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论文范文
1. Introduction Over the past three decades, deployable structures have been extensively used in space missions because they own the properties of high stiffness, low mass, and small folding volume [1–4]. And with the rapid development of aerospace industry, higher demands for these structures have been proposed. One of the most important is higher deployment accuracy, which is affected by thermal and flexible effects [5]. In order to achieve higher accuracy, the precise deployment dynamics characteristic of deployable structures is essential because it is fundamental to the optimization design [6] and the control process [7]. However, due to the high cost of the imitated space environment on the ground, it is difficult to predict the dynamic capability of these structures by experiment. So some practical methods are developed for dynamic analysis of these flexible structures. The most classical approach is the floating frame of reference formulation [8], but it is deficient in dynamic stiffening and will lead to an imprecise simulation result. To overcome this drawback, Shabana presented a new approach called the absolute nodal coordinate formulation (ANCF) [9], which can satisfy the dynamic stiffening automatically [10, 11] and leads to a constant mass matrix and zero centrifugal and Coriolis forces [12]. Because of these advantages, several beam elements [11, 13–16], plate elements [17], and brick elements [18] applied to analyze various objects of study have been developed within this formulation. A two-dimensional shear beam element proposed by Omar and Shabana [11] to consider the shear deformation effect is among them. However, in a later research, it was found out that this beam element deriving elastic forces on the basis of the nonlinear elastic theory suffers from volumetric Poisson’s locking, thickness locking, and shear locking, which influence the accuracy and computational efficiency of ANCF greatly [19, 20]. In order to avoid the Poisson’s locking, an exact description of elastic forces is presented by Sopanen and Mikkola [21], but the simplest way is setting the Poisson ratio to zero directly. Possible alternatives to solve other locking problems are selective reduced integration [22–24] and the redefinition of elastic forces based on the Hellinger-Reissner principle [20, 25]. |
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