Engineering Transactions, 47, 2, pp. 183–201, 1999
10.24423/engtrans.628.1999

Mass Minimization of Dynamically Loaded Machine Foundations Using Different Subsoil Models

Z. Sienkiewicz
Technical University of Koszalin
Poland

B. Wilczyński
Technical University of Koszalin
Poland

The effect of variation of the shear wave velocity profile of a layered soil on a minimal mass of a rigid machine foundation under behavior constraints on vibration and normal stress contact amplitudes and side constraints is numerically studied. The nonlinear programming problem has been solved by an iterative application of a sequential linear programming. The dynamic response of the machine foundation to unbalanced forces is evaluated including the dynamic soil-block interaction. The mixed-boundary value problem of elastodynamics was formulated as the system of Fredholm integral equations of the first kind with the Green's functions for a half-space as kernels and contact tractions as unknowns. The solution of the integral equations was accomplished numerically by a Boundary Element Method. In addition, the effect of embedment of the block into the soil was included by means of a local dynamic boundary used to simulate the backfill. Numerical results illustrate the sensitivity of the optimum design with respect to variations in problem preassigned parameters.
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

J. LIPIŃSKI, Foundations for machines [in Polish], Arkady, Warszawa 1985.

P.J. MOORE [Ed.], Analysis and design of foundations for vibrations, A. A. Balkema, Rotterdam 1985.

G. GAZETAS, Analysis of machine foundation vibrations: state-of-the-art, Soil Dyn. Earthquake Engng., 3, 1, 2–42, 1983.

J.P. WOLF, Dynamic soil-structure interaction, Prentice-Hall, Englewood Cliffs, N.J. 1985.

Z. SIENKIEWICZ, Forced vibrations of rectangular foundations embedded in a half-space, Archives of Civil Engng, 38, 35–58, 1996.

K. DEMS and W. GUTKOWSKI, 2D shape optimization with static and dynamic constraints, Structural Optimization, 15, 3/4, 201–207, 1998.

B. ESPING, Design optimization as on engineering tool, Structural Optimization, 10, 3/4, 137–152, 1995.

Z. SIENKIEWICZ and B. WILCZYŃSKI, Minimum-weight design of machine foundation under vertical load, ASCE J. of Engng. Mech., 119, 1781–1797, 1993.

Z. SIENKIEWICZ and B. WILCZYŃSKI, Shape optimization of a dynamically loaded machine foundation coupled to a semi-infinite inelastic medium, Structural Optimization, 12, 29–34, 1996.

Z. SIENKIEWICZ and B. WILCZYŃSKI, Shape optimization of a dynamically loaded machine foundation coupled to layered subsoil, W. Gutkowski and Z. Mróz [Eds.], Proc. Second World Congress of Structural and Multidisciplinary Optimization, WCSMO-2, Zakopane, May, 26–30, Poland, 637–642, 1997.

Z. SIENKIEWICZ and B. WILCZYŃSKI, Weight minimization of dynamically loaded 3-D foundation on layered medium, S. Hernandez and C.A. Brebbia [Eds.], Computer-Aided Optimum Design of Structures V, Computational Mechanics Publications, Southampton, 131–140, 1997.

L.A. SCHMIT and K.J. CHANG, Optimum design sensitivity based on approximation concepts and dual methods, Int. J. Numer. Meth. in Engng., 20, 39–75, 1984.

Y. HAN, Coupled vibration of embedded foundation, ASCE J. of Geotechnical Engng, 115, 1227–1238, 1989.

A.C. ERINGEN, E.S. SUHUBI, Elastodynamics, Vol. 2. Linear theory, Academic Press, New York 1975.

M. NOVAK, T. NOGAMI, F. ABOUL-ELLA, Dynamics soil reactions for plane strain case, ASCE J. of Engng. Mech. Div., 104, 953–959, 1978.

A. BORKOWSKI, K. DEMS, W. GUTKOWSKI and Z. MRÓZ, Optimization methods, [In:] M. Kleiber [Ed.] Computer methods of solid mechanics, [in Polish] PWN, Warszawa 1995, 519–645.

J.-F.M. BARTHELEMY and R.T. HAFTKA, Approximation concepts for optimum structural design-a-review, Structural Optimization, 5, 129–144, 1993.

U. KIRSCH, Effective move limits for approximate structural optimization, ASCE J. of Structural Engng., 123, 210–217, 1997.

K. SCHITTKOWSKI, C. ZILLOBER and R. ZOTEMANTEL, Numerical comparision of nonlinear programming algorithms for structural optimization, Structural Optimization, 7, 1–19, 1994.

T.-Y. CHEN, Calculation of the move limits for the sequential linear programming method, Int. J. Num. Meth. Engng., 36, 2661–2679, 1993.

J.E. Luco and R.J. APSEL, On the Green's functions for layered half-space: part I, Bull. Seism. Soc. Am., 73, 909–924, 1983.




DOI: 10.24423/engtrans.628.1999