Abstract
A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.
Highlights
The formal theorems of plastic limit analysis provide the theoretical framework necessary to allow direct evaluation of the load required to cause collapse of a body or structure, without the need for intermediate calculation steps
While early work in the field focused on the development of hand-type limit analysis methods, which are still widely used in engineering practice, more recent research has focused on the development of computational methods, such as finite-element limit analysis [1,2,3]
The aim of this paper is to develop a DLObased formulation that can be applied to three-dimensional problems involving Tresca and Mohr–Coulomb materials
Summary
The formal theorems of plastic limit analysis provide the theoretical framework necessary to allow direct evaluation of the load required to cause collapse of a body or structure, without the need for intermediate calculation steps. Park & Kobayashi [4] were among the first to develop a limit analysis formulation for threedimensional problems, referred to as the ‘rigid-plastic finite-element method’ Their approach involved relaxing the flow rule to obtain a direct estimation of the collapse load. Lyamin & Sloan [5,6] proposed a three-dimensional finite-element limit analysis formulation that used nonlinear programming to obtain solutions Their formulation could be applied to problems involving any yield function that is everywhere differentiable. A principal aim of the research described in the present paper was to develop a method that overcomes this obvious drawback, allowing a much wider range of failure mechanisms to be modelled, and without having to turn to SDP algorithms to obtain a solution The development of such a method is described, and its efficacy demonstrated through application to various benchmark problems considered in the literature
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