5,055 research outputs found
On the numerical modelling of bond for the failure analysis of reinforced concrete
The structural performance of reinforced concrete relies heavily on the bond between reinforcement and concrete. In nonlinear finite element analyses, bond is either modelled by merged, also called perfect bond, or coincident with slip, also called bond-slip, approaches. Here, the performance of these two approaches for the modelling of failure of reinforced concrete was investigated using a damage-plasticity constitutive model in LS-DYNA. Firstly, the influence of element size on the response of tension-stiffening analyses with the two modelling approaches was investigated. Then, the results of the two approaches were compared for plain and fibre reinforced tension stiffening and a drop weight impact test. It was shown that only the coincident with slip approach provided mesh insensitive results. However, both approaches were capable of reproducing the overall response of the experiments in the form of load and displacements satisfactorily for the meshes used
Tight Sum-of-Squares lower bounds for binary polynomial optimization problems
We give two results concerning the power of the Sum-of-Squares(SoS)/Lasserre
hierarchy. For binary polynomial optimization problems of degree and an
odd number of variables , we prove that levels of the
SoS/Lasserre hierarchy are necessary to provide the exact optimal value. This
matches the recent upper bound result by Sakaue, Takeda, Kim and Ito.
Additionally, we study a conjecture by Laurent, who considered the linear
representation of a set with no integral points. She showed that the
Sherali-Adams hierarchy requires levels to detect the empty integer hull,
and conjectured that the SoS/Lasserre rank for the same problem is . We
disprove this conjecture and derive lower and upper bounds for the rank
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