#7074. A Derivation of the Beam Theory of Second-Order with Shear, Starting from a Continuum Mechanics-Based Extension of the Reissner Finite-Strain Beam Theory

December 2026publication date
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Journal’s subject area:
Mechanical Engineering;
Mechanics of Materials;
Materials Science (all);
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Abstract:
A consistent derivation of the beam theory of second order with shear is presented. The geometrically exact Reissner finite-strain beam theory is taken as the starting point, utilizing a continuum mechanics-based extension with respect to stress–strain constitutive formulations. Corresponding incremental relations for small deformations superimposed upon an intermediate configuration with (possibly) finite deformations are presented, from which the second-order beam theory with shear eventually is derived using two slight approximations.
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