We report a new slippage system based on p-tert-butylbenzyl-terminated imidazolium ions and di(ethylene glycol)containing macrocycles and their use as linking units for the construction of a prototypical molecular "Lock & Lock" box from a resorcinarene-based cavitand "bowl" and a porphyrin "cover". The multivalent structure with four slippage linkers provided the molecular box with high stability, yet the system dissociated into its two components upon application of suitable external stimuli.
This paper is concerned with the nonlinear dynamic analysis of framed structures using a reduction method recently proposed by the authors. The reduction method is originally devised for structural static reanalysis and has been applied in optimal design of structures to speed up the design process. For nonlinear dynamic analysis of framed structures, the incremental or iterative equations of motion can be transformed into an algebraic system of equations if appropriate integration methods such as Newmark's method are used to integrate the equations of motion. The resulting algebraic system, referred to as the effective system in this paper, changes during the simulation for a nonlinear dynamic problem. Therefore, from the point of view of solving systems of equations, a nonlinear dynamic problem is very similar to an optimal design problem in that the system of equations changes for both types of problems. Hence, any reanalysis technique can be readily applied to carry out a nonlinear dynamic analysis of structures. As demonstrated from the presented numerical examples, the response obtained by the adopted reduction method is as accurate as that obtained by the Cholesky method, and as estimated from the operation counts involved in the method, it is more ef®-cient than the Cholesky method when the half-band width is greater than about 50.
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