Large Deformations Of Piezoelectric Laminated Beams And Plates Based On The Absolute Nodal Coordinate Formulation

Soft robots and intelligent folding structures including large deformations become research hotspots nowadays.Piezoelectric beams and plates can be deformed into many patterns and have potential application prospect in the field of smart foldable structures.The traditional finite element method(FEM)is difficult to accurately describe the motions and deformations of a large deformation structure,but the absolute nodal coordinate formulation(ANCF)is a method suitable for describing large deformations.Knowing the large deformation actuation mechanism of such structures via theoretical modeling is the basis in the soft machine design.In this paper,using the Equivalent Single-layer model,a new flexible piezoelectric laminated beam element and thin plate element based on the Absolute Nodal Coordinate Formulation(ANCF)is established.The constitutive equation of the piezoelectric material is introduced to derive the elastic force and the piezoelectric force.The correctness of the new beam element are validated by comparing with the analytical solution,the results from the equivalent bending moment equation,and the results from the ABAQUS.Research in this work can be helpful to the understanding of complicated coupled nonlinear mechanics of flexible or soft structures with covered smart piezoelectric materials.The main research content is divided into the following aspects:(1)Based on the ANCF,the equations of motion of the two-dimensional laminated beam element and the thin plate laminated element in the three-dimensional space are derived.The laminated beam and plate elements contain three layers.The base layer contains the linear elastic material,and the top and bottom layers both contain the piezoelectric materials;(2)The correctness of the elements proposed in this paper is verified by a series of comparisons.A group of large deformation patterns of the laminated beam and plate are given to prove the applicability of the proposed element.Results show that when various voltages are applied to the piezoelectric actuators that located in arbitrary positions of the base beam and plate,the flexible beam can achieve the desired shape smoothly;(3)Dynamic responses of a highly flexible pendulum with and without piezoelectric layers are investigated,and also dynamic responses of a thin plate with concentrated force.