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Structures with adaptive capabilities offer many potentials to achieve future needs in efficiency, reliability, and intelligence. To this end, bistable CFRP (Carbon Fibre Reinforced Polymers) composites with asymmetric fiber layout are a promising concept that has shown shape morphing capabilities that adapt to the changes in the environment such as external forces and moments. This adaptability opens them to endless application potentials, ranging from small micro-switches to large airfoil sections in airplane wings or wind turbine blades. To harness this potential, it is essential to predict these composites’ physical shapes and behavior accurately. To this end, Hyer and Dano devised the first analytical model based on the concepts of Classical Lamination Theory, and this model has become the cornerstone of almost all subsequent studies. However, this theory uses Kirchoff’s theory of thin plates that are limited by several assumptions. As a result, Hyer’s theory can predict the overall shape of these laminates but lacks accuracy. A reason for this model’s underperformance is that it ignores the inter-laminar stresses and strains, but such stresses/strains play a vital role in the balance of the overall stress field and are found significantly higher near the free edges. To overcome these fundamental limitations, we propose a new analytical approach by combining the Reissner-Mindlin theory with concepts from the Classical Lamination Theory. This new model introduces in-plane rotations as two additional degrees of freedom. Thus, it has five independent variables compared to only three in Hyer and Dano’s model and its derivatives. Hence, we have a more complex but more accurate model. This paper outlines our new analytical approach by 1) introducing these two additional degrees of freedom; 2) selecting appropriate polynomial approximations; 3) formulating inter-laminar stresses that are functions of these added rotations; and 4) incorporating these inter-laminar stresses in the potential energy equation. By comparing this model’s prediction with the finite element simulation results, we found the new model slightly under predicts the laminate deformation, but the overall accuracy is promising, as evidenced by high R-squared correlation. 

Thin bistable composite laminates can be used for shape morphing applications by virtue of their material properties and asymmetric ply layup. These laminates are called bistable because they can be snapped into two or more stable shapes. A single bistable patch can result in simple cylindrical shapes and when multiple such patches are assembled into a single multi-patch laminate they result in more complex shapes and multiple stable shapes that can find wide practical use in shape morphing applications. Analytical models exist that can approximate the stable shapes of the laminates from the input of material properties and laminate geometry. And these models correlate with FEA and experiment to a satisfactory degree and could be used for the design of multi patch laminates. In this research, we make use of these analytical models that solve for a four-patch grid laminate and create a design method based on optimization to solve the reverse problem to arrive at the laminate parameters given the target shape(s). Two approaches are presented wherein one targets a single stable shape and the other targets two stable shapes which are the shapes before and after snap through. This work would be useful to understand how multi-patch laminates could be designed using optimization.