By Manolis Papadrakakis, George Stefanou
This ebook comprises the complaints of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of fabrics and buildings that used to be held at Santorini, Greece, September nine – eleven, 2013. It involves 20 chapters that are divided in 5 thematic issues: harm and fracture, homogenization, inverse problems–identification, multiscale stochastic mechanics and stochastic dynamics.
Over the previous couple of years, the serious examine job at micro scale and nano scale mirrored the necessity to account for disparate degrees of uncertainty from quite a few resources and throughout scales. As even over-refined deterministic ways cannot account for this factor, a good mixing of stochastic and multiscale methodologies is needed to supply a rational framework for the research and layout of fabrics and constructions. the aim of this IUTAM Symposium was once to advertise achievements in uncertainty quantification mixed with multiscale modeling and to inspire examine and improvement during this starting to be box with the purpose of bettering the protection and reliability of engineered fabrics and structures.
Special emphasis was once put on multiscale fabric modeling and simulation in addition to at the multiscale research and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media used to be additionally completely tested in numerous shows. numerous subject matters of multiscale stochastic mechanics, comparable to identity of fabric versions, scale coupling, modeling of random microstructures, research of CNT-reinforced composites and stochastic finite components, were analyzed and mentioned. plenty of papers have been eventually dedicated to leading edge equipment in stochastic dynamics.
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Extra info for Multiscale Modeling and Uncertainty Quantification of Materials and Structures: Proceedings of the IUTAM Symposium held at Santorini, Greece, September 9-11, 2013.
Example text
Ru C r T u/ is the infinitesimal strain tensor, the superscript T denotes the transpose operator, Œu D Tr "ŒuI C 2 "Œu is the Cauchy stress tensor, I is the identity tensor, and Tr denotes the trace operator. Equivalently, one can use the Young’s modulus E and the Poisson’s ratio instead of the Lamé constants. 1 C / (2) The functional space is Vs D L 2 . ˝s //3 ; vj D D 0g. Endowed with the appropriate inner product and norm, Vs is a Hilbert space. Using Lax-Milgram theorem, it can be proved that the problem (1) has a unique solution us (see for instance Babuška et al.
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19) is used to remove the over-parameterization of the functional space Vc . Indeed we note that the subspace of constant (in space) deterministic functions of R Vc can be described either only with v or T . We therefore impose a condition that Fc vdx D 0. It is also possible to impose rather EŒ T D 0 but this would be less trivial in a Monte-Carlo-based simulation. Likewise, there x ? and R x ? , and we impose Ris redundancy between the elements  Âdx D 0. We therefore obtain S by summing C along all the DOFs of the c Fc lines.