| As a new type of functional material,the application areas of piezoelectric materials affect all aspects of the national economy,such as medical imaging,electronic appliances,aerospace,communications,national defense and military industry.Nowadays,piezoelectric materials are widely used in sensors,captors,transformers,actuators,transducers and other piezoelectric intelligent components.During the service of piezoelectric intelligent structures,the working condition of the structures are often complex and changeable,and the mechanical properties are significantly affected by the change of temperature and humidity,and the mechanical,electricity,humidity and heat multi-field coupling effect directly determines the mechanical characteristics,safety and reliability of the piezoelectric intelligent structure.In order to improve the mechanical performance of piezoelectric structures under the mechanic-electro-hygro-thermal coupled field,it has become one of the current research hotspots at home and abroad to carry out research on the mechanical properties of piezoelectric material structures under the hygrothermal environment,which provides the theoretical basis for the design,development,application and evaluation of piezoelectric intelligent structures.At present,there are mainly experimental,analytical and numerical methods for solving this problem.The experimental method is limited by the experimental conditions,experimental cost and experimental period,and the analytical method can only solve some simple problems and has a small scope of application.And numerical methods have become a necessary tool for studying various multi-field coupled problems.Thus,to analyze the mechanical properties of piezoelectric materials in the complex hygrothermal environment and to further improve the performance of piezoelectric smart devices,a reliable and effective numerical method is urgently needed to investigate the mechanical properties of piezoelectric materials under the multi-field coupling effect.Finite element method(FEM),based on the weak form,is the most mature numerical method.And it has been widely used in various engineering practical problems and various commercial software.However,it still has some shortcomings in solving problems,such as,‘over-stiffness’of structural stiffness matrix and being sensitive to mesh distortion,leading to a small displacement solution and inaccurate stress solution.In addition,generating high quality of the mesh significantly increases the pre-processing workload and raises computational costs.To improve the accuracy of FEM,based on the G-space theory and the weakened weak(W~2)form formulas,combined with the smoothed radial point interpolation method(S-RPIM)and the stabilized terms obtained from generalized strain gradient,the mechanic-electric/mechanic-electro-thermal/mechanic-electro-hygro/mechanic-electro-hygro-thermal coupled stable node-based S-RPIM(SNS-RPIM)is proposed and used to solve the mechanical properties of piezoelectric structures under the coupling of mechanical,electric,moisture and thermal fields in the node-based smooth domain in this paper,which has high accuracy and good stability.The main work of this paper is as follows:Firstly,according to the basic equations and boundary conditions of the piezoelectric material structure,using G-space theory and W~2 form,the mechanic-electric coupled stable node-based S-RPIM is proposed in the node-based smoothed domain by constructing stable terms obtained from the generalized strain gradient.And this stable node integration algorithm cures the‘over-stiffness’of FEM and the‘over-soft’property of the node-based integral model.By calculating and analyzing typical piezoelectric structures,the correctness and high accuracy of the method are verified by comparing the obtained calculation results with the exact solution.Secondly,based on the thermodynamic theory,the constitutive equations of piezoelectric materials in the steady-state thermal environment are derived.Combined with the basic equations and the stable node integration algorithm,the mechanic-electro-thermal coupled stable node-based S-RPIM is proposed and the static and dynamic computational models of piezoelectric material structure under steady-state thermal environment are constructed.The mechanic-electro-thermal coupled transient response problem of a typical piezoelectric material structure is solved by using the degree of freedom coalescence method and the Newmark method.And the eigenvalue problem of the structure is analyzed by applying the subspace iterative method,and the mechanical properties of the piezoelectric material structure under the steady-state thermal environment are studied.Thirdly,considering the mechanic-electro-hygro multi-field coupled effect of piezoelectric structure in humid environment,the constitutive equations are derived.And based on the generalized equilibrium equations,generalized geometric equations and boundary conditions of piezoelectric materials,the mechanic-electro-hygro coupled stable node-based S-RPIM is proposed with stable node integration algorithm.Through typical numerical cases,the static and dynamic problems of piezoelectric structures in humid environment are investigated to verify its correctness in analyzing the mechanic-electro-hygro coupled problems of piezoelectric structures and analyze the effects of different humidity variations on the mechanical properties of the structures.Fourthly,considering the mechanic-electro-hygro-thermal multi-field coupled effect of piezoelectric structure,and combining the thermodynamic theory,the fundamental equations of piezoelectric materials and the mechanic-electric coupled stable node-based S-RPIM,the mechanic-electro-hygro-thermal coupled stable node-based S-RPIM is proposed.The computational model of piezoelectric structures under coupled mechanic-electro-hygro-thermal fields is established and the static problem of piezoelectric structures is solved.And the dynamic problems of piezoelectric structures under the hygrothermal conditions are solved by using the degree of freedom coalescence method,subspace iteration method and Newmark method.And the effects of different factors on the mechanical properties of piezoelectric structures are analyzed.Finally,for the mechanic-electro-hygro-thermal multi-field coupled problem of functionally graded piezoelectric material structure,the inhomogeneous mechanic-electro-hygro-thermal coupled stable node-based S-RPIM is proposed by introducing the non-homogeneous properties of materials into mechanic-electro-hygro-thermal coupled stable node-based S-RPIM.And the analytical model of functionally graded piezoelectric structure under hygrothermal coupled field is constructed.The static and dynamic problems of the functional graded piezoelectric structure under hygrothermal conditions are analyzed,and the high accuracy of the method in calculating the inhomogeneous mechanic-electro-hygro-thermal multi-field coupled problem is verified,and the effects of different factors on the mechanical properties of the mechanic-electro-hygro-thermal multi-field coupled of the inhomogeneous piezoelectric structure are further investigated.In summary,the multi-physical field coupled stable node-based S-RPIM has accurate and reliable calculation results in analyzing the mechanic-electro-hygro-thermal multi-field coupled problem of piezoelectric structures,and can effectively analyze the mechanical properties of piezoelectric structures under the mechanic-electric/mechanic-electro-thermal/mechanic-electro-hygro/mechanic-electro-hygro-thermal coupled effect.The research results provide fundamental data for further application,development,design and analysis of piezoelectric smart structures under mechanic-electro-hygro-thermal multi-field coupled effect. |
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