Dynamics of geometrically nonlinear rods. I: Mechanical models and equations of motion (Q1871141)

The author deals with large motions of slender thread-like bodies (e.g., cables, ropes, textile threads, belts) building up a mechanical-mathematical model of homogeneous isotropic linearly elastic, geometrically nonlinear one-dimensional continua. Only small strains, but large deflections are possible. The author presents kinematics (coordinate systems, Bernoulli hypothesis, strains, volume and area alteration), kinetics (forces and stresses, balance laws, field equations, material laws, constitutive equations), equations of motion (Timoshenko beam, inextensible and extensible Euler-Bernoulli beams with circular cross-section, vanishing bending and torsional stiffness, and energy balance) and the corresponding boundary conditions. The formulations of the problems in standard and concentrated form can be applied to many technical problems as space and marine engineering.