Explicit unconditionally stable approaches for built-up shell structural configurations

Built-up structures, especially those involving shell-type components, are encountered in many areas of engineering. Since full three-dimensional modeling may be cost prohibitive, shell-type elements have played an important role in dynamic simulations; however, the nonlinear dynamic analysis is still relatively expensive because of the enormous computations involved. Most often, implicit approaches such as the Newmark β= 0.25 are commonly employed. With the motivation of further enhancing the accuracy and efficiency of analysis of large practical structural problems, we describe explicit, unconditionally stable approaches newly developed by the authors to analyze the dynamics of linear/nonlinear shell structures and subsequently show the applicability to large-scale practical structural dynamics problems. The explicit nature of the formulations and the unconditionally stable algorithmic stability and excellent algorithmic attributes in conjunction with efficient numerical computational features indeed lend themselves well for the analysis of a wide class of complex shell-type structural configurations. The computational and implementation aspects and the numerical evaluation of the so-called VIP (virtual-pulse) time integral methodology that inherits these attributes for general shell-type structural dynamics problems are presented here. Comparisons are also drawn between the VIP methodology and the Newmark family of methods on the aspects of the accuracy and computing time. The numerical results given, which were performed on the Cray supercomputer, show the applicability of the VIP methodology for practical problems, and the computations demonstrate the significant reduction in computing time compared with the most widely advocated Newmark family of methods for given accuracy conditions.