基于PINNs的压电半导体梁的非线性多场耦合力学分析

压电半导体(PS)具有压电性和半导体特性共存耦合的特征,在新型多功能电子/光电子学器件中有广阔应用前景.因此,理论分析压电半导体结构在外载作用下的多场耦合力学响应是十分重要的.然而,描述压电半导体多场耦合力学行为的控制方程中含有非线性的电流方程,属于物理非线性;而且很多半导体器件通常工作在大变形模式下,在力学上属于几何非线性问题.物理非线性和几何非线性给问题的求解带来了挑战.该文针对压电半导体梁结构,基于物理信息神经网络(physics informed neural networks, PINNs),构建了能高效求解其非线性多场耦合力学问题的PINNs方法.通过依次删除网络结构中载流子项和压电项,该方法即可退化到压电结构和纯弹性结构的情况.利用所构建的PINNs,分析了压电半导体梁在均布压力下的多场耦合力学响应.数值结果表明：该文所提出的基于PINNs的模型能有效求解压电半导体、压电以及纯弹性结构非线性多场耦合问题,相对而言,其在求解压电和纯弹性结构的力学响应时具有更高的精度.     

轴对称金属模具电磁热裂纹止裂中热应力场的分析

为求解金属模具脉冲放电止裂瞬间裂纹尖端附近的热应力场,选择具有半埋藏环形裂纹的金属凹模为研究对象,采用复变函数方法求解了凹模内外环面均匀通入强脉冲电流放电止裂时的热应力场．理论分析结果证实：由于放电瞬间脉冲电流的绕流集中效应,使金属凹模内部环形裂纹尖端附近金属迅速升温,金属熔化形成堆焊,并由于瞬间温升产生热压应力场．研究结果表明：应用电磁热效应止裂技术可以减小裂纹尖端的应力集中,形成的热压应力场有效地阻止金属模具中干线裂纹源的开裂趋势,达到了裂纹止裂目的．     

带合作行为的平均场模型的依全变差稳定性

该文考虑一个带合作行为的平均场模型的稳定性问题. 应用耦合方法, 建立了相应于这个平均场模型的扩散过程的依全变差稳定性.     

轻质热防护系统多层材料组合结构的热应力分析

提出了轻质热防护系统外面板使用多层结构的概念,设计了2种热防护材料组合构成的3种铺层方案．通过模拟飞行器再入大气层时受到的机械和热载荷条件,数值计算得到了层间剪切力、底部温度和y方向位移．计算结果发现,层间剪切力发生在边缘部位且呈反对称分布;选用高热导率和高热容材料能够减少材料内的温度梯度,进而有效地降低结构的热应力和热变形;在均匀温度场情况下,两种材料的热膨胀系数之差越小,则层间剪切力越小．该研究表明不同的材料组合和铺层次序的多层结构,可以满足不同设计要求,具有优化设计潜力．     

三维浮式结构的流固耦合动力特性分析

对于采用位移-压力有限元格式从流固耦合系统导出的大型非对称矩阵特征值问题,构造出了一种新格式的迭代Arnoldi方法进行非对称特征值分析来获得浮式结构的动力特性．该迭代格式在克服零频的移频技术中,可以高效地计算出Arnoldi向量．实例分析结果表明,流固耦合作用对水上大型薄壁浮式结构动力特性具有重要影响．     

对基频光与低强高频光形成的双色场的计算与分析

基频光及一弱的辅助高倍频光（9倍 、1３倍甚至120倍频光等）的双色场（该场高频光强度仅为基频光的1/100）作用于氦离子He⁺,发现高次谐波辐射的效率有了很大的提高,尤其是相应于入射高频光频率对应级次及邻近级次的谐波效率有极大提高. 加入不同的低强高频光对双色场高次谐波产生的影响进行计算及讨论,并对其物理机制进行初步阐释.     

负Poisson比热电器件的热-电-力耦合弯曲特征及强度分析

随着智能可穿戴设备的快速发展,对供电元件的续航时间、便捷性以及轻量化等提出了更高要求.热电器件可以直接将人体新陈代谢释放的热能转换为电能,为可穿戴设备持续供电.利用整体-局部、细观-宏观相结合的分析方法,该文研究了负Poisson比热电器件的热-电-力耦合弯曲行为及其强度失效问题.首先,通过建立负Poisson比热电器件的均质化分析模型,获取了器件的宏观弯曲特征,并给出了应力最大的截面.然后,建立热电蜂窝的受力分析模型,利用热力学强度理论导出了胞壁的细观强度失效临界荷载.研究发现：热电蜂窝的应力水平随着内凹角增大呈现先减小后增加的趋势;对于负Poisson比热电蜂窝,强度失效首先发生在中间部位;对于传统的六边形热电蜂窝,端部比中间部位先发生强度破坏;热电器件发生断裂破坏时,中间和端部的临界裂纹长度近似相等,可以拟合为内凹角的指数函数.     

具有二阶逼近效应场多维Landau-Lifshitz 方程解的极限行为

本文给出在Rⁿ⁺¹ 到S² 整体光滑映射控制下的极大值原理, 通过这个原理建立具有二阶逼近效应场多维Landau-Lifshitz 方程的δ- 黏性上解和δ- 黏性下解. 利用这些δ- 黏性上下解, 我们建立具有二阶逼近效应场多维Landau-Lifshitz 方程的黏性解并获得解的极限行为, 即存在两个不相交的开子集M 和N 使得δ- 黏性上解和δ- 黏性下解分别在M 内任一紧子集上趋于(0, 1, 0), 在N 内任一紧子集上趋于(0,?1, 0).     

预倒出口箱区的多场桥调度优化

在集装箱出口箱区堆场的实际作业中,常将待提箱提前翻倒至一空闲箱区,使其装船前以船舶配载图的倒序堆垛,以提高装船效率。为提高初始出口箱区的预翻作业效率,针对该箱区的多场桥调度优化问题进行研究。以实施预翻作业的某一出口箱区为研究对象,在船舶配载图已知的前提下,考虑作业场桥间保持安全距离且不可跨越的条件,兼顾满足经验翻箱规则等现实约束,侧重作业过程中实时翻箱,构建了以场桥作业总行走时间最小为优化目标的线性规划模型,并设计了分支定价算法。在算例实验中,通过与非实时预翻箱方案、FCFS方案以及下界进行对比,验证了模型及算法的有效性,可为集装箱码头出口箱堆场的场桥调度提供参考。     

多分量的KN族与可积耦合及其它们的哈密顿结构

Firstly,a vector loop algebra (~G)3 is constructed,by use of it multi-component KN hierarchy is obtained.Further,by taking advantage of the extending vector loop algebras (~G)6 and (~G)9 of (~G)3 the double integrable couplings of the multi-component KN hierarchy are worked out respectively.Finally,Hamiltonian structures of obtained system are given by quadratic-form identity.     

纵向磁场激励下简支输流微梁的动力学行为研究

受磁场驱动的微机电系统在工作中存在着力、磁、流-固耦合等非线性特征,其力学行为非常复杂,并将影响系统运行的安全性与可靠性.该文采用非局部Euler梁模型研究磁场激励下简支输流微梁（一种微机电系统）的动力学行为,通过动力系统分支理论和谐波平衡法来考察系统的稳定性和幅频特性曲线.结果表明,可以采用改变磁场强度、流速和阻尼的三重方式调节微机电系统的频率.研究中还发现,小尺度效应和磁场强度可以影响临界流速,阻尼的存在可以改变临界流速的个数和系统的分岔类型.     

Prediction,measurement and comparison of fluid-structure interaction using mathematical and experimental models

Without presenting all the associated mathematics this paper considers the combined use of theoretical and experimental methods in the investigation of the fluid structure interaction of rigid and articulated structures. The structures considered are the rigid body form of the Lancaster Flexible Bag (LFB) and an articulated Cockerell raft system.In the case of the LFB the Salvesen-Tuck-Faltinsen strip theory is shown to predict vertical and horizontal bending moments which are generally consistent with measured trends (almost) irrespective of whether 2D-based or 3D-based calculated hydrodynamic active and reactive coefficients are used. The non-repeatability of some of the measured results used in the comparison caused some concern and the additional required model testing is discussed.In direct comparison application difficulties were encountered when using theoretical analyses to assist with the organization of the experiments to investigate the hydrodynamic loading of articulated systems. The finite element program PAFEC 75 was used to predict the vibration frequencies of the framework used to support the Cockerell raft model and the actuator system used to force oscillate the model. The 3D diffraction programme MATTHEW provided predictions of pressure distributions over the raft to assist with sensible positioning of the pressure transducers on the physical model. The difficulties encountered in applying these prediction tools are discussed, also the current research programme is reported.     

A one-sweep method in the solution of finite-element equations: An application to the vibration of structures in heavy fluids

A one-sweep method for the numerical solution of finite-element equations is presented. This procedure is especially efficient in computing time and storage when the solution is required at only a few nodes of the finite-element mesh. Furthermore, the method is particularly useful in dealing with problems on infinite or semi-infinite domains. Artificial boundaries must be introduced in such cases, and the one-sweep method affords an extremely efficient algorithm by which the dependence of the solution on the location of these boundaries can be assessed. An application of the method to the vibration of a half-submerged circular cylinder in a heavy fluid is presented.The second author wishes to express his thanks to Professor J. L. Sackman for reviewing this work.(deceased).     

论理想流体与线弹性结构的耦联振动

本文对理想流体与线弹性结构的耦联振动问题作理论分析和数值分析.文中证明了耦联振动的固有频率存在并且均为正实数.将流-固耦合系统分析转化为单一结构物在真空中的自由振动分析后,频率方程中不再含有流体变元.使问题得以大大简化.给出了数值解的收敛性证明,以保证解的可靠性.文中还综合里兹法、边界元和有限元方法,提出一种分析转化后结构的混合算法.利用该算法,只需对现有结构分析程序稍作改进,就可分析那些理想流场与结构的耦合问题.一些数例说明了算法的有效性.     

Coupled parabolic–hyperbolic Stokes–Lamé PDE system: limit behaviour of the resolvent operator on the imaginary axis

This article is focused on an established, genuinely physical fluid-structure interaction model, whereby the structure is immersed in a fluid with coupling taking place at the boundary interface between the two media. Mathematically, the model is a coupled parabolic–hyperbolic system of two partial differential equations in three dimensions with non-standard coupling at the boundary interface: the (dynamic) Stokes system (parabolic, modelling the fluid) and the Lamé system (hyperbolic, modelling the structure). This system generates a contraction semigroup on the natural energy space [G. Avalos and R. Triggiani, The coupled PDE system arising in fluid/structure interaction, Part I: explicit semigroup generator and its spectral properties, Fluids and Waves, Amer. Math. Soc. Contemp. Math. 440 (2007), pp. 15–59] (canonical model) and [G. Avalos and R. Triggiani, Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction, Discr. Contin. Dyn. Sys. Series S, 2(3) (2009), pp. 417–447]. The boundary interface may or may not include a ‘damping’ (or dissipative) term. If damping is active on the entire interface, then uniform (exponential) stabilization is ensured, regardless of the geometry of the structure [G. Avalos and R. Triggiani, Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface, Discrete Contin. Dyn. Syst. 22(4) 2008, pp. 817–835, special issue, invited paper] (canonical model) and [G. Avalos and R. Triggiani, Boundary feedback stabilization of a coupled parabolic–hyperbolic Stokes–Lamé PDE system, J. Evol. Eqns 9(2009), pp. 341–370]. This article emphasizes the case of, at most, partial damping. At any rate, the main result is a precise uniform-operator limit behaviour of the resolvent operator of the semigroup generator on the imaginary axis of interest in itself, which holds true with or without damping. It, in turn, then implies a fortiori strong stability results: most notably, on the whole state space, under at least partial damping at the interface; and, in the absence of damping, on the whole state space, after factoring out an explicit one-dimensional null eigenspace, at least for a large class of geometries of the structure: these are characterized by a uniqueness property of a special over-determined elliptic problem.     

A finite element technique for tape-head interaction problems in high-speed recording: The steady-state case

This paper presents a finite element technique to model the steady-state response of a flexible tape during high-speed recording. The tape is modeled as a flexible plate, including geometric nonlinearities due to large deflections. The air-film pressure field is described by using a modified version of the Reynolds equation for compressible fluids. A new nonlinear finite element that couples both air-film and tape mechanics is described in detail. This element, which has been incorporated into a standard finite element code (MSC/NASTRAN®), allows one to determine the pressure field and the air-film thickness due to tape-head interaction. An example demonstrates the usefulness of this technique.     

肾动脉变窄和流-固结构相互作用对非Newton脉动流的影响——一个真实的腹部主动脉和肾动脉模型

研究肾动脉狭窄(RAS)对血液流动和血管壁的影响.根据CT扫描图像,重建腹部主动脉和肾动脉的解剖模型,通过模型的脉动流进行了仿真计算,计算中考虑了流体-固体结构的相互作用(FSI).研究RAS对血管壁剪切应力和位移的影响,RAS使得肾动脉中流量减少,肾素-血管紧缩素系统可能被激活,从而导致严重的高血压.     

有限流体域内不同位置处的柔性管涡致振动机理研究

针对有限流体域内柔性管的涡致振动问题,将柔性管离散为若干空间梁单元,流体域采用实体单元离散,建立了有限流体域内柔性管系统的流固耦合模型及数值计算方法,设计并加工圆柱流体域内柔性管振动专用实验装置,采用GWT 2B双轴加速度传感器对柔性管的振动进行监测,并与数值模拟结果进行对比,吻合程度较好.基于该文的模型和方法,对圆柱流体域内不同位置处柔性管的涡致振动机理进行研究.结果表明,柔性管偏离入口流速位置的角度越大,越容易发生流体弹性不稳定性,柔性管的振动愈剧烈;而正对入口流速的位置,不易发生流体弹性不稳定性,柔性管振动减弱.     

考虑流固耦合效应的重力坝水力劈裂模拟

裂缝的高压水力劈裂是混凝土高坝安全评估的重要部分,研究其过程中的流固耦合作用是准确预测在各种情况下裂纹扩展路径和危险程度的关键.该文利用扩展有限元法在模拟裂纹扩展方面的优势,对大坝的裂纹进行水力劈裂模拟研究.裂纹中的水压分布模型采用Brühwiler和Saouma水力劈裂试验的成果,体现了水压和裂纹宽度的耦合关系,给出了扩展有限元在裂纹面上施加水压力荷载的实施方法,对一典型重力坝裂纹的水力劈裂进行了数值模拟分析.研究结果表明：采用扩展有限元法模拟水力劈裂,克服了常规有限元法存在的缺点,裂纹扩展时不用重新划分网格,裂纹的实时宽度可以由加强节点的附加自由度得到,裂纹面上水压的施加也变得简单易行.当考虑裂纹内的流固耦合效应时,裂纹的扩展路径相比不考虑耦合效应时的扩展路径(均布全水头水压),扩展角变大,扩展距离变短.