A modified shape function for calculating stable configurations and natural frequencies of bi-stable [0/90]T composite laminates

In this paper, thermal and vibration response of cross-ply bi-stable composite laminated plates were studied using semi-analytical, finite element and experimental method. In order to evaluate the semi-analytical and finite element results, a bi-stable composite plate was manufactured using a special procedure. Next, geometrical characteristics and displacement of different paths on the plate were measured experimentally at room temperature. In semi-analytical approach, the two stable states and the first natural frequency of cross-ply laminates are calculated based on Rayleigh–Ritz approach combined with Hamilton’s principle. In this study, a modified shape function was introduced that allows the curvatures to vary in both longitudinal and transverse directions. Using the modified shape function, the displacement of the plate in its stable configuration and the first natural frequency of the plate can be more accurately predicted in compared to the Hyer’s shape functions. The obtained results from the proposed shape function are in good agreement with the finite element and experimental data. The proposed shape functions can also be used in dynamic and vibration analysis to determine the snap-through load of the cross-ply laminates.