Developing Equations for Free Vibration Parameters of Bistable Composite Plates Using Multi-Objective Genetic Programming

Abstract

For the last three decades, bistable composite laminates have gained publicity because of their outstanding features, including having two stable shapes and the ability to change these states. A common challenge regarding the analysis of these structures is the high computational cost of existing analytical methods to estimate their natural frequencies. In the current paper, a new methodology combining the Finite Element Method (FEM) and Multi-Objective Genetic Programming (MOGP) is proposed for the analysis of bistable composite structures, leading to some analytical relations derived to obtain the modal parameters of the shells. To achieve this aim, the data extracted from FEM, consisting of the ratio of the length to width (a/b) and the thickness (t) of the laminate, is split into Train and Validation, and Test, subsets. The former is used in MOGP, and four formulas are proposed for the prediction of the free vibration parameters of bistable laminates. The formulas are checked against the Test subset, and the statistical indices are calculated. An excellent performance is observed for all GP formulas, which indicates the reliability and accuracy of the predictions of these models. Parametric studies and sensitivity analyses are conducted to interpret the trend of input parameters in the GP models and the level of sensitivity of each natural frequency formula to the input parameters. These explicit mathematical expressions can be extended to the other bistable laminates to obtain their natural frequencies on the basis of their geometrical dimensions. The results are validated against the experimental data and verified against FEM outcomes.

Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates

“…In the 'Force' module, the boundary conditions of the laminate are defined, where the laminate is fixed at the centre. We can simulate the manufacturing process using the 'Predefined Field' option in this module by choosing 165 • C and 25 • C for the curing and room temperatures, respectively [5,11].…”

“…Bistable composite laminates not only exhibit two stable shapes but can also switch their shapes between these states in response to appropriate loads. These outstanding features lead to their employment in a range of applications, including energy harvesting [1,2], soft robots [3], and other structures [4][5][6][7][8][9]. The bistability of unsymmetric laminates is a result of the residual thermal stresses generated from the inequality of the thermal expansion coefficients in each ply which are produced during the curing process [10].…”