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Johann Guilleminot Christian Soize Djimedo Kondo Christophe Binetruy 《International Journal of Solids and Structures》2008,45(21):5567-5583
Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen–Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. In particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered. 相似文献
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Dr. Johann Lang 《Journal of Geometry》1989,34(1-2):114-126
In [8] the author gave a report on some properties of flag space motions, especially of the composition of screw motions or rotations in flag space. Planet motions more generally are motions which can be composed by two one-parameter-groups. These motions are investigated with respect to their orbits, their multiple ways of construction and the tubular surfaces they can determine. Some of them yield tubular screw surfaces, some others move every sphere the way that it again envellopes a sphere. These motions, which have no Euclidean counterpart, determine non-trivial, kinematically generated LIE-transformations in flag space. 相似文献
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Periodic solutions of nonlinear differential equations involving the method of scalar nonlinearities
Johann Kreyenberg 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1988,39(1):105-117
Summary The recently developed method of scalar nonlinearities is applied to establish a new type of existence proof for periodic solutions of nonlinear differential equations. It is proved that given a periodic solution of a certain linear differential equation whose coefficients are subject to some nonlinear constraint, a nonlinear differential equation, which is closely related to the linear one, has a periodic solution (of the same period) as well. While, in general, the nonlinear equation will not be explicitly resolvable, the linear equation (with constraint) will allow for explicitly given solutions.The proof is carried out by constructing a homotopy (between appropriately chosen integral operators) and is based on Leray-Schauder theory. Thus, an essential hypothesis is the a-priori boundedness of certain intermediate problems. The very definition of the homotopy, which seems to be unprecedented in the literature, bears resemblance with the introduction of Dirac's-function.The theory is applied to Duffing's equation, resulting in an abstract existence statement as well as the explicit construction of numerically tractable intermediate problems. 相似文献
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The reaction of 2-chlorooxiranes 1 with thioamides and thioureas provides access to thiazoles, 4-hydroxy-4,5-dihydrothiazoles and 2-imino-2,3-dihydrothiazoles under mild conditions and with excellent yields. With 1 and selenourea, near quantitative yields of selenazoles are obtained. 相似文献
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