Uncertainty Quantification And Multi-scale Analysis Of Mechanical Properties Of Piezoelectric Structure Based On IGA-FEM

Piezoelectric ceramics have been widely used in the fields of medical imaging,acoustic sensors,and engineering monitoring due to their fast electromechanical response,high piezoelectric coupling performance,and ease of preparation.However,the inhomogeneous of green body density of piezoelectric ceramic can lead to small changes in the mechanical property parameters of piezoelectric ceramic,which can influence the mechanical properties of piezoelectric ceramic.Therefore,it is necessary to quantify the uncertainties in the parameters of the piezoelectric ceramic and perform modeling and mechanical properties analysis on macroscopic and microscopic scales to accurately predict the mechanical properties of the piezoelectric ceramic.In this paper,the statistical characteristics of the electric potential of piezoelectric ceramic structure are computed using the isogeometric finite element method and the generalized nth-order perturbation method.The efficiency of the IGA-FEM-GNP is also studied by comparing the statistical characteristics of the electric potential obtained through other uncertainty quantification methods.IGA-FEM and Monte Carlo simulation(MCs)are used to study the important material parameters influence the natural frequencies in the uncertainty quantification of piezoelectric ceramic structure.In addition,the mechanical properties of piezoelectric composite structure under different loading conditions are studied based on the direct FE~2method.The main contents of the paper are as follows:(1)Based on IGA-FEM-GNP method,the statistical characteristics(expected value and standard deviation)of piezoelectric ceramic structure electric potential under two random input parameters(elastic constant and piezoelectric constant)and two sets of coefficient of variation are computed,and compared with the statistical characteristics of electric potential computed by MCs and polynomial chaos expansion(PCE).The results show that the IGA-FEM-GNP method only takes 1second to calculate the statistical characteristics of the electric potential,which is much faster than the MCs and PCE methods.(2)Based on the IGA-FEM method,numerical simulations of different piezoelectric ceramic structures are performed to study the influence of piezoelectric effect on the displacement modes and natural frequencies of the structures.The statistical characteristics of the natural frequencies are calculated using the MCs method.Finally,the elastic constants are determined to be important material parameters influence the natural frequencies of the piezoelectric ceramic structures.(3)Based on the Direct FE~2method,the Mises stress of piezoelectric ceramic composite structures under tensile,compressive and electric potential loading are studied and compared with the Mises stress obtained from Direct Numerical Simulation(DNS).The results show that the Direct FE~2method can improve the computational efficiency of numerical simulations of piezoelectric ceramic composite structures.