A study on design and realization of layered bistable shell structures with arbitrary shape

Abstract

In this dissertation, the numerical analysis model and design technique of plate and shell is proposed based on the Gausss Theorema Egregium, in order to materialize the bistable shell structure with arbitrary shape. The classical bistable plate and shell structure is limited to the cylindrical shape. Besides which, the curvature value of cylindrical shape does not change independently without changing the thickness and material locally. The morphological limitation is blocking progress in the application research on the bistable plate and shell structure. In summary, this problem is categorized into two main engineering issue: how to change the cylindrical curvature value of classical bistable structure? and how to induce the bistable structure with non-cylindrical shape?. In order to address this problem, firstly, curvature tailoring technique of classical bistable shell structure is suggested by using the initially curved tool-plate. The suggested method is verified by Rayleigh-Ritz analysis and experiment. Secondly, second-generation technique which inducing bistable structure with arbitrary shape is proposed based on the Gausss Theorema Egregium. The suggested method is also verified numerically and experimentally. Specifically, the second-generation technique, which inducing bistable structure with arbitrary shape, is motivated from the geometrical characteristic that shear deformation does not occur in the case of transformation between two isometric surfaces. Based on this geometrical characteristic, the realization method of bistable shell structure with arbitrary shape is suggested through face-to-face perfect bonding of two non-developable surfaces. In the analysis of bistable structure in order to handle the above issue, various efficient and accurate numerical models are developed. Firstly, the classical bistable structure analysis model is mostly based on displacement field in order to build up the total potential energy. However, the total potential energy is not explicitly expressed by displacement field. For this reason, the analysis from the model based on the displacement field is not efficient. In order to address this problem, the new analysis model is proposed, which is combining the approximated implicit strain field and the compatibility equation. The efficiency and accuracy of the suggested model is validated, by comparing with the result obtained by FE analysis. Secondly, the classical bistable structure analysis model is mostly based on the plate theory due to the limitation of numerical derivative precision and the complexity of calculation, although the deformed curvature of bistable plate and shell is large. In this dissertation, however, in order to obtain the accurate solution, the bistable structure analysis model is developed based on the shell theory. In the development of corresponding shell model, the limitation problem of numerical derivative precision and the complexity of calculation are addressed by utilizing the matrix derivative method. As a result, the analysis of bistable plate and shell has become so accurately and so easily. Finally, for the practical application of the bistable shell structure, the effect of initial shape of bistable shell structure on the snap-through load is studied. Based on the snap-through load obtained from numerical analysis, the Shape memory alloy spring is suggested as actuator. At first, specification of SMA spring is suggested. The performance of SMA spring is simulated by FE analysis where the constitutive model of shape memory alloy is implemented based on the Lagoudas model. Then, for the verification of snap-through by means of SMA spring, snap-through FE analysis of the bistable structure with SMA spring is performed. From this FE analysis, it is verified that the snap-through of bistable shell structure is well induced when SMA spring is utilized as actuator. The morphological design technique and model of bistable plate and shell structure, which are developed and verified in the dissertation, overcome the morphological limitation of the existing bistable structure and improve the design degree freedom of it. If the improved design degree freedom and the bistability is applied into the classic mechanical system which have been focus on the mechanical property (i.e. strength or mass), the new mechanical system accompanied by the concept of morphing can be designed and expected as the high value-added system breaking stereotype.