A multiscale component mode synthesis method for dynamic analysis of nanostructures.

摘要

Nanoscale structures, materials and systems have found widespread applications in many areas including communications, information technology, medical, mechanical, and aerospace technologies. For the last decade, advances in nanotechnology as well as nanomachining techniques have enabled rapid development of novel nanodevices. The design, optimization, and fabrication of nanomaterials and nanosystems for various applications can be accelerated by developing accurate physical theories and computational design tools that describe the motion and operation of nanostructures. There are two major challenges in the physical modeling and computational analysis of nanostructures. First, when the characteristic length of the nanomaterials scales down to several tens of nanometers, nanoscale effects such as material defects and surface effects become significant. Classical theories based on continuum mechanics that have been developed for microsystems and macrosystems may not be directly applicable for nanosystems because of the small scale effects. Second, although the characteristic length of nanostructures is often a few nanometers, the entire system could still be the size of micrometers. Therefore, a typical nanostructure can still contain millions of atoms. In this case, atomistic simulation methods such as ab initio methods, molecular dynamics(MD) and Monte Carlo simulations, are computationally impractical for design and optimization of the nanostructures.;This thesis describes a method for multiscale dynamic analysis of nanostructures. The multiscale approach consists of a top-down hierarchical substructure decomposition and a bottom-up component mode synthesis. At the bottom level, atomistic descriptions are employed to compute the vibrational modes in the atomistic substructures where "nano effects" are significant. The vibrational modes are computed for the continuum substructures by using continuum theories. A component mode synthesis (CMS) technique is employed to synthesize the vibrational modes of the bottom-level substructures to construct the vibrational modes for the top-level structure. At the top-level, the constructed global vibrational modes are used to generate a reduced-order system by using the mode superposition method to perform the dynamic analysis. In this work, the multiscale component mode synthesis approach is first developed for linear dynamic analysis of nanostructures and then extended to solve systems with higher physical complexity which includes nonlinear dynamics and finite temperature effects.;In comparison with other existing multiscale approaches, the proposed multiscale component mode synthesis method has the following advantages. First, the multiscale decomposition combined with component mode synthesis reduces the system degrees of freedom significantly. Second, as the global continuous modes are used to couple the components of different length scales, the artificial reflection of the high-frequency waves at atomistic-continuum interfaces is eliminated. Third, multiscale component mode synthesis can have the same time scale in both the atomistic and continuum regions. Finally, in this method, each component can be independently modeled and arbitrary combined. These advantages make the multiscale component mode synthesis method well suited for modeling and simulation of the large and complex nanosystems.