Design of Material Properties That Yield a Prescribed Global Buckling Response

[+] Author and Article Information
S. S. Antman

Department of Mathematics, University of Maryland, College Park, MD 20742

C. L. Adler

Department of Physics, Brown University, Providence, RI 02912

J. Appl. Mech 54(2), 263-268 (Jun 01, 1987) (6 pages) doi:10.1115/1.3173005 History: Received July 07, 1986; Revised October 27, 1986; Online July 21, 2009


In the context of the large buckling of a nonlinearly elastic column under end thrust, this paper treats the design of (constitutive) functions appearing in bifurcation problems so as to produce a prescribed first bifurcating branch (e.g., a branch having a prescribed number of wiggles, which produce a prescribed pattern of hysteresis with snap bucklings in loading-unloading processes). The solution of this design problem also yields a method for determining a constitutive function from a single buckling experiment. A dual variational formulation is used to reduce the design problem to the solution of a linear Volterra integral equation of the first kind with a singular kernel. Effective numerical methods for the solution of such ill-posed equations are described and then applied to some physically interesting examples. Generalizations are discussed.

Copyright © 1987 by ASME
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