Computational performance of Free Mesh Method applied to continuum mechanics problems

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.     

一种改进的无单元伽辽金方法

使用单位分解积分,对传统的无单元伽辽金方法进行改进.有限覆盖和单位分解是单位分解积分的数学基础,对单位分解积分进行了严格证明,并指出使用Shepard函数作为单位分解函数是一个很好的选择.数值实例表明,使用单位分解积分进行数值求积的无单元伽辽金方法是一种真正的无网格方法,与经典的背景网格积分相比具有更高的精度.     

石墨烯/羟基磷灰石复合材料力学性能的数值研究

为了研究石墨烯/羟基磷灰石复合材料力学性能（弹性模量和泊松比）,开发了石墨烯/羟基磷灰石复合材料的随机分布模型自动生成算法及相应的计算程序;建立石墨烯/羟基磷灰石复合材料的有限元模型,计算添加不同质量分数的石墨烯对复合材料力学性能的影响,通过与实验数据对比验证算法的有效性.结果表明：添加0.25%~1.25%（质量分数）的石墨烯可使复合材料的弹性模量增加12%~50%,表明添加少量石墨烯即能有效地改善羟基磷灰石的力学性能.     

光学CT中的图像重建算法

从理论上研究了利用正向模型求解逆问题的迭代算法，特别是其中Ｊａｃｏｂｉ矩阵的有限元解法，引入了图像恢复了领域广泛采用的规则化方法用于处理逆问题中的奇异性问题；作为总结，最后给出了ＦＥＭ法求解光学ＣＴ问题的完整步骤。     

大型轻质反射镜加工支撑状态的有限元分析研究

根据大型轻质镜加工过程中的受力情况 ,用有限元对镜子进行静力学分析和计算。分别计算了镜子的自重、磨盘正压力、磨盘剪切力等对镜面变形的影响情况。根据镜面变形规律设计了一系列支撑结构 ,最终确定了符合面形质量要求的支撑结构。     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

Selectivity of seismic electric signal (SES) of the 2000 Izu earthquake swarm: a 3D FEM numerical simulation model

Although seismic electric signal (SES) has been used for short-term prediction of earthquakes, selectivity of SES still remains as one of the mysterious features. As a case study, we made a numerical simulation based on a 3D finite element method (FEM) on the selectivity of SES observed in the case of the 2000 Izu earthquake swarm. Our numerical results indicated that the existence of conductive channel under Niijima island could explain the reported SES selectivity.     

A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes

A carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular FEM models, and to reconstruct a strain field with an adjustable parameter α. A novel Galerkin-like weakform derived from the Hellinger–Reissner variational principle is proposed for establishing the discretized system equations. The new weak form is very simple, possesses the same good properties of the standard Galerkin weakform, and works particularly well for strain construction methods. A superconvergent alpha finite element method (SαFEM) is then formulated by using the constructed strain field and the Galerkin-like weakform for solid mechanics problems. The implementation of the SαFEM is straightforward and no additional parameters are used. We prove theoretically and show numerically that the SαFEM always achieves more accurate and higher convergence rate than the standard FEM of triangular elements (T3) and even more accurate than the four-node quadrilateral elements (Q4) when the same sets of nodes are used. The SαFEM can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an α. In addition, a preferable-α approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm. Furthermore, a model-based selective scheme is proposed to formulate a combined SαFEM/NS-FEM model that handily overcomes the volumetric locking problems. Intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the SαFEM.     

一种抗单元逆转的软组织有限元模型

由于Green应变具有单元翻转不变性,在大变形的仿真中有可能会出现单元的逆转,破坏模型网格的拓扑结构,导致仿真失败,因此提出一个新的有限单元模型,在采用Green应变度量变形同时把单元体积变化率和单元内压强关系引入到本构方程中,解决单元逆转问题;同时,模型导出的单元弹性势能是单元结点位移的多项式函数,有效地简化了共轭梯度法的求解,效率显著提高.实验结果表明,该模型可以应用于软组织大变形的实时仿真中.     

物理参数变化对短脉冲激光激励温度场的影响

 为研究多物理参数（耦合系数、电子热导率、电子热容、晶格热容）同时随温度变化对短脉冲激光辐照金属材料产生温度场分布的影响,基于双温耦合理论,建立了短脉冲激光辐照金属材料金的加热过程的有限元求解模型。在同时考虑脉冲激光的空间、时间分布和多参数同时随温度变化的情况下,得到短脉冲激光辐照金属材料金激励产生的温度场二维瞬态分布,并进一步比较了多物理参数同时随温度变化和采用室温物理参数两种情况下温度场分布的区别。数值结果表明：多物理参数同时随温度变化使电子温度和晶格温度的上升变快,最大值变大,而且使得材料中激光穿透直接辐照到的区域温度变高。     

Optimal design and lifetime calculation of the belt chamber by finite element method

Abstract

A mixed numerical-analytical method for an optimal strength design is presented. Optimal number n of components and optimal radii r_j are calculated for an equivalent cylindrical model of the compound vessel. An iterative numerical method is proposed for evaluation of optimal overlaps Δr_j. A finite element method (FEM) elastic-plastic program has been developed to estimate the vessel lifetime.     

应用高阶有限元-局部共形完全匹配层算法分析电磁散射问题

提出局部共形完全匹配层在高阶有限元中的实现方法,用于分析三维电磁散射问题.基于定义在局部高阶单元上的实坐标、复坐标以及参数坐标三者之间的映射关系,局部共形完全匹配层不仅能够贴近复杂结构散射体的外廓形状设置截断区域,有效地缩减有限元分析区域,而且由于保证了较高的几何拟合精度,可以有效地提高数值计算结果的准确性.利用这种结合局部共形完全匹配层的高阶有限元方法分析不同目标的电磁散射特性,数值结果表明方法的正确性和有效性.     

Finite element modelling of the elastic-plastic stress and strain state and lifetime of the belt chamber

Abstract

A special finite element method (FEM) programme has been developed, reflected all significant phenomena connected with assembly and exploration of the Belt chamber. A nonhomogeneous temperature field is taken into account. Isotropic, kinematic and mixed hardening rules can be considered.     

短脉冲激光加工双温方程的优化运算

为研究双温方程中电子热传导项和电子与晶格耦合项对激光辐照物体表面温度场求解的影响,对这两项施加了约束条件。由于飞秒和亚皮秒激光与物质相互作用时间短,电子与晶格来不及耦合,所以对耦合项施加时间约束;根据相分离条件(CPPS),对热传导项施加空间约束。利用有限元方法建立了激光烧蚀金属铜膜表面的有限元模型。通过分析双温方程中热传导项和耦合项对计算结果的影响,发现短脉冲激光与铜金属相互作用过程中电子与晶格耦合项可以忽略,而传导项不可忽略。求解适当激光功率下的双温方程,得到了激光作用中心电子与晶格在不同脉冲宽度激光辐照下的温度变化关系。根据100 fs激光作用后晶格温度场的空间分布情况,研究了激光作用的相分离区域、相爆炸区域以及熔融区域的分布情况。     

Nonlinear constitutive behavior of ferroelectric materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results. Supported by the National Natural Science Foundation of China (Grant No. 10572138)     

计算超薄镜最接近球面的非球面梯度法及有限元分析

利用超薄镜的弹性变形,通过主动光学技术将超薄球面镜变形为所需精度的非球面镜,可以避开大口径超薄非球面镜的制造难题。在分析了传统的非球面超薄镜最接近球面选择原则的基础上,提出了以非球面梯度作为选择原则的依据。针对一个实例,用非球面梯度法和最小二乘法分别求出两个最接近球面并对它们进行有限元法的变形分析,对它们变形后的面形精度和最大应力进行了比较。结果表明,在相同的边界条件、加载个数和加载位置的条件下,以非球面梯度法求出的最接近球面在变形后不仅应力小,且更有利于提高面形精度。     

Broadband and low-driving-power LiNbO<Subscript>3</Subscript>electrooptic modulators

Microwave and optical properties of lithium niobate electrooptic modulators are investigated in this paper. The effect of simultaneous matching of optical and microwave velocities and impedance matching, conductor loss, dielectric loss on the optical bandwidth of an ultra-high-speed lithium niobate modulator are presented here. The metal electrode design, buffer thickness, ridge depth, and the gap between electrodes at different operating frequencies on device performance are thoroughly investigated by using the finite element method.     

任意不可压多介质流的粒子有限元方法模拟

基于粒子有限元方法(particle finite element method,PFEM),利用细分混合单元的界面识别思想,模拟种类任意多的不可压多介质流问题.对分步算法采用基于有限增量微积分理论的稳定措施,以适应流体特性差异;将混合单元细分为代表单一流体的小单元,进而得到流体间的边界;通过加密边界、控制粒子速度、自动检查穿透来防止粒子穿透外部边界.瑞利-泰勒不稳定性和水柱在空气中倒塌的模拟与已有结果的对比验证了PFEM及界面识别方法的可靠性和准确性.七种流体混合的模拟结果表明PFEM可有效处理任意多种类不相溶流体的混合流动问题.     

空芯光子带隙光纤纤芯-包层交界面的设计

利用平面波展开法计算了圆六边形空气孔按三角形排列的光子晶体带隙,基于带隙图设计了移去7根玻璃毛细管形成纤芯、传输波长λ=1.55 μm的空芯光子带隙光纤的结构参量.随后利用全矢量有限元法计算了所设计的在纤芯-包层交界面处引入石英环的光纤,给出了在不同半径情况下沿z轴方向的光强分布、光强等高线分布图和损耗随引入石英环相对厚度的变化曲线.得出了光纤消除表面模、减小损耗的纤芯外半径取值范围为1.55Λ～1.7Λ,石英环的相对厚度取值范围为1.3～1.5或3.4～3.8.通过分析发现石英环的引入既可以抑制表面模也可以激发表面模,抑制还是激发有赖于纤芯外半径和石英环厚度的选择.     

钢结构装配式住宅墙板连接方式对隔声性能的影响

为提升钢结构装配式住宅隔声性能,通过有限元法数值分析,比较了不同位置墙板的连接方式对房间隔声性能的影响.结果表明:侧墙墙板柔性连接处理对侧向传声的抑制作用显著,当侧墙墙板采用柔性连接后,房间的隔声量在低频段平均可以提升3 dB左右;公共隔墙墙板的柔性连接对房间低频段隔声量提升不明显,甚至在160 Hz、400 Hz、5...