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.

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.

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 Smoothed Finite Element Method for the Static and Free Vibration Analysis of Shells

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

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.

Multi-resolution technique integrated with smoothed particle element method (SPEM) for modeling fluid-structure interaction problems with free surfaces

Free-surface flows, especially those associated with fluid-structure interactions(FSIs), pose challenging problems in numerical simulations. The authors of this work recently developed a smoothed particle element method(SPEM) to simulate FSIs. In this method, both the fluid and solid regions are initially modeled using a smoothed finite element method(S-FEM) in a Lagrangian frame, whereas the fluid regions undergoing large deformations are adaptively converted into particles and modeled with an improved smoothed particle hydrodynamics(SPH) method. This approach greatly improves computational accuracy and efficiency because of the advantages of the S-FEM in efficiently treating solid/fluid regions showing small deformations and the SPH method in effectively modeling moving interfaces. In this work, we further enhance the efficiency of the SPEM while effectively capturing local fluid information by introducing a multi-resolution technique to the SPEM and developing an effective approach to treat multi-resolution element-particle interfaces. Various numerical examples demonstrate that the multiresolution SPEM can significantly reduce the computational cost relative to the original version with a constant resolution.Moreover, the novel approach is effective in modeling various incompressible flow problems involving FSIs.

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO:A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging(A-Kriging)into an improved partial swarm optimization algorithm(IPSO)to give a so-called A-Kriging-IPSO for maximizing the buckling load of laminated composite plates(LCPs)under uniaxial and biaxial compressions.In this method,a novel iterative adaptive Kriging model,which is structured using two training sample sets as active and adaptive points,is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process.The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples.The cell-based smoothed discrete shear gap method(CS-DSG3)is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets.The buckling load of the LCPs is maximized by utilizing the IPSO algorithm.To demonstrate the efficiency and accuracy of the proposed methodology,the LCPs with different layers(2,3,4,and 10 layers),boundary conditions,aspect ratios and load patterns(biaxial and uniaxial loads)are investigated.The results obtained by proposed method are in good agreement with the literature results,but with less computational burden.By applying adaptive radial Kriging model,the accurate optimal resultsebased predictions of the buckling load are obtained for the studied LCPs.

A strain smoothing formulation for NURBS-based isogeometric finite element analysis

A strain smoothing formulation for NURBS (non-uniform rational B-splines) based isogeometric finite element analysis is presented. This approach is formulated within the framework of assumed strain methods and strain smoothing operations. The strain smoothing is defined through strain averaging in the element sub-domains which are subsequently used for numerical integration of the Galerkin weak form. This formulation satisfies the orthogonality condition of the assumed strain methods. Meanwhile the present formulation totally avoids the gradient computation of the rational NURBS basis functions in the formulation of stiffness matrix. A transformation method is employed to accurately enforce the displacement boundary conditions. Numerical results demonstrate that the present formation gives very satisfactory solution accuracy simultaneously with improved computational efficiency.

一种适用宽速域冲击的明胶鸟弹数值建模方法

明胶鸟弹在不同撞击速度下表现出不同的响应特性。为解决传统明胶鸟弹本构表征方法在不同速度范围内不能通用的问题,开展了330 g明胶鸟弹以70~190 m/s速度、60°或90°入射刚性铝合金平板试验,记录了冲击力数据及撞击形貌。结果表明,随着撞击速度的提高,鸟弹碎裂得更充分,碎块体积减小。利用LS-DYNA建立了自适应FEM-SPH(finite element method-smoothed particle hydrodynamics)鸟体模型。依据试验结果反演得到一组鸟体本构参数:切线模量为1.33MPa,剪切模量为115.95MPa,Murnaghan状态方程参数γ为10.49,k_(0)为69.77 MPa,体积模量为246.4 MPa,失效塑性应变为1.15,初始屈服应力为0.21 MPa。仿真结果与试验结果具有很好的一致性,冲击力峰值的相对误差在2%以内,冲量的相对误差在10%以内。自适应FEM-SPH鸟体模型具有比SPH模型和拉格朗日模型更高的精度。由自适应模型得到的Hugoniot压强与理论结果具有相同的变化趋势,滞止压强与理论值较接近。

大型风力机叶片前缘的雨滴冲击动力学响应机制

随着近年海上风力机设计的大型化,叶片前缘的雨蚀失效问题变得愈发突出,不仅影响机组的风能转化效率,对结构的稳定运行也构成潜在威胁。采用光滑粒子流体动力学(smooth particle hydrodynamics,SPH)法研究雨滴内部的本构关系,以有限元法(finite element method,FEM)建立叶片前缘的代表性体积单元(representative volume element,RVE)模型,两者相互耦合,研究雨滴在叶片表面形成的冲击响应过程。考虑自然降雨的实际工况,建立与降雨强度相关联的雨滴尺寸模型,以及雨滴的空间分布模型;通过单雨滴的冲击仿真,研究叶片表面冲击载荷以及雨滴内部的速度分布,从而解构雨滴冲击的物理过程,并通过冲击的应力、应变场分析,为潜在损伤区提供评价;建立多雨滴冲击的仿真模型,研究冲击应力场之间的耦合作用以及涂层表面的塑性应变累积效果。研究结果表明,水锤冲击是造成塑性应变累积的关键因素,虽然横向喷射阶段的应力响应幅值小并呈现一定的无序特征,但如果存在多雨滴耦合冲击的情况,则会在耦合区内出现应力峰值,并对叶片变形和失效存在潜在影响。

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%)。

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。

掏槽爆破成腔空孔效应数值模拟研究与分析

掏槽爆破是巷道掘进单自由面爆破的关键。为探究空孔对掏槽爆破效果的影响,基于空孔作用理论,利用有限元-粒子流耦合方法,建立单空孔掏槽爆破三维数值模型,并结合现场掏槽爆破试验结果,分析多段掏槽爆破空孔附近岩石应力分布特征,岩石破碎、抛掷及槽腔成形过程对空孔响应规律。研究结果表明:空孔对近场岩石应力场的分布具有导向作用,并在空孔周围形成明显的应力集中效应,增加应力高峰值区范围,进而为后续爆破提供有利条件;岩石抛掷效果以及槽腔大小与空孔之间表现出强相关性,单空孔掏槽爆破与无空孔相比,抛掷速度提升34.7%,抛掷效率提高了10.2%,现场试验中腔体体积增加17.1%,掏槽深度增加了16.3%,但槽腔整体形状变化不明显;研究结果对实际掏槽爆破参数设计和优化提供了部分理论依据。

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。

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。