Solution for an Irregular Perturbation Problem of Viscoplastic Spherical Container Under Internal Pressure
An irregular perturbation problem around a quasi-static solution for a motion of a thick-walled spherical container made from viscoplastic material and subjected to a time-dependent internal pressure is dealt with. Only the first perturbations are taken into account. A practically important case of a power excess stress function above the static yield stress is considered.
References
S.R.BODNER and P.S.SYMONDS, Experimental and theoretical investigation of the plastic deformation of cantilever beams subjected to impulsive loading, J. Appl. Mech., 29, 4, 719-729, 1962.
W.EKHAUS, Matched asymptotic expansions and singular perturbations, North-Holland Mathematics Studies., 6, North-Holland/American Elsevier 1973.
N.JONES et al., The dynamic plastic behaviour of shells, [in:] Dynamic response of structures, [Ed.:] G.HERRMAN and N.PERRONE, Pergamon Press, 1-29, 1972.
A.NAYFEH, Perturbation methods, Pure and Appl. Math., J. Wiley and Sons, New York-London-Sydney-Toronto 1973.
P.PERZYNA, Theory of viscoelasticity [in Polish], PWN, Warszawa 1966.
W.WOJNO, Perturbation solution for rigid-viscoplastic container, Arch. Mech., 31, 407-422, 1979.
W. WOJNO and T. WIERZBICKI, On perturbation solution for impulsively loaded viscoplastic structures, ZAMP, 30, 41-55, 1979.
W.WOJNO and T.WIERZBICKI, Perturbation solution for impulsively loaded viscoplastic plates, Int. J. of Non-Linear Mech., 15, 211-223, 1980.
W.WOJNO, Perturbation solution for viscoplastic beam under ideal impulse loading, Arch. Mech., 33, 1, 83-97, 1981.
W.WOJNO, Perturbation solution for a viscoplastic spherical container subject to an internal pressure [in Polish], IFTR Reports, 3/1989.