Constitutive computational modelling foundation of piezoelectronic microstructures and application to high-frequency microchip DSAW resonators

This paper establishes a piezoelectric constitutive computational approach based on generalized eigenvalue and multivariable finite element solutions with potential applications to accurate and effective analysis of layered piezoelectric microstructures of arbitrary geometries and different anisotropic materials, to ease the limitation of current computer capacity in analyzing large-scale high-frequency disturbed surface acoustic waves (DSAW) by mounted electrodes in piezoelectric devices such as microchip SAW resonators. A new incompatible generalized hybrid/mixed element GQM5 is also proposed for improving predictions of the piezoelectric surface mount thermal stresses that are shear-dominated. The (generalized) plane strain constitutive model is numerically verified for piezoelectric finite element computation. With the help of computational piezoelectricity (electro-mechanics) for general layered structures with metal electrodes and anisotropic piezoelectric substrates, some new interesting, reliable and fundamental constitutive finite element results are obtained for high-frequency piezoelectric and mechanical SAW propagations and can be used for further applications. The ST-cut FEA results agree quite well with available exact and lab solutions for free surface case. The project supported by SRF for ROCS, SEM of China, the past Rutgers Univer-Seiko Epson Joint Fund and Zhejiang Provincial NSF     

在材料研制中的连续介质细观力学有限元建模现状评论（译文）

评述了机械载荷下材料力学行为有限元模拟的先进技术.分析 了考虑材料微观及细观结构情况下，对材料变形、损伤、断裂进行模 拟时各种方法的优缺点及发展前景.阐述了对材料行为模拟方法的发 展，包括基本的及先进的方法，如体胞方法、真实结构模拟、粘结区 模型等.分析了在先进新材料的开发中运用有限元方法的可能性     

正交异性光弹性应力分离的边界元法

本文对平面正交各向异性复合材料模型引入正应力线性和及边界上正应力线性和流的概念,提出从应力相容方程出发.用边界元法计算正交异性光弹性模型内任一点的正应力线性和位的方法,再与正交异性光弹性法中所给出的应力同的关系结合,即可进行正交异性光弹性应力的分离.最后,对边界元方法的精度进行了讨论.     

Computational modeling of rate-dependent domain switching in piezoelectric materials

In this contribution a micromechanically motivated model for rate-dependent switching effects in piezoelectric materials is developed. The proposed framework is embedded into a three-dimensional finite element setting whereby each element is assumed to represent an individual grain. Related dipole (polarization) directions are thereby initially randomly oriented at the element level to realistically capture the originally un-poled state of grains in the bulk ceramics. The onset of domain switching processes is based on a representative energy criterion and combined with a linear kinetics theory accounting for time-dependent propagation of domain walls during switching processes. In addition, grain boundary effects are incorporated by making use of a macromechanically motivated probabilistic approach. Standard volume-averaging techniques with respect to the response on individual grains in the bulk ceramics are later on applied to obtain representative hysteresis and butterfly curves under macroscopically uniaxial loading conditions at different loading frequencies. It turns out that the simulations based on the developed finite element formulation nicely match experimental data reported in the literature.     

Time-harmonic BEM for 2-D piezoelectricity applied to eigenvalue problems

We will derive the fundamental generalized displacement solution, using the Radon transform, and present the direct formulation of the time-harmonic boundary element method (BEM) for the two-dimensional general piezoelectric solids. The fundamental solution consists of the static singular and the dynamics regular parts; the former, evaluated analytically, is the fundamental solution for the static problem and the latter is given by a line integral along the unit circle. The static BEM is a component of the time-harmonic BEM, which is formulated following the physical interpretation of Somigliana’s identity in terms of the fundamental generalized line force and dislocation solutions obtained through the Stroh–Lekhnitskii (SL) formalism. The time-harmonic BEM is obtained by adding the boundary integrals for the dynamic regular part which, from the original double integral representation over the boundary element and the unit circle, are reduced to simple line integrals along the unit circle.The BEM will be applied to the determination of the eigen frequencies of piezoelectric resonators. The eigenvalue problem deals with full non-symmetric complex-valued matrices whose components depend non-linearly on the frequency. A comparative study will be made of non-linear eigenvalue solvers: QZ algorithm and the implicitly restarted Arnoldi method (IRAM). The FEM results whose accuracy is well established serve as the basis of the comparison. It is found that the IRAM is faster and has more control over the solution procedure than the QZ algorithm. The use of the time-harmonic fundamental solution provides a clean boundary only formulation of the BEM and, when applied to the eigenvalue problems with IRAM, provides eigen frequencies accurate enough to be used for industrial applications. It supersedes the dual reciprocity BEM and challenges to replace the FEM designed for the eigenvalue problems for piezoelectricity.     

Thermal analysis of the roll in the strip casting process

Coiled strip can be directly produced through the twin-roll strip casting process from the melt by incorporating casting and hot rolling together into a single step. In this unique process, the strip formation from the molten metal critically relies upon the casting rolls. Thus, the design of the rolls is extremely essential. The coupled heat transfer and deformation analysis of the casting roll is carried out in a two-dimensional numerical model, using a finite element program (MARC) to examine the thermal stress and displacement. The effects of several factors such as the nickel overlay thickness on the roll surface, the casting speed, and the roll diameter on thermal characteristics are investigated.     

一种新的金属压缩试验方法的有限元分析

对一种新的金属压缩试验方法进行了有限元数值分析，论证了这种方法的可行性和有性，并且对不同尺寸的试件进行了有限元计算．     

大体积混凝土结构随机温度徐变应力计算方法研究

首次尝试将随机有限元法引入大体积混凝土结构随机温度徐变应力的计算．综合考虑各种随机因素，对于由材料物理参数随机性引起的随机温度场的影响，本文给出了相应于初应变隐式解法的随机有限元计算方法；对于周期平稳随机温度场对徐变应力场的影响，本文提出了复模量隐式解法，并首次视复频响应函数为材料参数的随机函数，给出了相应的复频响应－随机有限元列式；而对于一般非平稳绝热温升温度场的影响，本文提出了参数调幅逐段简化的方法．本文方法有效地克服了前人不能考虑材料参数随机性或需弹模不随时间变化的局限性     

有初内力的板的内共振

本文利用非线性时空有限方法和样条有限元技术对具有初内力的板的非线性频响特性进行了分析，计算了在不同初始内力下方板的大振幅自由振动、有阻尼强迫振动和矩形板的内共振。     

A linearization technique for multi-species transport problems

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor’s series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.