Abstract
Closed-form solutions are derived for elastica with axial and shear deformations, using elliptic integrals. The theories used here are the Timoshenko beam theory of finite displacements with finite strains and that with small strains. Elliptic integral solutions are further transformed to normal forms to obtain accurate solutions. As a result, both of the closed-form solutions are expressed in normal forms from the first to the third kind of elliptic integrals. With these solutions, two kinds of structures are analyzed to examine the effect of shear deformations along with the accuracy of the approximate theory of finite displacements with small strains.
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