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

## TL;DR

This paper introduces a new stacking pattern for carbon fiber laminates to achieve more uniform bending stiffness, which is important for precision optical systems.

## Contribution

The paper proposes a new stacking pattern (Pattern III) and a method (NDFBS) to achieve more uniform bending stiffness in laminates.

## Key findings

- Pattern III achieves more uniform bending stiffness faster than existing patterns.
- Theoretical and experimental results confirm improved dimensional stability with Pattern III.
- Pattern III requires fewer cycles to achieve similar uniformity compared to Pattern II.

## Abstract

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 ([(θ1)m/(θ2)m/…/(θp)m]S and [(θ1/θ2/…/θp)m]S) and our proposed new stacking pattern, Pattern III ([(θ1/θ2/…/θp)S]m) based on the initial quasi-isotropic laminates, [θ1/θ2/…/θp]. 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 m 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.