eXtended finite element methods for thin cracked plates with Kirchhoff–Love theory

A modelization of cracked plates under bending loads in the XFEM framework is addressed. The Kirchhoff–Love model is considered. It is well suited for very thin plates commonly used for instance in aircraft structures. Reduced HCT and FVS elements are used for the numerical discretization. Two kinds of strategies are proposed for the enrichment around the crack tip with, for both of them, an enrichment area of fixed size (i.e. independant of the mesh size parameter). In the first one, each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip. The second strategy consists in introducing these functions in the finite element basis with a single degree of freedom for each one. An integral matching is then used in order to ensure the ??¹ continuity of the solution at the interface between the enriched and the non‐enriched areas. Finally, numerical convergence results for these strategies are presented and discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Love waves on a half-space with a gradient piezoelectric layer by the geometric integration method

The propagation of Love waves on an elastic homogeneous half-space with a piezoelectric gradient covering layer is studied by the geometric integration method in this article. First, the state transfer equation of a Love wave is derived from the governing equations and constitutive relations. Then, the transfer matrix of the state vector is obtained by solving the state transfer equation of a Love wave and then the stiffness matrix is obtained. By combining transfer matrices and the stiffness matrices of the gradient covering layer and the homogeneous half-space, the total surface stiffness matrix of a Love wave is obtained. Lastly, the application of the electrically open circuit and short circuit conditions and mechanically traction-free conditions gives the frequency dispersive relation of a Love wave. For the gradient covering layer, the material constants at the bottom of the covering layer may be greater or smaller than that at the top of the covering layer. The two situations and three kinds of gradient profiles for each of these two situations are investigated. The numerical results show that the Love wave speed is sensitive to not only the material constants at the bottom and the top of the covering layer, but also the gradient profiles of the covering layer.     

涂覆聚合物膜的Love波传播特性

该文计算了涂覆聚合物膜的Love波传感器波速和波导层相对膜厚的关系,并进行了实验验证。Love波器件以ST-90°X石英晶体为基片,在基片表面镀一层不同膜厚的聚乙烯醇(PVA)膜作为波导层兼吸湿层。采用网络分析仪测量了相对湿度35%左右器件的工作频率和插入损耗分别随膜厚的变化,算出Love波波速和PVA相对膜厚的关系,当PVA膜厚度从0增大到波长的5%时,Love波速度由约4 992m/s降低到4 840m/s,和理论计算结果一致。     

A discontinuous Galerkin formulation of non‐linear Kirchhoff–Love shells

Discontinuous Galerkin (DG) methods provide a means of weakly enforcing the continuity of the unknown‐field derivatives and have particular appeal in problems involving high‐order derivatives. This feature has previously been successfully exploited (Comput. Methods Appl. Mech. Eng. 2008; 197 :2901–2929) to develop a formulation of linear Kirchhoff–Love shells considering only the membrane and bending responses. In this proposed one‐field method—the displacements are the only unknowns, while the displacement field is continuous, the continuity in the displacement derivative between two elements is weakly enforced by recourse to a DG formulation. It is the purpose of the present paper to extend this formulation to finite deformations and non‐linear elastic behaviors. While the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple‐stress from the displacement field at the mid‐surface of the shell, the non‐linear formulation considered implies the evaluation of the general stress tensor across the shell thickness, leading to a reformulation of the internal forces of the shell. Nevertheless, since the interface terms resulting from the discontinuous Galerkin method involve only the resultant couple‐stress at the edges of the shells, the extension to non‐linear deformations is straightforward. Copyright © 2008 John Wiley & Sons, Ltd.     

功能梯度压电层/压电半空间结构中Love波的传播:一种改进的拉盖尔多项式方法

使用传统的拉盖尔多项式方法求解层状半空间结构时,存在因层间材料差异所造成的应力、电位移不连续的现象。为了克服此方法的不足,提出了一种改进的拉盖尔多项式方法,研究了功能梯度压电层状半空间中Love波的传播特性。与文献中应用WKB法得到的结果进行对比,验证了该方法的正确性。计算和分析了相应的频散曲线、应力和电位移分布曲线。结果表明:该方法能够避免因层间材料差异所造成的应力、电位移不连续现象的出现;高频Love波的应力和电位移主要分布在功能梯度压电层中速度较低的一侧。该研究为基于Love波传感器的设计与优化奠定了一定的理论基础。     

地基含倾斜界面时Love波弥散特性

利用有限元法及解析法相结合的方法建立了地基含有倾斜层时Ｌｏｖｅ波弥散特征方程和位移计算公式。利用这一方法研究了该类地基Ｌｏｖｅ波弥散特性，并与水平成层地基（α＝０°）进行比较     

检测B型葡萄球菌肠毒素的Love波免疫传感器研究

报道了一种可用于检测B型葡萄球菌肠毒素(SEB)的Love模式声表面波压电免疫传感器。传感器本身由压电石英基片、叉指换能器和S iO2声波导层构成。通过APTES和戊二醛层交联蛋白A,实现抗体分子的定向固定,在Love波传感器的表面构建出抗体分子探针的传感界面。建立了基于网络分析仪的传感器测试系统,对抗体分子固定化过程以及10-6g/mL SEB的响应过程进行了实时监测,相位的偏移随时间表现出明显而规律性的改变,与戊二醛共价交联法进行了对比,并用原子力显微镜(AFM)对蛋白A法固定抗体以及捕获了SEB后的表面进行了成像表征。     

The Golden Age: Between Wilderness and Utopia

Artist Dominic Shepherd pursues the imaginative and a sense of mystery in his work; his 2012 one-man show at Charlie Smith London was entitled ‘Jerusalem’. Here he reflects on the Golden Age as depicted in Cranach's masterpiece of that name, and ruminates on the cyclical nature of the pastoral, a landscape that is tended and nurtured by generations of hands.     

乐甫波的液体粘度传感研究

利用部分波理论和边界条件精确推导,对“粘性液体/非压电薄膜/压电基底”3层乐甫波结构建模,分析得出随叉指周期变小,液体粘度灵敏度提高,传播衰减增大;随“薄膜厚度与波长之比”增大,液体的粘度灵敏度随之先减小再增大,液体密度灵敏度几乎为零。优化设计了以36°钽酸锂和SiO₂为基底和薄膜的乐甫波器件,制作并测试实物,实验结果与数值仿真基本一致,表明了理论模型的正确性。     

基于PVA/ST-90°X石英的Love波湿度传感器的实验研究

报道了覆盖聚合物敏感膜的Love波传感器的湿度检测性能。该传感器采用在ST-90°X石英基底上旋涂聚乙烯醇(PVA)膜作为波导层兼吸湿层,测量了密闭空间中相对湿度从9%增加到88%时器件的工作频率及损耗。实验表明,频率偏移和损耗增量均由吸附后质量负载所产生,其变化规律遵循第III类等温吸附曲线。