Dynamic Behaviors Of Composite Structure With Piezoelectric Actuators Via Absolute Nodal Coordinate Formulation

Soft robots have been widely applied in complex and natural environment due to their remarkable features such as flexibility,large deformability and strong adaptability.The actuation applied on soft robots are usually formed by composite structures,which are combined with hard actuating material and flexible medium.The geometrical and material nonlinearity features make it difficult to describe accurately the large deformation during the motion of the composite flexible structure with traditional finite element methods.Meanwhile,the accurate modelling of the composite structure becomes complicated considering the multi-element coupling with the actuators.Therefore,the dynamic modelling of the composite flexible structure is of great importance to the motion control and dynamic analysis for soft robots.Aiming at the accurate modelling of the composite flexible structure under piezoelectric actuation,plate and beam elements are introduced based on absolute nodal coordinate formulation(ANCF)for the accurate description of deformation of the flexible structure with nonlinear features.The deformation compatibility conditions at the interface of the elements are proposed to establish the composite multi-element model and derive the dynamic equations for the composite structure.Piezoelectric actuator is involved to investigate the dynamic behaviors of the composite flexible structure under piezoelectric actuation with various parameters.The dynamic analysis results may provide guidance for the dynamic modelling and actuation design for soft robots.The main contents are as below:(1)Dynamic modelling for the composite structure based on ANCFComposite beam-plate element model with C~1 continuity condition is established based on the deformation compatibility conditions with ANCF plate and beam elements.Mooney-Rivlin hyperelastic constitutive model and the piezoelectric material constitutive equations are introduced into the elements,and the stiffness matrices,the mass matrices,the electric force matrix and the generalized external force matrix are derived to establish the dynamic equation of the composite structure with piezoelectric actuators.(2)Effects of various parameters on the dynamic behaviors of the composite structure under piezoelectric actuationThe dynamic behaviors of the composite flexible structure under piezoelectric actuation are studied through a number of numerical examples by using MATLAB software.Voltages and material parameters are changed to investigate their influence on the vibration motion and the deformation forms of the composite structure.Results show that the deformation of the composite structure increases with the increase of applied voltage,and decreases nonlinearly with the increase of elastic modulus.(3)Study on the performance of the piezoelectric actuation with various actuation modesComposite structure with dual piezoelectric beam actuators is modelled based on deformation compatibility conditions across elements.The dynamic behaviors of Hookean plate structure and Mooney-Rivlin hyperelastic plate structure under various actuation modes are studied,and the actuation performances with single piezo-actuator and dual piezo-actuators are compared.