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A variational asymptotic methodology of smart slender structure modeling.

機譯：智能細(xì)長結(jié)構(gòu)建模的變分漸近方法。

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The present research is an attempt to develop a one-dimensional model for electro-mechanical slender structure by application of the Variational Asymptotic Method. A coupled electro-mechanical analysis methodology for beam-like slender structure has been developed by a two-step procedure of dimensional reduction. First, the 3D governing variational statement for an electro-mechanical system has been approximated asymptotically, followed by a cross-sectional minimization on the approximated functional. Depending on the type of electrode arrangements the whole problem has been classified into two separate categories: Axial-problem and Radial-problem. If the end surfaces of a slender structure are partially or fully electroded, then it is classified as an Axial-problem and if the lateral surfaces of a slender structure is partially or fully electroded, then it is classified as a Radial-problem. For an Axial-problem, externally given electric potential comes as boundary conditions during the one-dimensional beam analysis and for a Radial-problem it comes as constraints during the cross-sectional minimization process. For the type of electrode arrangements present in an Axial-problem, the classical cross-sectional model of one-dimensional electro-mechanical structure is of dimension 5 x 5 and has one extra electrical degree of freedom along with four mechanical degrees of freedom. For the refined theory, a Timoshenko like model has been developed by taking into consideration two extra shear strain measures, giving a 7 x 7 electro-mechanical stiffness matrix as the cross-sectional model. For a Radial-problem type electrode arrangement, the classical one-dimensional electro-mechanical cross-sectional model is contributed by a 4 x 4 stiffness matrix and a 4 x I actuating force vector. In the refined theory, we get a 6 x 6 stiffness matrix and a 6 x 1 actuating force vector.; The last part of the work is devoted to developing a simplified thin-walled model for getting initial design parameters for pre-twisted and pre-curved thin-walled structures with or without active inclusion in it. Considering the mechanical influence of the constituent material a classical type cross-sectional model for thin-walled structures with open or closed cross-sections has been developed. The structural coupling effects arising due to the presence of pre-twist and pre-curvature have been captured for open as well as closed sections.
機譯：本研究是通過應(yīng)用變分漸近方法開發(fā)機電細(xì)長結(jié)構(gòu)的一維模型的嘗試。通過減少尺寸的兩步程序，開發(fā)了一種用于梁狀細(xì)長結(jié)構(gòu)的耦合機電分析方法。首先，已漸近地近似了機電系統(tǒng)的3D控制變化陳述，然后在近似函數(shù)上最小化了橫截面。根據(jù)電極布置的類型，整個問題已分為兩類：軸向問題和徑向問題。如果細(xì)長結(jié)構(gòu)的端面被部分或完全電極化，則將其分類為“軸向”問題，如果細(xì)長結(jié)構(gòu)的側(cè)面被部分或全部電極化，則將其分類為“徑向”問題。對于軸向問題，在一維束分析過程中，外部給定的電位作為邊界條件；對于徑向問題，在橫截面最小化過程中，其作為約束條件。對于存在于軸向問題中的電極布置類型，一維機電結(jié)構(gòu)的經(jīng)典橫截面模型的尺寸為5 x 5，并具有一個額外的電氣自由度以及四個機械自由度。對于改進(jìn)的理論，已經(jīng)通過考慮兩個額外的剪切應(yīng)變措施開發(fā)了類似Timoshenko的模型，給出了7 x 7的機電剛度矩陣作為橫截面模型。對于徑向問題型電極布置，經(jīng)典的一維機電橫截面模型由4 x 4剛度矩陣和4 x I驅(qū)動力矢量貢獻(xiàn)。在改進(jìn)的理論中，我們得到6 x 6的剛度矩陣和6 x 1的致動力矢量。工作的最后一部分致力于開發(fā)簡化的薄壁模型，以獲取預(yù)扭曲和預(yù)彎曲的薄壁結(jié)??構(gòu)的初始設(shè)計參數(shù)，其中可以包含或不包含主動包含在內(nèi)?？紤]到構(gòu)成材料的機械影響，已開發(fā)出具有開放或封閉橫截面的薄壁結(jié)構(gòu)的經(jīng)典橫截面模型。由于存在預(yù)扭曲和預(yù)曲率而產(chǎn)生的結(jié)構(gòu)耦合效應(yīng)已針對開放和封閉截面進(jìn)行了捕獲。

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