employed to solve the discretized system. Every step of the inner iteration is equivalent to solving a relevant elastic problem. According to Melan's theorem, a nonlinear finite element programming formulation for static shakedown analysis is established by using hybrid stress finite element to construct the self-equilibrated stress field with the yield criterion of the mean. In order to avoid the dimension obstacle of large scale nonlinear programming, a new technique, e.g. elastic-plastic dimension reduction-based iteration approach is proposed and suitably applied to the shakedown analysis of the pressure vessels with volume defects. In light of the proposed methods, numerical limit and shakedown ana- lyses are performed for the pressure vessels with volume defects. The effects of various shapes and sizes of volume defects on the limit and shakedown loads are investigated and evaluated. Two kinds of typical failure modes cor- responding to different dimensions of volume defects are studied. The re- search has lead to a series of computational curves as well as the fit formulae for the limit and shakedown loads. The calculated results can provide theo- retical foundations for the safety assessment of the pressure vessels with vol- ume defects. Ph. D. Candidate Liu Yinghua (Solid Mechanics) Directed by Professor Xu Bingye & Professor Cen Zhangzhi...