Abstract
A three dimensional nonlinear equilibrium theory of elastic rods, applicable to large displacements and small strains, and accounting for extensibility and shear deformation is developed. Integrals of the governing equations are determined for the case of specified end force and moment. A class of solutions is obtained for an initially straight, untwisted rod and compared to the classical solution. The effects of extensibility and shear deformation are discussed.
Zusammenfassung
In dieser Arbeit wird eine dreidimensionale nichtlineare Gleichgewichtstheorie der elastischen Stäbe entwickelt, welche auf grosse Verschiebungen und kleine Dehnungsstreckung anwendbar ist. Dieselbe schliefst Ausdehnung und Schubdeformation ein. Es werden die Lösungsintegrale der diesbezüglichen Gleichungen bestimmt für voraus gegebene Kräfte und Kraftmomente am Ende des Stabes. Man erhält eine Gruppe von Lösungen für den anfänglich geraden unverdrehten Stab welche mit den klassischen Lösungsansätzen verglichen wird. Die Einbeziehung der Dehnungsund Schubdeformation werden gleichfalls besprochen.
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Whitman, A.B., DeSilva, C.N. An exact solution in a nonlinear theory of rods. J Elasticity 4, 265–280 (1974). https://doi.org/10.1007/BF00048610
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DOI: https://doi.org/10.1007/BF00048610