Abstract:SUMMARYIn the numerical analysis of 2‒D bimodular materials, strain discontinuity is problematic, and the traditional iterative algorithm is frequently unstable. This paper develops a stable algorithm for the large‒displacement and small‒strain analyses of 2‒D bimodular materials and structures. Geometrically nonlinear formulations are based on the co‒rotational approach. Using the parametric variational principle (PVP), a unified constitutive equation is created to resolve the problem induced by strain discon… Show more
Wrinkling, a common phenomenon found in space membrane structures, is the main factor affecting the performance, stability, and dynamic characteristics of these membrane structures. This article presents an active control method to improve the surface accuracy of membrane structures. A model of a thin rectangular membrane subjects to uniaxial uniform tensile stress is discussed. Initially, the relationship between the out-of-plane deformation of the wrinkles and the boundary conditions is built with the Föppl–Von Karman plate theory by introducing the slow varying Fourier series. Because vertical tensions perpendicular to the direction of the initial wrinkles are necessary to reduce these wrinkles, reasonable locations and magnitudes of these tensions are the key problems. The finite element method and variational principle method are used to solve this issue. Finally, a manufacturing error is added to the model as an initial defect, and the robustness of the controller is verified. Simulation results show that wrinkles are reduced quickly and effectively with the proposed method.
Wrinkling, a common phenomenon found in space membrane structures, is the main factor affecting the performance, stability, and dynamic characteristics of these membrane structures. This article presents an active control method to improve the surface accuracy of membrane structures. A model of a thin rectangular membrane subjects to uniaxial uniform tensile stress is discussed. Initially, the relationship between the out-of-plane deformation of the wrinkles and the boundary conditions is built with the Föppl–Von Karman plate theory by introducing the slow varying Fourier series. Because vertical tensions perpendicular to the direction of the initial wrinkles are necessary to reduce these wrinkles, reasonable locations and magnitudes of these tensions are the key problems. The finite element method and variational principle method are used to solve this issue. Finally, a manufacturing error is added to the model as an initial defect, and the robustness of the controller is verified. Simulation results show that wrinkles are reduced quickly and effectively with the proposed method.
“…Jenkins and Leonard [4] proposed a membrane model by introducing a relaxed energy density. Stein developed the viable Poisson's ratio method [5], which is extended by Ding and Yang [6] and Zhang et al [7]. A viable Poisson's ratio and a viable Young's modulus are introduced to modify the constitutive relation.…”
Wrinkles always produce to counteract the compressive stress in the thin membrane structures, which has become a popular topic. In this paper, for the inhomogeneous membrane structure with depth-dependent Young’s modulus, a power-law index is introduced. The effect of inhomogeneity on the displacement and stress fields is analyzed. On this foundation, the membrane structures with uniform normal tension loadings are studied to be accorded with practical cases of engineering application. The stress fields are derived by the superposition of the concentrated tension solution based on the Airy stress superposition theory. Compressive stress generally leads to wrinkling, then the wrinkle regions under different tension conditions are predicted accurately. The proposed stress model is simple, and the computation complexity is reduced without using a finite element solution.
“…Different methods of analyzing the stress fields of membrane structures have been proposed; Wong and Pellegrino 4,5 studied the in-plane stress field in a square membrane with discrete forces applied on the membrane vertices and found that the stress field comprises identical corner regions under purely radial stress and a central region under uniform biaxial stress, with wrinkles appearing within the uniaxial stress regions. Zhang and colleagues 6,7 proposed a membrane model with viable Young’s modulus and Poisson’s ratio, and then adopted parametric finite element discretization and a smoothing Newton method to obtain a numerical solution. The finite element method 8,9 has been widely adopted; however, its use readily leads to divergent results.…”
Maintaining surface accuracy is crucial to realizing the required performance of membrane structure. However, compressive stress inevitably leads to wrinkling, and the accurate analysis of the stresses becomes significant. The present study analyzed membrane structures with discrete loads. First, a simple method was proposed and the stress field was accurately described using an Airy stress model. The first and second principal stresses were obtained, and regions of wrinkling with negative stress were predicted. Second, for a square membrane structure, vertical tensions around the boundary were applied such that in-plane stresses were more evenly distributed. Finally, to reduce the wrinkling areas more effectively, an arc-edge structure was designed by removing some areas of low-stress. Simulation results showed that the in-plane stress field distribution was described accurately and the wrinkling regions were diminished effectively with the proposed method.
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