热载荷下压电复合板有限元建模与形变控制

热载荷是引起在轨空间结构形变的重要因素之一，采用压电材料对结构热变形进行主动补 偿，需要建立热、电、力场相互耦合的动力学模型. 基于高阶位移场、高阶电势分布和线性 温度模型，推导了压电复合板结构的热、电、力场耦合的高阶有限元模型. 通过对压电双晶 片梁的分析，得到了压电片中电势沿厚度方向的抛物线型分布，而非通常文献中假设的线性 化分布模型的结果. 针对表面粘贴压电片的压电复合板，计算了热载荷作用下压电复合板的变形、 传感器的电压以及主动补偿后的结构变形，与文献给出的结果基本一致，验证了模型的正 确性. 同时还指出热电效应对结构变形和传感器电压具有十分重要的影响.     

Two-scale finite element method for piezoelectric problem in periodicstructure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic struc- ture under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element...     

Two-scale finite element method for piezoelectric problem in periodic structure

The prediction of the mechanical and electric properties of piezoelectric fibre composites has become an active research area in recent years. By means of introducing a boundary layer problem, some new kinds of two-scale finite element methods for solutions to the electric potential and the displacement for composite material in periodic structure under the coupled piezoelectricity are derived. The coupled two-scale relation of the electric potential and the displacement is set up, and some finite element approximate estimates and numerical examples which show the effectiveness of the method are presented.     

压电结构的热弹性比拟建模方法

通过比较逆压电效应本构方程和热弹性本构方程,在线性范围内建立逆压电效应和热弹性效应的比拟关系:将驱动电压比拟为温度载荷,压电应变系数比拟为热膨胀系数,用热弹性有限元方法分析逆压电效应,并采用热弹性比拟方法求解基于长度伸缩逆压电效应和厚度剪切逆压电效应的驱动器问题,给出了平面结构“热-机-电”耦合问题的热弹性比拟求解方法。热弹性比拟方法为快速建立复杂压电结构的有限元模型提供了一种有效的途径,可缩短复杂压电主动结构的设计周期,降低设计成本。最后给出数值算例说明文中方法的有效性。     

HEAT TRANSFER CHARACTERISTICS OF CONDUCTIVE MATERIAL UNDER INNER NON-UNIFORM ELECTROMAGNETIC FIELDS

Electronic transport properties can be influenced by the applied electromagnetic fields in conductive materials. The change of the electron distribution function evoked by outfields obeys the Boltzmann equation. In this paper, a general law of heat conduction considering the non-uniform electromagnetic effect is developed from the Boltzmann equation. An analysis of the equation leads to the result that the electric field gradient and the magnetic gradient in the conductive material are responsible for the influences of electromagnetic fields on the heat conduction process. A physical model is established and finite element numerical simulation reveals that heat conduction can be increased or delayed by the different directions of the electric field gradient, and the existence of the magnetic gradient always hinders heat conduction.     

具有非线性表面换热系数半圆柱薄壳在快速冷却过程中的热分析

用实验和数值计算相结合的方法，得到半圆柱壳体快速冷却过程中内外表面的非线性表面换热系数。在此基础上，用有限单元法对半圆柱壳体的热应力和变形进行了分析。在数值计算中，模拟钢的CCT图，计算了奥氏体、珠光体、贝氏体和马氏体的体积百分比，并将热物理性质和力学性能处理为相变体积百分比和温度的函数。所得结果表明，在半圆柱壳体快速冷却过程中的热应力和变形计算中，有必要考虑非线性表面换热系数、相变等非线性效应。     

Magneto-thermo-elastic waves in an infinite perfectly conducting elastic solid with energy dissipation

The generalized thermo-elasticity theory, i.e., Green and Naghdi （G-N） Ⅲ theory, with energy dissipation （TEWED） is employed in the study of time-harmonic plane wave propagation in an unbounded, perfectly electrically conducting elastic medium subject to primary uniform magnetic field. A more general dispersion equation with com- plex coefficients is obtained for coupled magneto-thermo-elastic wave solved in complex domain by using the Leguerre＇s method. It reveals that the coupled magneto-thermoelastic wave corresponds to modified dilatational and thermal wave propagation with finite speeds modified by finite thermal wave speeds, thermo-elastic coupling, thermal diffusivity, and the external magnetic field. Numerical results for a copper-like material are presented.     

Static analysis of simply supported functionally graded and layered magneto-electro-elastic plates

In this article, static analysis of functionally graded, anisotropic and linear magneto-electro-elastic plates have been carried out by semi-analytical finite element method. A series solution is assumed in the plane of the plate and finite element procedure is adopted across the thickness of the plate such a way that the three-dimensional character of the solution is preserved. The finite element model is derived based on constitutive equation of piezomagnetic material accounting for coupling between elasticity, electric and magnetic effect. The present finite element is modeled with displacement components, electric potential and magnetic potential as nodal degree of freedom. The other fields are calculated by post-computation through constitutive equation. The functionally graded material is assumed to be exponential in the thickness direction. The numerical results obtained by the present model are in good agreement with available functionally graded three-dimensional exact benchmark solutions given by Pan and Han [Pan, E., Han, F., in press. Green’s function for transversely isotropic piezoelectric functionally graded multilayered half spaces. Int. J. Solids Struct.]. Numerical study includes the influence of the different exponential factor, magneto-electro-elastic properties and effect of mechanical and electric type of loading on induced magneto-electro-elastic fields. In addition further study has been carried out on non-homogeneous transversely isotropic FGM magneto-electro-elastic plate available in the literature [Chen, W.Q., Lee, K.Y., Ding, H.J., 2005. On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates].     

Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties

In this paper, second order statistics of large amplitude free flexural vibration of shear deformable functionally graded materials (FGMs) beams with surface-bonded piezoelectric layers subjected to thermopiezoelectric loadings with random material properties are studied. The material properties such as Young’s modulus, shear modulus, Poisson’s ratio and thermal expansion coefficients of FGMs and piezoelectric materials with volume fraction exponent are modeled as independent random variables. The temperature field considered is assumed to be uniform and non-uniform distribution over the plate thickness and electric field is assumed to be the transverse components E _z only. The mechanical properties are assumed to be temperature dependent (TD) and temperature independent (TID). The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics. A C ⁰ nonlinear finite element method (FEM) based on direct iterative approach combined with mean centered first order perturbation technique (FOPT) is developed for the solution of random eigenvalue problem. Comparison studies have been carried out with those results available in the literature and Monte Carlo simulation (MCS) through normal Gaussian probability density function.     

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials,electric displacements,elastic deformations,and thermoelasticity,and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures(cylinder or sphere),subjected to mechanical load and electric potential.The material properties,thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution.In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material,reinforced by elastic isotropic fibers,this material is considered as structurally anisotropic material.The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity,and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin’s approximation method.Finally,numerical results are carried out and discussed.     

无限长圆柱体中广义电磁热弹耦合问题研究

基于L-S广义热弹性理论,研究了处于磁场中无限长理想圆柱导体在边界受热冲击作用时的电磁热弹耦合问题.建立了广义电磁热弹耦合的有限元方程,为避免积分变换方法求解带来的精度丟失.采用将有限元方程直接在时间域求解的方法,得到了圆柱体中的温度、位移、应力、感应磁场和感应电场的分布规律,反映了热的波动性及电磁热弹的耦合效应.结果表明,将有限元方程直接在时间域求解,可以获得各物理量的准确分布.得到温度在热波波前处的阶跃,准确地反应热波的波动效应.     

Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.     

Sensitivity analysis of the thermomechanical response of welded joints

A computational procedure is presented for evaluating the sensitivity coefficients of the thermomechanical response of welded structures. Uncoupled thermomechanical analysis, with transient thermal analysis and quasi-static mechanical analysis, is performed. A rate independent, small deformation thermo-elasto-plastic material model with temperature-dependent material properties is adopted in the study. The temperature field is assumed to be independent of the stresses and strains. The heat transfer equations emanating from a finite element semi-discretization are integrated using an implicit backward difference scheme to generate the time history of the temperatures. The mechanical response during welding is then calculated by solving a generalized plane strain problem. First- and second-order sensitivity coefficients of the thermal and mechanical response quantities (derivatives with respect to various thermomechanical parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility. Numerical results are presented for a double fillet conventional welding of a stiffener and a base plate made of stainless steel AL-6XN material. Time histories of the response and sensitivity coefficients, and their spatial distributions at selected times are presented.     

FUNDAMENTAL SOLUTION BASED GRADED ELEMENT MODEL FOR STEADY-STATE HEAT TRANSFER IN FGM

A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials (FGMs). The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element (FE) model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional FEM and boundary element method (BEM). Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.     

聚醚醚酮基复合材料的热性质和物理性质预测及其摩擦销三维温度场的数值模拟

通过研究填料含量对聚醚醚酮(PEEK)基复合材料密度、比热和导热系数等热学和物性参数影响的规律,提出了三相PEEK基复合材料热学和物理性质的计算模型;以销/盘摩擦副作为研究对象,采用有限元分析法计算模拟了复合材料摩擦销的温度分布,给出了销的三维稳态和瞬态温度场,并讨论了填料含量对摩擦销端面温升的影响规律.结果表明,计算结果与试验结果吻合较好.     

电磁弹性动力学初边值问题12类变量广义变分原理

基于Yao建立的电磁弹性固体广义变分原理,运用关于非传统Hamilton型广义变分原理的方法,建立了电磁弹性动力学初边值问题的12类变量广义变分原理,可反映该问题的全部特征,其独立变分变量为该问题的全部变量,即位移、速度、动量、应变、应力、电位移、磁感应强度、电场强度、磁场强度、电标量势、磁标量势和磁矢量势.本文建立的...     

A new Finite Element Method for magneto-dynamical problems: two-dimensional results

A mixed Lagrange finite element technique is used to solve the Maxwell equations in the magneto-hydrodynamic (MHD) limit in an hybrid domain composed of vacuum and conducting regions. The originality of the approach is that no artificial boundary condition is enforced at the interface between the conducting and the insulating regions and the non-conducting medium is not approximated by a weakly conducting medium as is frequently done in the literature. As a first evaluation of the performance of the method, we study two-dimensional (2D) configurations, where the flow streamlines of the conducting fluid are planar, i.e., invariant in one direction, and either the magnetic field (“magnetic scalar” case) or the electric field (“electric scalar” case) is parallel to the invariant direction. Induction heating, eddy current generation, and magnetic field stretching are investigated showing the usefulness of finite element methods to solve magneto-dynamical problems with complex insulating boundaries.     

Investigation of effective material properties in composites with internal defect or reinforcement particles

This paper is concerned with the investigation of the effective material properties of internally defective or particle-reinforced composites. An analysis was carried out with a novel method using the two-dimensional special finite element method mixing the concept of equivalent homogeneous materials. A formulation has been developed for a series of special finite elements containing an internal defect or reinforcement in order to assure the high accuracy especially in the vicinity of defects or reinforcements. The adoption of the special finite element can greatly simplify numerical modeling of particle-composites. The numerical result provides the effective material properties of particle-reinforced composite and explains that the size of particles has great influence on the material properties. Numerical examples also demonstrate the validity and versatility of the proposed method by comparing with existing results from literatures.     

Homogenization in probabilistic terms: The variational principle and some approximate solutions

Studying of materials with evolving random microstructures requires the knowledge of probabilistic characteristics of local fields because the path of the microstructure evolution is controlled by the local fields. The probabilistic characteristics of local fields are determined by the probabilistic characteristics of material properties. In this paper it is considered the problem of finding the probabilistic characteristic of local fields, if the probabilistic characteristics of material properties are given. The probabilistic characteristics of local fields are sought from the variational principle for probabilistic measure. Minimizers of this variational problem provide all statistical information of local fields as well as the effective coefficients. Approximate solutions are obtained for electric current in composites for two cases: multi-phase isotropic composites with lognormal distribution of conductivities and two-phase isotropic composites. The solutions contain a lot of statistical information that has not been available previously by analytical treatments.