Structural Designs for Bounds on Dynamic Response

by J.-M. Chern, Res. Engr.; Foster Wheeler Corp.,
J. F. Dafalias, Res. Asst.; Dept. of Civ. Engrg., Univ. of California, Berkeley, CA.,
John B. Martin, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Cape Town, Cape Town, South Africa,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 2, Pg. 261-270

Document Type: Journal Paper


An upper bound on the displacement at a particular point on an elastic beam resulting from impulsive loading may be established. For a given volume of material in a beam of sandwich cross section, a necessary and sufficient condition for a local minimum in the displacement bound for a prescribed loading is developed by means of the calculus of variations. Optimal design based on this condition is illustrated by examples of statically determinate and indeterminate beams. It is shown that the procedure leads to a significant reduction of the displacement bound in comparison to uniform beams.

Subject Headings: Beams | Displacement (mechanics) | Structural design | Structural dynamics | Dynamic response | Impulsive loads | Elastic analysis | Cross sections

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