Advanced computation in plastic collapse structures

Accurate prediction of the ultimate load bearing capacity of structures plays an important role in the design of many practical engineering structural systems. Traditional elastic design provides a good estimation of safety margin when the structure is subjected to normal service/loading conditions, but it cannot evaluate the ultimate load carrying capacity of the structure because the plasticity effect is not taken into consideration. The incremental elastic-plastic analysis, on the other hand, may be quite cumbersome and convergence of the nonlinear solution can be a critical issue for large-scale structures. Therefore, approaches based on limit analysis are opening an alternative way to predict accurately the ultimate behavior of structures in the plastic regime. Nowadays, limit analysis has well known as an efficient direct tool for assessing the safety load factor of engineering structures.

The aim of this project is to develop a robust computational tool of kinematic theorem for predicting the plastic limit loads in structures. The basic idea in this method is to use two levels of mesh repartitioning for the finite element limit analysis. The master level begins with an adaptive primal-mesh strategy guided by a dissipation-based indicator. The slave level consists of further subdividing each triangle into three sub-triangles and creating a dual mesh through a careful selection of a pair of two sub-triangles shared by the corresponding common element edge. By applying a strain smoothing projection operator to the strain rates on the dual mesh, the flow rule constraint is enforced over the edge-based strain smoothing domains, and likewise everywhere in the problem domain. This numerical procedure is performed for a cohesive-frictional material. This numerical procedure is also performed necessarily to overcome the volumetric locking problem for a purely cohesive material. The optimization formulation of limit analysis is next presented by the form of a second-order cone programming (SOCP) for the purpose of exploiting the efficiency of interior-point solvers. The present method uses linear triangular elements and handles a low number of optimization variables. This leads to a convenient way to design and solve the large-scale optimization problems effectively. Several numerical examples are given to demonstrate the simplicity and effectiveness of our method in both academics and applications.

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