On the Movement of Granular Materials in Bins and Hoppers Part I: Two-Dimensional Problems
Abstract
The paper is devoted to commemoration of the contribution of Professor Jerzy Litwiniszyn to the development of the mechanics of granular media A simple numerical procedure for determining the field of displacements of granular media in bins and hoppers is proposed. The procedure is based on the concept of Jerzy Litwiniszyn, who treated the gravity flow of granular media as a stochastic process. He and his co-workers presented analytical solutions to a certain number of simple problems concerning deformations of terrain caused by underground mining operations. The numerical procedure proposed in this paper is much more effective in solving numerous problems of practical significance.References
1. W. SZCZEPIŃSKI, Limit states and kinematics of granular materials [in Polish], PWN, 1974.
2. V.V. SOKOLOVSKY, Statics of granular media, Pergamon Press, New York 1965.
3. J. LITWINISZYN, Application of the equation of stochastic process to mechanics of loose bodies, Arch. Mech. Stos., 8, 393–411, 1956.
4. J. LITWINISZYN, An application of the random walk argument to the mechanics of granular media, Proc. IUTAM Sym. on Rheology and Soil Mechanics, Grenoble, April 1–8, 1964, Springer Verlag, 1966.
5. J. LITWINISZYN, Stochastic methods in mechanics of granular bodies, CISM Courses and Lectures No. 93, Springer Verlag, Udine 1974.
6. W. SZCZEPIŃSKI, Z. KOTULSKI, Error analysis with applications in engineering, Lastran Co., Rochester, NY, 2000 (translated from the Polish original published by PWN in 1998).
7. H.S. CARSLAW, J.C. JAEGER, Conduction of heat in solids, Oxford at the Clarendon Press, 1959.
8. A.Z. SMOLARSKI, On same applications of linear mathematical models of the strata mechanics, Prace Komisji Nauk Technicznych, PAN Oddział w Krakowie, Seria Mechanika, 3, 1967.
9. H. GILL, The theory of strata mechanics, PWN–Elsevier, 1991.
10. A.W. JENIKE, Better design for bulk handling, Chemical Engineering, Dec. 1954.
11. J. NACHIMOWICZ, J. PIWNIK, S. POSKROBKO, Dead zoes in gravitational flow of char-lock and pea in cylindrical hopper [in Polish], Zeszyty Nauk. Politechniki Białostockiej, Mechanika, 10, 45–62, 1993.
2. V.V. SOKOLOVSKY, Statics of granular media, Pergamon Press, New York 1965.
3. J. LITWINISZYN, Application of the equation of stochastic process to mechanics of loose bodies, Arch. Mech. Stos., 8, 393–411, 1956.
4. J. LITWINISZYN, An application of the random walk argument to the mechanics of granular media, Proc. IUTAM Sym. on Rheology and Soil Mechanics, Grenoble, April 1–8, 1964, Springer Verlag, 1966.
5. J. LITWINISZYN, Stochastic methods in mechanics of granular bodies, CISM Courses and Lectures No. 93, Springer Verlag, Udine 1974.
6. W. SZCZEPIŃSKI, Z. KOTULSKI, Error analysis with applications in engineering, Lastran Co., Rochester, NY, 2000 (translated from the Polish original published by PWN in 1998).
7. H.S. CARSLAW, J.C. JAEGER, Conduction of heat in solids, Oxford at the Clarendon Press, 1959.
8. A.Z. SMOLARSKI, On same applications of linear mathematical models of the strata mechanics, Prace Komisji Nauk Technicznych, PAN Oddział w Krakowie, Seria Mechanika, 3, 1967.
9. H. GILL, The theory of strata mechanics, PWN–Elsevier, 1991.
10. A.W. JENIKE, Better design for bulk handling, Chemical Engineering, Dec. 1954.
11. J. NACHIMOWICZ, J. PIWNIK, S. POSKROBKO, Dead zoes in gravitational flow of char-lock and pea in cylindrical hopper [in Polish], Zeszyty Nauk. Politechniki Białostockiej, Mechanika, 10, 45–62, 1993.
