Investigation of the Quasi-Homogenous Laminate by Means of the Direction Factor of the Bending Stiffness
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Investigation of the Quasi-Homogenous Laminate by Means of the Direction Factor of the Bending Stiffness Qingnian Liu 1 & Yong Cai 1 & Xiaojing Liu 2 & Zhiyong Yang 1 Received: 8 December 2018 / Accepted: 17 December 2018/ # Springer Nature B.V. 2019
Abstract The direction factor of the bending stiffness was defined in terms of the proportional coefficient of the bending stiffness corresponding to the identical ply orientations, as well as a new iterative mode, cycle after symmetry, of the laminate. On the basis of the quasi-isotropic laminate, the method of the direction factor of bending stiffness considerably reduces the computational capacity with respect to the quasi-homogeneity. By means of the method of the direction factor and comparison of the direction factors corresponding to three kinds of laminates, the iterative mode of cycle after symmetry has superior performance than the common iterative modes, which is applicable to the design and optimization of the laminate, especially for the homogeneous laminate. Keywords CFRP. Equivalent bending stiffness . Direction factor of the bending stiffness . Quasiisotropic laminate . Quasi-homogeneity laminate . Iterative mode
1 Introduction Compared with the traditional materials, carbon fiber reinforced plastics (CFRP) provide distinct advantages, such as, high specific modulus and strength, low density, near-zero thermal expansion properties, which have been widely used in the fields of aircraft, space, medical devices, sporting goods [1–3]. Unidirectional CFRP is anisotropic, however, it could be designed to satisfy the specify load or stiffness requirement for a given range of applications [4–6]. Quasi-isotropic layups, such as [0/±60] S and [0/±45/90]S, have the identical extensional stiffness, but their bending stiffness are still anisotropic [7–9]. Meanwhile, since the thermal steady is very significant with
* Qingnian Liu [email protected]
1
Aerospace Research Institute of Materials & Processing Technology, Beijing 100076, China
2
Institute of High Energy Physics, Chinese Academy of sciences, Beijing 100049, China
Applied Composite Materials
respect to the space mirror, which will be frequently subjected to hydrothermal effect during the employment, there is an urgent need for a quasi-homogeneous laminate, namely the bending stiffness are nearly equivalent in any direction, which is usually defined based on the quasi-isotropic layup sequence [3–5, 9–12]. For the sake of achieving the required the layup sequence, many researchers carried out several investigation usually depending on a symmetric and balance laminate or Werren and Norris rule, namely the same plies aligned along n directions with the orientation angles difference by π/n [7, 13]. By means of weight factors, Wu gained several the fully isotropic laminates which there are 36 plies at least [14]. The method regularization stiffness coefficient or the method of regularization geometric factors were also proposed to search for the laminates close to quasi-isotropic [15, 16]. Fukunaga and
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