A local–global model for the non‐linear analysis of locally defective shells of revolution

Abstract

AbstractIn this paper a local–global analysis technique is presented for the non‐linear analysis of shells of revolution with a localized material discontinuity in the form of a crack or a cutout. The local zone is modelled using two‐dimensional general shell elements. Axisymmetric shell elements with Fourier description in the circumferential direction are used away from this local zone. In contrast to the earlier work of the authors, the geometric non‐linearity is taken into account in the axisymmetric zone as well. The harmonic coupling in the axisymmetric zone is efficiently handled through the pseudo‐load approach. A special preconditioned conjugate gradient iterative method is employed in conjunction with the arc length method for achieving improved convergence and negotiating the limit points. The attractive features of this methodology are that the tangential stiffness matrix of the structure is never assembled and factorized and that most of the computations are simple matrix–vector multiplications which are carried out efficiently at the element level. Numerical examples are presented to demonstrate the applicability of this method.