دانلود رایگان مقاله انگلیسی الگوریتم تکراری موثر برای تحلیل محدود ساختارهای خمشی خرپایی با یک رویکرد سینماتیک - الزویر 2018

abstract

A former algorithm of Limit Analysis (LA) at the continuum mechanics scale by a kinematic, upper-bound approach is here re-interpreted in the realm of LA of large-scale 3D truss-frame structures and effectively implemented toward fast and convenient collapse load multiplier and mechanism evaluation. First, the algorithm is described in its iterative design, and convergence is demonstrated. Some initial applications to truss-frame test structures under bending and torsion are also discussed. Then, the algorithm is successfully applied to two benchmark multi-story frames. It is shown that very consistent and quick evaluations of the collapse characteristics are obtained by this direct method, in comparison to those provided by alternative classical mathematical programming approaches and much expensive evolutive step-by-step solutions of the whole structural elastoplastic response. The algorithm shows a superior performance, with the kinematic multiplier truly precipitating from above on the collapse one, in very few iterations, with a consistent associated estimation of the plastic collapse mechanism.

4. Conclusions

In the paper, an efficient approach for the kinematic LA of (3D) truss-frame structures has been presented. It is based on an existing approach for LA of (2D) continua and adapted to beams with a Rankine-type boxed-form yield domain. The iterative algorithm involved in the procedure is described in detail; the proof of convergence of the iterative process is provided. Four numerical examples have been presented. The first two consist of a space truss-frame cantilever beam under bending and torsion, respectively. In these cases the effectiveness of the proposed algorithm is proven by the comparison between the results obtained from the proposed procedure and those coming from an analytically determined solution. These numerical tests deserve attention also for demonstrating the effectiveness of the algorithm in capturing the collapse load multiplier and one of the collapse mechanisms of the structure even in the presence of an infinite number of collapse mechanisms. Then, the kinematic algorithm has been adopted for the LA of two multi-story 3D frame structures proposed in the literature, with available computational results. Moreover, results coming from an independent step-by-step evolutive approach have been computed for comparison purposes. The effectiveness of the proposed procedure turned out to be very satisfactory, considering both the available sets of results. The algorithm rapidly converges, with a kinematic multiplier quickly precipitating toward the sought collapse load multiplier, illustrating the feasibility and convenience of this new algorithm.