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LE, J. ELIÁŠ, J. BAŽANT, Z.
Originální název
Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation
Typ
článek v časopise - ostatní, Jost
Jazyk
angličtina
Originální abstrakt
Engineering structures must be designed for an extremely low failure probability, i.e. Pf < 10-6. To determine the structural strength corresponding to such a low failure probability, a physical model of the probability distribution of structural strength is required. Recent study showed that the strength distribution of quasibrittle structures, which fail at the macro-crack initiation from one representative volume element (RVE), can be statistically modeled as a finite chain of RVEs. It has been further demonstrated that, based on atomistic fracture mechanics and a statistical multi-scale transition model, the strength distribution of each RVE can be approximately described by a Gaussian distribution, onto which a Weibull tail is grafted from the far-left end a point of the probability of about 10-4 to 10-3. The model implies that the strength distribution of quasibrittle structures depends on the structure size, varying from the Gaussian distribution modified by a far-left Weibull tail for small-size structures to the Weibull distribution for large-size structures. Compared to the classical Weibullian strength distribution, which is limited to perfectly brittle structures, the grafted Weibull-Gaussian distribution makes the calculation of strength distribution of quasibrittle structures much more complicated. This paper presents two methods of computing the strength distribution of quasibrittle structures: 1) for structures with a simple stress field, an approximate closed-form expression of the strength distribution is proposed based on the Taylor series expansion of the grafted Weibull-Gaussian distribution, and 2) for structures with a complicated stress field, a random RVE placement method is developed based on the centroidal Voronoi tessellation. Through some numerical examples including three-point and four point bend beams as well as a 2D model of Malpassets dam, it is shown that the strength distribution calculated by the proposed approximated analytical formulation agrees well with that calculated by the numerical methods such as the random placement method as well as a previously proposed nonlocal boundary method.
Klíčová slova
Finite weakest link model; Strength statistics; Representative volume element; Structural safety; Fracture; Concrete structures; Composites
Autoři
LE, J.; ELIÁŠ, J.; BAŽANT, Z.
Rok RIV
2012
Vydáno
15. 7. 2012
Místo
USA
ISSN
0733-9399
Periodikum
Journal of Engineering Mechanics
Ročník
138
Číslo
7
Stát
Spojené státy americké
Strany od
888
Strany do
899
Strany počet
12
BibTex
@article{BUT98323, author="Jia-Liang {Le} and Jan {Eliáš} and Zdeněk P. {Bažant}", title="Computation of Probability Distribution of Strength of Quasibrittle Structures Failing at Macrocrack Initiation", journal="Journal of Engineering Mechanics", year="2012", volume="138", number="7", pages="888--899", issn="0733-9399" }