Research On Isogeometric Analysis Algorithm Of Axially Polarized Piezoelectric Beam

With the development of intelligent driving and Internet of Vehicles technology,sensors have been widely used in automobile and other industrial fields.Sensitive materials play the role of signal conversion in sensors,which is the key factor to determine the performance of sensors.Piezoelectric beam has the characteristic of high sensitivity,which shows unique advantages in pressure,accelerometer and other signal measurement.In order to analyze the signal conversion process of the piezoelectric beam,it is necessary to calculate the deformation and electric potential of the piezoelectric beam under the coupling action of force field and electric field.Therefore,this paper studies the electromechanical coupling analysis model of axially polarized piezoelectric beam,and proposes an simulation algorithm of isogeometric analysis for piezoelectric beams with high computational efficiency and better accuracy.The main research contents of this paper include:1.The electromechanical coupling simulation model of piezoelectric beam structure based on beam theory is established.The electric enthalpy equation of three dimensional solid piezoelectric materials is simplified by using the constitutive model characteristics of common piezoelectric materials.The displacement and strain fields of piezoelectric beam are described by Euler and Timoshenko beam theory,and the simulation of piezoelectric materials is simplified from three-dimensional solid problem to one-dimensional beam problem.Based on the characteristics of the electric potential distribution of the piezoelectric beam structure,the quadratic polynomial distribution assumption of the electric potential on the cross section of the piezoelectric beam is proposed.The material parameters of piezoelectric beam were modified by the stress hypothesis to improve the calculation accuracy of the piezoelectric beam electromechanical coupling model based on beam theory.2.A simulation algorithm of piezoelectric beam electromechanical coupling based on isogeometric analysis is proposed.The displacement and potential of the piezoelectric beam were described by the B-spline basis function using the isogeometric analysis method to improve the calculation accuracy of the simulation model.The singularity problem of piezoelectric beam stiffness array is solved by using parameter order correction method.The simulation program of piezoelectric beam electromechanical coupling was programmed based on C++ language.3.Some important piezoelectric beam structures such as PZT-5H and ZnO nanobeams were simulated.The algorithm and program of this paper were used to calculate the deformation and potential of the piezoelectric beam under stretching and bending conditions.The effect of slenderness ratio and parameters of piezoelectric materials on potential were studied.The mechanical and electrical coupling deformation characteristics of piezoelectric beam are summarized.Commercial simulation software COMSOL is used to conduct comparative tests to verify the accuracy of the proposed algorithm.In this paper,based on the beam theory and the electromechanical coupling model of piezoelectric materials,a simulation analysis model for axial polarized piezoelectric beam structures is proposed.In this paper,the simulation model of piezoelectric beam is simplified from a threedimensional solid problem to a one-dimensional beam problem,which greatly reduces the computational cost.By introducing the stress hypothesis and using the isogeometric analysis model,the calculation accuracy of the proposed model is guaranteed.