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Homogenization and bridging multi-scale methods for the dynamic analysis of periodic solids.

機(jī)譯：均質(zhì)化和橋接多尺度方法對(duì)周期固體進(jìn)行動(dòng)力學(xué)分析。

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This work investigates the application of homogenization techniques to the dynamic analysis of periodic solids, with emphasis on lattice structures. The presented analysis is conducted both through a Fourier-based technique and through an alternative approach involving Taylor series expansions directly performed in the spatial domain in conjunction with a finite element formulation of the lattice unit cell. The challenge of increasing the accuracy and the range of applicability of the existing homogenization methods is addressed with various techniques. Among them, a multi-cell homogenization is introduced to extend the region of good approximation of the methods to include the short wavelength limit. The continuous partial differential equations resulting from the homogenization process are also used to estimate equivalent mechanical properties of lattices with various internal configurations. In particular, a detailed investigation is conducted on the in-plane behavior of hexagonal and re-entrant honeycombs, for which both static properties and wave propagation characteristics are retrieved by applying the proposed techniques. The analysis of wave propagation in homogenized media is furthermore investigated by means of the bridging scales method to address the problem of modelling travelling waves in homogenized media with localized discontinuities. This multi-scale approach reduces the computational cost associated with a detailed finite element analysis conducted over the entire domain and yields considerable savings in CPU time. The combined use of homogenization and bridging method is suggested as a powerful tool for fast and accurate wave simulation and its potentials for NDE applications are discussed.
機(jī)譯：這項(xiàng)工作研究了均質(zhì)化技術(shù)在周期性固體動(dòng)力學(xué)分析中的應(yīng)用，重點(diǎn)是晶格結(jié)構(gòu)。通過基于傅立葉的技術(shù)和涉及泰勒級(jí)數(shù)展開的替代方法（包括在晶格單元格的有限元公式中直接在空間域中執(zhí)行）來進(jìn)行分析。利用各種技術(shù)解決了提高現(xiàn)有均質(zhì)化方法的準(zhǔn)確性和適用范圍的挑戰(zhàn)。其中，引入多細(xì)胞均質(zhì)化以擴(kuò)展方法的良好近似范圍，使其包括短波長(zhǎng)范圍。由均化過程得到的連續(xù)偏微分方程也被用來估計(jì)具有各種內(nèi)部構(gòu)造的晶格的等效機(jī)械性能。尤其是，對(duì)六角形和凹形蜂窩的平面內(nèi)行為進(jìn)行了詳細(xì)的研究，通過應(yīng)用所提出的技術(shù)，可同時(shí)獲得其靜態(tài)特性和波傳播特性。此外，還通過橋接尺度法研究了均質(zhì)介質(zhì)中波傳播的分析，以解決對(duì)具有局部不連續(xù)性的均質(zhì)介質(zhì)中行波建模的問題。這種多尺度方法減少了與在整個(gè)域上進(jìn)行的詳細(xì)有限元分析相關(guān)的計(jì)算成本，并節(jié)省了大量CPU時(shí)間。建議將均質(zhì)化和橋接方法結(jié)合使用，作為快速，準(zhǔn)確的波仿真的有力工具，并討論了其在NDE應(yīng)用中的潛力。

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