On Bickford's consistent higher order beam theory (Q1060610)

In this paper the author compared some variants of refined theories [\textit{W. B. Bickford}, A consistent higher order beam theory. Developments theor. appl. Mech. 11, 137 ff (1982); the author, J. Sound Vib. 74, 81-87 (1981; Zbl 0453.73058); \textit{G. R. Cowper}, J. Appl. Mech. 33, 335-340 (1966; Zbl 0151.379)] for three beam problems. He showed, that variationally consistent theories based on kinematic hypotheses may provide inferior results than some ''inconsistent'' theories based on properly chosen ad hoc assumptions. The problem discussed in the paper deals only with the interior solution of this dimension reduction problem and therefore only corrective terms of order \(\epsilon^ 2=h^ 2/l^ 2\) are obtained. In exact asymptotic approximation boundary effects of order \(\epsilon\) may also be present.