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Polyhedral Robust Minkowski-Lyapunov Functions

Abstract

This article creates a numerical platform for practical utility of the recently introduced theoretical framework of robust Minkowski-Lyapunov functions. Systems of affine inequalities and equalities whose feasibility verifies the robust Lyapunov nature of polyhedral Minkowski functions with respect to the recently introduced robust Minkowski-Lyapunov inequality are derived. The theoretically exact verification of the robust Minkowski-Lyapunov inequality in the polyhedral setting is reduced to the feasibility stage of a linear program. The topological flexibility of the proposed methods is illustrated by two examples.

article Article

date_range 2024

language English

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Rakovic Sasa

Zhang Sixing

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Featured Keywords

Lyapunov methods

Linear matrix inequalities

Optimization

Numerical stability

Surveys

Stability criteria

Linear programming

Linear inclusions

Minkowski functions

polyhedral sets

robust Lyapunov functions

stability

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Effect of corrosion on flexural strength of reinforced concrete beams with polypropylene fibers

Abstract

An experimental study was performed to investigate the effects of polypropylene fibers on uncorroded and corroded reinforced concrete beams. Three different volume fractions of polypropylene fibers having 0, 0.5, and 1.5%, were tested at four corrosion levels of 0% and approximately 5, 7, and 9%. A full scale of an accelerated corrosion pool was used for the accelerated corrosion process. Reinforced concrete beams were used for an under monotonic bending test. The contribution of the actual corrosion levels of transverse and longitudinal reinforcement bars to the total corrosion levels were obtained from reinforcement bars fully extracted from concrete. Flexural strength, bond-slip, and moment-curvature relationships were examined for uncorroded and corroded reinforced concrete beams. A new model was developed to predict the flexural strength of corroded reinforced concrete beams. The proposed model for predicting the residual flexural strength of corroded beams was compared with test data published in previous studies. Furthermore, a novel model is presented for improved predictions between the actual and theoretically estimated corrosion mass losses, based on Faraday’s law, with the aid of fully extracted reinforcement bars. The model used to predict the flexural strength of corroded reinforced concrete beams with large sizes demonstrated good agreement with current and previously published literature data. In the case of corroded beams comprising differing amounts of polypropylene fibers, the performance of the corroded beams was limited by a fiber volume fraction of 1.5% at low corrosion levels.

article Article

date_range 2018

language English

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