Investigation of a New Stacking Pattern of Laminates with Approximately Constant Bending Stiffness

To achieve laminates with constant bending stiffness to match the high precision requirement of optical systems made of carbon fiber reinforced plastic (CFRP), a new method, the normalized direction factor of bending stiffness (NDFBS), is proposed based on the normalized geometric factor of bending stiffness. Using NDFBS and its variance (VNDFBS), we investigate two common stacking patterns, I and II ([(<i>θ</i>₁)<i>_m</i>/(<i>θ</i>₂)<i>_m</i>/…/(<i>θ_p</i>)<i>_m</i>]_S and [(<i>θ</i>₁/<i>θ</i>₂/…/<i>θ_p</i>)<i>_m</i>]_S) and our proposed new stacking pattern, Pattern III ([(<i>θ</i>₁/<i>θ</i>₂/…/<i>θ_p</i>)_S]<i>_m</i>) based on the initial quasi-isotropic laminates, [<i>θ</i>₁/<i>θ</i>₂/…/<i>θ_p</i>]. The bending stiffness of the stacking sequence [(45/-45/0/90)_S]₂ tends to be more uniform than that of [45/-45/0/90]_2S, and the order of uniformity in bending stiffness of other stacking sequences is [(60/0/-60)_S]₄ > [60/0/-60]_4S > [(60/0/-60)_S]₂ > [60/0/-60]_2S. Both theoretical deviations and experimental observations confirm that as the cycle number <i>m</i> increased, the uniformity in bending stiffness is improved gradually, except for that of Pattern I. As the cycle number increased, the speed of Pattern III approaching the constant bending stiffness was faster than that of Patterns I and II_. Notably, to achieve a nearly identical uniformity in bending stiffness, only the square root of the cycle number of Pattern II was enough for Pattern III. Based on the same initial laminate and cycle number, Pattern III exhibited more uniform bending stiffness and strength, which are appropriate for precision optical components that require dimensional stability, such as space mirrors.