Transient response of an impulsively loaded plastic string on a plastic foundation

M. Mihăilescu-Suliciu, I. Suliciu, T. Wierzbicki, M. S. Hoo Fatt
1996 Quarterly of Applied Mathematics  
The problem of an impulsive loading of a long rigid-plastic string resting on a rigid-plastic foundation is studied. A closed form solution is obtained by disregarding the longitudinal motion and considering an arbitrarily large transversal motion. Expressions for the final shape of the string are derived in terms of the magnitude of the applied impulse. It is found that the stress and the foundation reaction force are not uniquely determined, while the shape of the string is. Notation. a =
more » ... . Notation. a = Cq/^oXq) = constant in Eq. (15), Co = {N/Qo)lt2 = transversal wave speed, i, j -unit vectors along ox,oy axes, respectively, Io = Poto = applied impulse per unit length, N = yield stress of the string, P,Pq = pressure load, pressure amplitude, q = foundation reaction force, qo = yield limit of the foundation reaction force, Q = dimensionless foundation reaction force, r = r (X, t) = position vector, = real numbers, S = dimensionless stress in the string,
doi:10.1090/qam/1388020 fatcat:7hhu3nb4lbfmhetyr7v26bsnb4