Stochastic Methods in Mechanics of Granular Bodies: Course by J. Litwiniszyn PDF

By J. Litwiniszyn

ISBN-10: 3211813101

ISBN-13: 9783211813102

ISBN-10: 3709128366

ISBN-13: 9783709128367

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Additional resources for Stochastic Methods in Mechanics of Granular Bodies: Course held at the Department of General Mechanics October 1972

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G. 12) jl(x,z + e,t + -;;) = pji(:r. 13) jl(x,z+ e,t + -r) = pP(x + a,z,t)- c"(x + a,z,t). , t - T) + + pft(x,z -a,t-t") + q«(x,z- Q, t- -r) = = P(x,~- Q,t -t"). 14) P(:x:,z + e,t+'t) = p[PCx-a,z ,t) + P(x+a,z,t)]- cP(x,z- e,t- T). This difference equation describes the probability of propagation of voids in a model representing a granular medium regarded as a collection of discrete elements. At the same time, equ! 14 is the starting point for obtaining the differential Heuristi c Models 31 equation s, assuming existenc e of appropr iate limits.

J(I) for ~ = 1,2,3 I describes the vector field iiT = iif(I) in the place x3= square matr:ix of function ~~~k • XI . k(J,II) is the matrix of the tran- General Model of Displacements 43 fWlctions from plane X 3 = Xr3 to plane x 3 =Xn3 > Xt3 • In accordance with postulate 3. 6 operator F should fulfil the condition of convergence to the boundary conditions. 9) where 6~k = { ~ &(I I) and [6CI, I)

11 the voids at a given point can be measured by measuring the depth of the trough ascribed to that point. Such measurements have been made in laboratory experiments on displacements in granular medium, and have also been observed in the earth 1 s crust undergoing displacement during subterranean mining operations. The results of these measurements and their confrontation with phenomena of moderately large displacements prompted an attempt at a general conception and construction of a model of the phenomenon based on a set of postulates * * The need of such a generalization arises from the following reasoning.

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Stochastic Methods in Mechanics of Granular Bodies: Course held at the Department of General Mechanics October 1972 by J. Litwiniszyn

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