Minimum‐Weight Design of Machine Foundation under Vertical Load
Publication: Journal of Engineering Mechanics
Volume 119, Issue 9
Abstract
In this paper a numerical model for the minimum‐weight design of a rectangular machine foundation under a harmonic vertical load is presented. The analysis of the dynamics of foundation‐soil interaction is based on frequency‐dependent dynamic properties of a semi‐infinite supporting medium and includes the shape of the foundation plan, the embedment of the foundation into the soil, and hysteretic material damping of the soil. Dimensions of the concrete block are assumed as design variables. Constraints are placed on resonant frequency, vertical displacement amplitude, stresses in the soil and dimensions of the foundation concrete block. A sequential programming method with variable move limits is used to obtain the optimal solution, which is affected by inertia properties of the machine‐foundation‐soil system, damping from dynamic soil‐foundation interaction and local soil conditions. Numerical examples are given to demonstrate the applications of the proposed approach.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bachmann, H., and Ammann, W. (1987). Vibrations in structures induced by man and machines, Int. Association for Bridge and Struct. Engrg., Zurich, Switzerland.
2.
Barkan, D. D. (1962). Dynamics of bases and foundations. McGraw‐Hill Book Co. New York, N.Y.
3.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw‐Hill, New York, N.Y.
4.
Das, B. M. (1983a). Advanced soil mechanics. McGraw‐Hill, New York, N.Y.
5.
Das, B. M. (1983b). Fundamentals of soil dynamics. Elsevier Science Publishers, New York, N.Y.
6.
Fleury, C. (1987). “Computer aided optimal design of elastic structures.” Computer aided optimal design: structural and mechanical systems, C. A. M. Soares, ed., Springer‐Verlag, Berlin, Germany, 831–900.
7.
Gass, S. I. (1964). Linear programming. 2nd Ed. McGraw‐Hill, New York, N.Y.
8.
Gazetas, G. (1983). “Analysis of machine foundation vibrations: State‐of‐the‐art.” Soil Dyn. Earthquake Engrg., 3(1), 2–42.
9.
Gazetas, G. (1991). “Formulas and charts for impedances of surface and embedded foundations.” J. Geotech. Engrg., ASCE, 117(9), 1363–1381.
10.
Hardin, B. O., and Richart, F. E. Jr. (1963). “Elastic wave velocities in granular soils.” J. Soil Mech. Found. Div., ASCE, 89(1), 33–65.
11.
Hardin, B. O., and Drnevich, V. P. (1972). “Shear modulus and damping in soils: Design equations and curves.” J. Soil Mech. Found. Div., ASCE, 98(7), 667–692.
12.
Huang, Z., and Hinduja, S. (1986). “Shape optimization of a foundation for large machine tool.” Int. J. Machine Tool Design, 26(2), 85–97.
13.
Kanagasundaram, S., and Karihaloo, B. L. (1991). “Minimum‐cost reinforced concrete beams and columns.” Comput. Struct., 41(3), 509–518.
14.
Karihaloo, B. L., and Kanagasundaram, S. (1988). “Comparison of NLP techniques in optimum structural frame design.” Structural optimization, G. I. N. Rozvany and B. L. Karihaloo, eds., Kluwer, Norwell, Mass., 143–150.
15.
Lipinski, J. (1985). Foundations for machines, Arkady, Warszawa (in Polish).
16.
Lysmer, J. (1980). “Foundation vibrations with the soil damping.” Civ. Engrg. Nuclear Power, ASCE, 10(4), 1–18.
17.
Major, A. (1980). Dynamics in civil engineering. Analysis and design, Vols. I–IV, Akademiai Kiado, Budapest, Hungary.
18.
McNeill, R. L. (1969). “Machine foundations. The state‐of‐the‐art.” Proc., Seventh Int. Conf. on Soil Mech. and Found. Engrg., Mexico City, Mexico, 67–100.
19.
Novak, M. (1974). “Effect of soil on structural response to wind and earthquake.” Earthquake Engrg. Struct. Dyn., 3(1), 79–96.
20.
Novak, M., Nogami, T., and Aboul‐Ella, F. (1978). “Dynamics soil reactions for plane strain case.” J. Engrg. Mech. Div., ASCE, 104(4), 953–959.
21.
Pais, A., and Kausel, E. (1988). “Approximate formulas for dynamic stiffnesses of rigid foundations.” Soil Dynamic Earthquake Engrg., 7(4), 213–278.
22.
Pedersen, P. (1981). “The integrated approach to FED‐SLP for solving problems of optimal design.” Optimization of distributed parameter systems, Vol. I, E. J. Haug, J. Cea, eds., Sijthoff and Nordhoff, Amsterdam, the Netherlands, 735–756.
23.
Prakash, S. (1981). Soil dynamics. McGraw‐Hill, New York, N.Y.
24.
Prakash, S., and Puri, V. K. (1988). Foundations for machines: Analysis and design. John Wiley and Sons, New York, N.Y.
25.
Richart, F. E. Jr., Hall, J. R. Jr., and Woods, R. D. (1970). Vibration of soils and foundations. Prentice‐Hall, Englewood Cliffs, N.J.
26.
Szymczak, C. (1978). “Optimization of a rigid block foundation resting on a randomly deformable base.” Archive Civ. Engrg., 24(3), 347–357 (in Polish).
27.
Topping, B. H. V., and Robinson, D. J. (1984). “Selection non‐linear optimization techniques for structural design.” Engrg. Comput., 1(3), 252–262.
28.
Vanderplaats, G. N. (1987). “Numerical optimization techniques.” Computer aided optimal design: structural and mechanical Systems, C. A. M. Soares, ed., Springer‐Verlag, Berlin, Germany, 197–239.
29.
Veletsos, A. S., and Verbic, B. (1973). “Vibration of viscoelastic foundations.” Earthquake Engrg. Struct. Dyn., 2(1), 87–102.
30.
Wolf, J. P. (1985). Dynamic soil‐structure interaction. Prentice‐Hall, Englewood Cliffs, N.J.
31.
Wolf, J. P., and Somaini, D. R. (1986). “Approximate dynamic model of embedded foundation in the time domain.” Earthquake Engrg. Struct. Dyn., 14(5), 683–703.
32.
Wolf, J. P. (1991a). “Consistent lumped‐parameter models for unbounded soil: Frequency independent stiffness, damping and mass matrices.” Earthquake Engrg. Struct. Dyn., 20(1), 33–41.
33.
Wolf, J. P. (1991b). “Consistent lumped‐parameter models for unbounded soil: Physical representation.” Earthquake Engrg. Struct. Dyn., 20(1), 11–32.
34.
Wolf, J. P., and Paronesso, A. (1991). “Errata: consistent lumped‐parameter models for unbounded soil.” Earthquake Engrg. Struct. Dyn., 20, 597–599.
35.
Yoshimi, Y., Richart, F. E. Jr., Prakash, S., Barkan, D. D., and Ilyichev, V. A. (1977). “Soil dynamics and its application to foundation engineering.” Proc., Ninth Int. Conf. on Soil Mechanics and Foundation Engineering, 2, 605–650.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 9 • September 1993
Pages: 1781 - 1797
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: May 7, 1992
Published online: Sep 1, 1993
Published in print: Sep 1993
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.