Large Plane Dynamics Postcritical Deformations of Elastic Beam
Large elastic deformations of a prismatic beam with inextensible axis are analysed. The beam at rest is an elastic arch formed by buckling from an initially straight beam and fixing its ends. The beam is modelled as a system of rigid elements connected by means of elastic hinges. The resulting motion equations are integrated numerically. The initial-boundary problem is solved with the use of Lagrange multipliers at each time step. Static characteristics are obtained with the use of the dynamic relaxation method.
E.A.WITMER, H.A.BALMER, J.W.LEECH, T.H.H.PIAN, Large dynamic deformations of beams, rings, plates, and shells, AIAA J., 1, 1848, 1963.
S.R.WOODALL, On the large amplitude oscillations of a thin elastic beam, Int. J. Non-linear Mechanics, 1, 217, 1966.
S.ATLURI, Nonlinear vibrations of a hinged beam including nonlinear inertia effects, J. of Applied Mech., 40,121, 1973.
J.R.H.OTTER, Computations for prestressed concrete reactor pressure vessels using dynamic relaxation, Nuclear Structural Engng., 1, 61, 1965.
J.W.BUNCE, E.H.BROWN, Non-linear bending of thin, ideally elastic rods, Int. J. Mech. Sci., 18, 435, 1976.