A variational asymptotic methodology of smart slender structure modeling.

摘要

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.