Some atrial contractile assist devices applied on the heart surface can be regarded as a laminated Liquid crystal elastomer (LCE) plate under steady temperature loads and a contact mechanical force. An exact solution for the deformation of the laminated LCE plate under combined thermal and mechanical loads is derived by solving the three-dimensional (3D) equilibrium equations including heat conduction and thermoelastic theory. The validity of mathematical formula and computer programming is proved by convergence and comparison examples with finite element method (FEM). In order to simplify the complex calculation of exact solution, a back propagation neural network (BPNN) is further trained with a database containing 9504 sets of thermo-mechanical load conditions and their corresponding deformation which is solved by the exact solutions. Then the deformations of LCE plate subject to combined thermo-mechanical load can be predicted by this BP neural network instead of complex numerical calculation. Moreover, it is also applied to inverse the contact mechanical force at the bottom surface of LCE plate with a given deformation and temperature conditions. The results show that: (1) The results from the exact theoretical solution are in consistence with that from FEM but have a higher computational efficiency and stability; (2) The deformation of the laminated plate is more sensitive to the layered thickness of LCE than the variation of the temperature; (3) 3-D elasticity solutions of a laminated LCE plate under the combined thermos-mechanical load can be effectively predicted by a trained BP neural network.

@en

This paper presents a convenient and efficient method to predict the mechanical solutions of a laminated Liquid Crystal Elastomers (LCEs) system subjected to combined thermo-mechanical load, based on a back propagation (BP) neural network which is trained by machine learning from a database established by analytical solutions. Firstly, the general solutions of temperature, displacement, and stress of any single layer in the LCEs system are obtained by solving the two-dimensional (2D) governing equations of both heat conduction and thermoelasticity. Then, the unknown coefficients in above general solutions are determined by a transfer-matrix method based on the continuity condition at the interface of adjacent layers and the combined thermo-mechanical loads condition at the surface of the LCEs system. The formula derivation and calculator program are verified through convergence studies and comparisons with FEM results. Finally, a database with displacements of LCEs system in a temperature field subjected to 561 sets of mechanical loads is established based on the presented analytical model. The BP neural network based on above database is further applied to establish the relationship between deformation and mechanical load to predict the elastic deformation of the LCEs system in a temperature field subjected to a mechanical load. Moreover, the BP network can also inverse the coefficients of mechanical load which induces the specific deformation in a temperature field. The numerical examples show that: (1) The deformation of a laminated LCEs system due to thermal load is limited within the range of human temperature changes from 36 °C to 40 °C. (2) The thickness of the LCE is a sensitive parameter on the deformation at the bottom surface of the system. (3) The accuracy of predicted displacements induced by the thermo-mechanical load and the inversed mechanical load based on deformation of the LCEs system in a temperature field using BP neural network reaches 99.6% and 98.5% respectively.@en