Static and free vibration analyses of functionally graded porous variable-thickness plates using an edge-based smoothed finite element method

The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method(NS-FEM)is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings.A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations.Numerical results obtained agree very well with those using the slip-line method,revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration.An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations.In addition,particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component.While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial,and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity.Both tables and charts are given for practical application to the seismic design of the foundations.

Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

Bubble-Enriched Smoothed Finite Element Methods for Nearly-Incompressible Solids

This work presents a locking-free smoothed finite element method(S-FEM)for the simulation of soft matter modelled by the equations of quasi-incompressible hyperelasticity.The proposed method overcomes well-known issues of standard finite element methods(FEM)in the incompressible limit:the over-estimation of stiffness and sensitivity to severely distorted meshes.The concepts of cell-based,edge-based and node-based S-FEMs are extended in this paper to three-dimensions.Additionally,a cubic bubble function is utilized to improve accuracy and stability.For the bubble function,an additional displacement degree of freedom is added at the centroid of the element.Several numerical studies are performed demonstrating the stability and validity of the proposed approach.The obtained results are compared with standard FEM and with analytical solutions to show the effectiveness of the method.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

A novel twice-interpolation finite element method for solid mechanics problems

Formulation and numerical evaluation of a novel twice-interpolation finite element method （TFEM） is presented for solid mechanics problems. In this method, the trial function for Galerkin weak form is constructed through two stages of consecutive interpolation. The primary interpolation follows exactly the same procedure of standard FEM and is further reproduced according to both nodal values and averaged nodal gradients obtained from primary interpolation. The trial functions thus constructed have continuous nodal gradients and contain higher order polynomial without increasing total freedoms. Several benchmark examples and a real dam problem are used to examine the TFEM in terms of accuracy and convergence. Compared with standard FEM, TFEM can achieve significantly better accuracy and higher convergence rate, and the continuous nodal stress can be obtained without any smoothing operation. It is also found that TFEM is insensitive to the quality of the elemental mesh. In addition, the present TFEM can treat the incompressible material without any modification.

Displacement fields denoising and strains extraction by finite element method

Optical full-field measurement methods are now widely applied in various domains. In general,the displacement fields can be directly obtained from the measurement,however in mechanical analysis strain fields are preferred.To extract strain fields from noisy displacement fields is always a challenging topic.In this study,a finite element method for smoothing displacement fields and calculating strain fields is proposed.An experimental test case on a holed aluminum specimen under tension is applied to validate this method.The heterogeneous displacement fields are measured by digital image correlation(DIC).By this proposed method,the result shows that the measuring noise on experimental displacement fields can be successfully removed,and strain fields can be reconstructed in the arbitrary area.

The smoothed finite element method (S-FEM):A framework for the design of numerical models for desired solutions

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects;2) upper-bound solutions;3) accurate solutions and higher convergence rates;4) insensitivity to mesh distortion;5) Jacobian?free;6) volumetric-locking-free;and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on Al-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

Selective Smoothed Finite Element Method

The paper examines three selective schemes for the smoothed finite element method （SFEM） which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method （FEM）. These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.

压电分流阵列板复能带结构计算的ES-FEM方法

为了提高压电分流阵列板复能带结构的计算精度,构造一种基于Mindlin假设的边光滑有限元法(ES-FEM)数值模型。以单个原胞为研究对象,采用三角形单元对其进行离散。基于背景单元的各条边,进一步构造相应的光滑域,依托梯度光滑技术(GST)建立光滑应变场。最后通过建立离散系统方程并结合Bloch定理对复能带结构进行求解,并进一步探究电学参量对带隙的影响规律。研究结果表明:ES-FEM方法能够有效提高压电分流阵列板复能带结构的计算精度;电阻和电感等参数分别对局域共振带隙的衰减峰值和位置有显著影响,而对布拉格带隙则影响较小。

含大石块泥石流冲击作用下框架结构房屋动力响应研究

基于光滑粒子流体动力学-有限元法(smoothed particle hydrodynamics-finite element method,SPH-FEM)耦合的数值方法,分别从结构破坏形态、冲击力时程、关键点位移和速度、系统能量等方面,研究含大石块泥石流冲击作用下框架结构房屋的动力响应和破坏机理。计算结果表明:SPH-FEM耦合方法能够较好地模拟泥石流冲击爬高、绕流扩散、淤积稳定过程。考虑了三种泥石流强度等级,在低、中强度冲击情况下,框架房屋填充墙受到破坏,房屋结构整体保持稳定;在高强度冲击情况下,可以观察到框架房屋的逐步倒塌过程,框架柱损坏模式体现了剪切破坏或塑性铰链失效机制。对于房屋结构而言,泥石流的冲击破坏能力主要来自龙头的冲击力,龙身冲击力相对于龙头降幅约34.2%,大石块的集中作用是结构柱体局部破坏的主要原因。系统能量主要通过泥石流动能转化为结构内能(17.8%)和摩擦耗能(82.8%)。

高铁大跨双肢墩连续刚构桥减震系梁地震易损性分析

为了解地震作用下减震系梁对高铁大跨双肢墩连续刚构桥的减震效果,以某主跨180 m的山区高铁双肢墩连续刚构桥为背景,分别建立采用钢筋混凝土(RC)系梁、2种新型减震系梁(可屈服钢系梁与斜交筒式黏弹性阻尼器系梁)方案的全桥有限元模型,对比分析不同系梁方案下的结构损伤、桥面平顺性指标等。结果表明:2种新型减震系梁均不会在地震作用下出现负刚度,新型减震系梁方案较RC系梁方案能有效降低系梁和主墩的结构损伤概率,主墩最大压应变降低83.3%;但减震系梁对震后桥面平顺性指标无明显改善,需采用更具针对性的技术措施。

二维复杂弹性空腔的边光滑有限元建模及分析

在弹性空腔结构上敷设被动约束层阻尼(passive constraint layer damping, PCLD)可达到减振降噪的效果,针对这类复杂结构建立了二维复合弹性空腔的边光滑有限元耦合动力学模型。其中,PCLD结构采用两节点四自由度的PCLD梁单元,声场采用边光滑有限元模型。以二维全敷设复合矩形空腔模型为数值算例,以精细网格下的有限元法结果作为参考解,对比研究了在相同背景网格下,边光滑有限元法和有限元法的频响结果,发现前者更接近参考解,说明同样的计算成本下,边光滑有限元法具有更高的精确性,特别是在中频计算中。最后,分析了PCLD结构对某汽车驾驶舱的降噪效果,以及黏弹层和约束层厚度参数的影响规律,发现黏弹层厚度增大,可一定程度上降低空腔噪声,而约束层厚度增大,并不能在整个频段得到很好的降噪效果。

接触与大变形问题的光滑有限元分析

橡胶材料因具有良好的抗震、吸能作用,在实际工程中应用广泛.然而橡胶超弹性材料的碰撞属于强非线性问题,分析橡胶材料的接触碰撞和大变形问题对于提高装置的缓冲性能具有重要意义.光滑有限元法(smoothed finite element method,S-FEM)是一种弱形式的数值计算方法,相比于传统的有限元方法,光滑有限元法对网格的质量要求不高,允许单元在计算过程中发生较大的变形,且光滑域的构造比较灵活,在不增加自由度的前提下,可以达到较高的精度.在光滑有限元法的基础上,采用双势方法进行接触计算,以充分利用光滑有限元法计算大变形问题的优点和双势方法求解接触力的优势.通过与有限元软件MSC.Marc的数值结果对比,验证了该算法的准确性和能量守恒性,并且分析了摩擦因数对碰撞体的影响.

基于新型快速收敛ES-FEM-T的三维固体黏弹塑性研究

虽然四面体网格具有强大的几何表征能力,但因其'过硬'特性而工程实践中较少采用。如何使四面体网格'变软'是目前数值计算研究重点。通过采用广义的应变光滑操作,对四面体网格采用一种新型基于四面体边的应变光滑方法(Edge-based smoothed finite element method of tetrahedron,ES-FEM-T),并将该方法拓展到三维固体中黏弹塑性材料分析中。数值算例表明:在相同的网格时,ES-FEM-T计算效率要高于有限元和基于面光滑操作的有限元。由于该方法既继承四面体强大的几何表征能力,具有较好的计算效率和精度,具有广阔的工程运用前景。

高超声速火箭橇凿削磨损机理分析

针对高超声速下火箭橇运行过程中凿削磨损产生的机理模糊不清问题,基于有限元-光滑粒子流体动力学法(FEM-SPH法),利用有限元软件ABAQUS构建了三维火箭橇靴-轨模型,FEM-SPH法是一种既能保证计算精度,又能克服网格畸变的新型模拟方法。在该模型中,滑靴和轨道所使用的材料分别为VascoMax 300钢、AISI 1080钢,并赋予各自材料属性,通过设定航向速度为2000 m/s,竖直速度为2.5 m/s以及温度为673 K,模拟了高超声速下靴-轨凿削磨损现象的演变过程。模拟结果表明:凿削磨损是在高温高应力作用下和靴-轨之间形成嵌入式结构后,经过持续地破坏滑靴底部所产生的,最终形成泪滴状蚀坑。进一步分析表明,竖直速度和温度的增加都会提高凿削发生的概率。在航向速度为2000 m/s、初始温度为673 K时,竖直速度超过1.50 m/s就会发生凿削现象;在航向速度为2000 m/s、竖直速度为2.5 m/s,温度超过293 K就会发生凿削现象。该研究成果不仅有助于高超声速下靴-轨凿削磨损的产生机理进一步完善,还为高超声速火箭橇试验的安全发射提供了新的理论支持。

声子晶体能带结构仿真的CS-FEM方法及其在拓扑优化设计中的应用

针对声子晶体拓扑优化设计时能带结构和灵敏度计算效率低的缺陷,构造了一种Cell-based光滑有限元法模型(CS-FEM),并结合双向渐进结构优化法(BESO)实现了声子晶体的带隙最大化设计。基于四边形单元构造光滑子域,将梯度光滑技术与Bloch定理结合,构建了声子晶体能带结构计算的CS-FEM数值模型,并将其用于正问题的仿真模拟。在渐进优化准则下,通过BESO算法完成了声子晶体的优化设计。数值算例表明:CS-FEM能够适当软化离散系统的刚度,提供更加准确、高效的能带结构仿真结果;基于CS-FEM进行正问题的计算,在优化设计中得到了最优的拓扑构型,并有效地提高了优化效率,对于实现声子晶体的高效设计具有重要的参考价值。

基于光滑有限元的隧道掌子面稳定性分析

隧道掌子面稳定是影响地下工程施工安全的重要问题之一。基于塑性上限和下限定理的极限分析方法是分析掌子面稳定性常用方法之一。其中,自适应混合常应力-光滑应变极限分析(MCSE-LA)方法在计算精度、效率以及收敛性方法已被证明比传统有限元极限分析方法具有一定的优势。基于此,首先验证自适应MCSE-LA在隧道掌子面稳定分析中的可行性,发现该方法求出的隧道掌子面稳定指标(稳定数)与传统有限元上限和下限法相同,同时,还可以通过基于最大剪应变率自适应网格加密技术获得掌子面失稳模式。另外,还将该方法用于分析隧道开挖未支护段长度对掌子面稳定性的影响,通过分析总结了稳定数随未支护长度的变化规律,对指导地下工程施工具有一定的意义。

刮板输送机中部槽耐磨性能优化与应用研究

为有效提高刮板输送机中部槽的耐磨性能和使用寿命,对中部槽结构进行优化设计。基于非光滑耐磨理论,使用SolidWorks和ANSYS软件建立了刮板输送机中部槽的三维有限元模型,对中部槽在光滑状态/非光滑状态下的接触应力进行模拟研究。结果表明:在中部槽中板表面设置凹槽结构可以显著改善摩擦磨损现象,提高耐磨性能;凹槽最优参数为直径2 mm、深度5 mm、横向及纵向间距50 mm,最大接触应力值为353.631MPa,下降幅度达到23.78%。将新结构中部槽应用于同忻煤矿8311工作面SGB620/80T刮板输送机,新结构中部槽结构及运行稳定,使用寿命提高1倍,对刮板输送机中部槽结构进行凹槽改进设计能有效地提高其耐磨性能,延长使用寿命,经济安全效益显著。