The shape of the strongest column and some related extremal eigenvalue problems

Open Access
Publisher Website
Google Scholar
Abstract
We determine the shape of the strongest column in the class of columns of length l l , volume V V , and having similar cross-sectional areas A ( x ) A(x) satisfying a ≤ A ( x ) ≤ b a \le A\left ( x \right ) \le b where a a and b b are prescribed positive bounds. In the special case where there are no constraints on the areas of cross-sections the problem has been solved by Keller [1] and by Takjbakhsh and Keller [2]. These authors observed that the problem is equivalent to an extremal eigenvalue problem and developed a variational technique for solving such problems. We treat a slightly more general class of extremal eigenvalue problems and give sufficient conditions for a given function to be a solution. Our work on the strongest constrained column demonstrates a procedure for finding functions satisfying these conditions.

This publication has 9 references indexed in Scilit: