A New Method For Solving The Thermo Mechanical Problems Of Piezoelectric Materials Based On Element Differential Method

Piezoelectric materials are widely used in aerospace and other fields due to their positive and negative piezoelectric effects.In the design of intelligent deformable wing,piezoelectric material can be used as a driver to realize the change of airfoil camber,and realize the airfoil adjustment,torsion and other functions.At the same time,piezoelectric material can be used as a sensor to convert the change of airfoil shape into electrical signal output detection.On the other hand,the anisotropic characteristics of materials and the complex environment of multi physical field coupling need to be considered in the engineering application of piezoelectric materials,which makes the simulation analysis and experimental verification of its mechanical properties face challenges.In order to better simulate and analyze the mechanical properties of piezoelectric materials under various loads,a new numerical simulation method for multi field coupling behavior analysis of piezoelectric intelligent materials is studied in this paper.Firstly,the element differential method is established to analyze the electromechanical coupling behavior of piezoelectric materials and structures.Firstly,the finite element isoparametric element technique is used to discretize the piezoelectric structure.The spatial partial derivatives of displacement and potential are derived by isoparametric element,and the first two partial derivatives of shape function to global coordinates are derived analytically.On this basis,by making the nodes inside the element satisfy the piezoelectric control equations and satisfying the balance conditions of traction force and charge and boundary conditions on the other nodes of the element,the system equations for solving the force electric coupling problem are constructed.The proposed method is similar to the strong form collocation method in that it does not need to integrate the equations in the element domain,which simplifies the calculation process.The numerical results of piezoelectric structures with different material properties show that the proposed method has high accuracy and efficiency.Secondly,the element differential method is proposed for the thermo mechanical electrical coupling behavior of piezoelectric materials and structures.Lagrange isoparametric element is used to complete the discretization.By interpolating temperature,displacement and electric potential,the isoparametric element of shape function and its first two derivatives are derived analytically.By placing the piezoelectric governing equations on the inner nodes of the element and satisfying the equilibrium conditions of traction force and charge and the prescribed boundary conditions on the other nodes of the element,the system equations of heat conduction and thermoelectric coupling problems for the analysis of thermopiezoelectric materials are constructed respectively.In the latter,the thermal expansion coefficient and pyroelectric coefficient in the constitutive equation can be replaced by the thermal stress coefficient in the governing equation,and the system equations can be directly established by using the temperature difference in the governing equation of the element differential method,which greatly reduces the processing complexity of the thermo electric coupling problem of piezoelectric structures.A numerical example is given to analyze the thermo electric coupling response of piezoelectric composite structures.The results show that the proposed method has high accuracy and reliability in dealing with the thermo electric coupling problem of piezoelectric structures.Finally,the mechanical response analysis of the piezoelectric material and structure of the deformable wing is carried out by using the element differential method.In order to solve the problem of orthotropic characteristics of piezoelectric materials in the design of deformable wing,the physical property conversion parameter module is developed in the element differential method,which realizes the conversion of Young’s modulus and stiffness coefficient,and further realizes the conversion of piezoelectric stress constant and piezoelectric strain constant.On this basis,the mechanical and electrical coupling response of the smart wing skin with a contraction type piezoelectric patch is simulated and analyzed,and the mechanical and electrical coupling problem of the wing skin with an extension type piezoelectric patch is further analyzed.The numerical results show that the element differential method proposed in this paper can be used to solve the anisotropic problems of piezoelectric materials and structures,and has a good engineering application prospect.