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

Gui-Rong Liu

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 456-477 doi: 10.1007/s11709-019-0519-5

摘要：

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 AI-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 on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

关键词： computational method finite element method smoothed finite element method strain smoothing technique smoothing domain weakened weak form solid mechanics softening effect upper bound solution

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3D finite element method (FEM) simulation of groundwater flow during backward erosion piping

Kristine VANDENBOER,Vera van BEEK,Adam BEZUIJEN

《结构与土木工程前沿（英文）》 2014年第8卷第2期页码 160-166 doi: 10.1007/s11709-014-0257-7

摘要： Backward erosion piping is an important failure mechanism for cohesive water retaining structures which are founded on a sandy aquifer. At present, the prediction models for safety assessment are often based on 2D assumptions. In this work, a 3D numerical approach of the groundwater flow leading to the erosion mechanism of backward erosion piping is presented and discussed. Comparison of the 2D and 3D numerical results explicitly demonstrates the inherent 3D nature of the piping phenomenon. In addition, the influence of the seepage length is investigated and discussed for both piping initiation and piping progression. The results clearly indicate the superiority of the presented 3D numerical model compared to the established 2D approach. Moreover, the 3D numerical results enable a better understanding of the complex physical mechanism involved in backward erosion piping and thus can lead to a significant improvement in the safety assessment of water retaining structures.

关键词： backward erosion piping groundwater flow 3D finite element method (FEM)

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Two-scale modeling of granular materials: A FEM-FEM approach

Yun-Zhu CAI, Yu-Ching WU

《结构与土木工程前沿（英文）》 2013年第7卷第3期页码 304-315 doi: 10.1007/s11709-013-0213-y

摘要： In the present paper, a homogenization-based two-scale FEM-FEM model is developed to simulate compactions of visco-plastic granular assemblies. The granular structure consisting of two-dimensional grains is modeled by the microscopic finite element method at the small-scale level, and the homogenized viscous assembly is analyzed by the macroscopic finite element method at large-scale level. The link between scales is made using a computational homogenization method. The two-scale FEM-FEM model is developed in which each particle is treated individually with the appropriate constitutive relations obtained from a representative volume element, kinematic conditions, contact constraints, and elimination of overlap satisfied for every particle. The method could be used in a variety of problems that can be represented using granular media.

关键词： homogenization two-scale representative volume element compaction granular assembly finite element method

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Concurrent fatigue crack growth simulation using extended finite element method

Zizi LU, Yongming LIU,

《结构与土木工程前沿（英文）》 2010年第4卷第3期页码 339-347 doi: 10.1007/s11709-010-0078-2

摘要： In this paper, a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method (X-FEM) for fatigue crack growth simulation. The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis. The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method. The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings. The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis. Model predictions are compared with available experimental observations for model validation.

关键词： small time scale model extended finite element method (X-FEM) crack growth multiaxial

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FEM-based strain analysis study for multilayer sheet forming process

Rongjing ZHANG,Lihui LANG,Rizwan ZAFAR

《机械工程前沿（英文）》 2015年第10卷第4期页码 373-379 doi: 10.1007/s11465-015-0371-9

摘要：

Fiber metal laminates have many advantages over traditional laminates (e.g., any type of fiber and resin material can be placed anywhere between the metallic layers without risk of failure of the composite fabric sheets). Furthermore, the process requirements to strictly control the temperature and punch force in fiber metal laminates are also less stringent than those in traditional laminates. To further explore the novel method, this study conducts a finite element method-based (FEM-based) strain analysis on multilayer blanks by using the 3A method. Different forming modes such as wrinkling and fracture are discussed by using experimental and numerical studies. Hydroforming is used for multilayer forming. The Barlat 2000 yield criteria and DYNAFORM/LS-DYNA are used for the simulations. Optimal process parameters are determined on the basis of fixed die-binder gap and variable cavity pressure. The results of this study will enhance the knowledge on the mechanics of multilayer structures formed by using the 3A method and expand its commercial applications.

关键词： finite element method (FEM) strain analysis multilayer sheet forming

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Ribbon bridge in waves based on hydroelasticity theory

Cong WANG, Shixiao FU, Weicheng CUI

《结构与土木工程前沿（英文）》 2009年第3卷第1期页码 57-62 doi: 10.1007/s11709-009-0005-6

摘要： For the design and operation of a floating bridge, the understanding of its hydroelastic behavior in waves is of great importance. This paper investigated the hydroelastic performances of a ribbon bridge under wave action. A brief introduction on the estimation of dynamic responses of the floating bridge and the comparisons between the experiments and estimation were presented. Based on the 3D hydroelasticity theory, the hydroelastic behavior of the ribbon bridge modeled by finite element method (FEM) was analyzed by employing the mode superposition method. And the relevant comparisons between the numerical results and experimental data obtained from one tenth scale elastic model test in the ocean basin were made. It is found that the present method is applicable and adaptable for predicting the hydroelastic response of the floating bridge in waves.

关键词： hydroelasticity ribbon bridge wave finite element method (FEM)

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Dynamic analysis of a rig shafting vibration based on finite element

Van Thanh NGO, Danmei XIE, Yangheng XIONG, Hengliang ZHANG, Yi YANG

《机械工程前沿（英文）》 2013年第8卷第3期页码 244-251 doi: 10.1007/s11465-013-0264-8

摘要：

In recently, finite elements method (FEM) has been used most popular for analysis of stress, vibration, heat flow and many other phenomena. Taking a rig shafting as an example, this paper studies the lateral vibration of the rig shafting with multi-degree-of-freedom by using FEM. The FEM model is created and the eigenvalues and eigenvectors are calculated and analyzed to find natural frequencies, critical speeds, mode shapes and unbalance responses. Then critical and mode shapes are determined. Finally, responses of unbalance force are analyzed in case of undamped and damped system, and peaks of response are compared.

关键词： Finite element method (FEM) lateral vibration rig shafting rotor-bearing system dynamic characteristics

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Fatigue of asphalt binder, mastic and mixture at low temperature

Dong WANG, Linbing WANG, Guoqing ZHOU

《结构与土木工程前沿（英文）》 2012年第6卷第2期页码 166-175 doi: 10.1007/s11709-012-0157-7

摘要： The fatigue damage is one of the most common distresses observed on the asphalt concrete pavement. To thoroughly understand the fatigue of asphalt concrete, the behaviors of the major components of asphalt concrete under cyclic loading are investigated respectively in this study. A new experiment method is developed to evaluate the performances of asphalt binder, mastic and fine aggregates mixture under cyclic tensile loading. The fatigue test results of asphalt binder show that the fatigue performance of asphalt binder is closely related with loading magnitude, temperature and loading rate. Mastic specimens with different filler content are tested and the results indicate that mastic specimens with 30% filler content show better fatigue resistance and higher permanent strain. The micro-structure analysis of mastic and mixture indicates that the fatigue resistance is closely related with the air void content of specimen. 3D digital specimens are developed to model the fatigue of the asphalt binder, mastic and mixture specimens based on the finite element method (FEM). Fatigue damage of asphalt concrete is simplified by a damage model. With proper selection of damage parameters, the simulation results agree well with laboratory test results and can be used as a basis for future fatigue research.

关键词： fatigue asphalt mixture asphalt binder mastic finite element method (FEM) X-ray tomography

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Maximum entropy based finite element analysis of porous media

Emad NOROUZI, Hesam MOSLEMZADEH, Soheil MOHAMMADI

《结构与土木工程前沿（英文）》 2019年第13卷第2期页码 364-379 doi: 10.1007/s11709-018-0470-x

摘要： The maximum entropy theory has been used in a wide variety of physical, mathematical and engineering applications in the past few years. However, its application in numerical methods, especially in developing new shape functions, has attracted much interest in recent years. These shape functions possess the potential for performing better than the conventional basis functions in problems with randomly generated coarse meshes. In this paper, the maximum entropy theory is adopted to spatially discretize the deformation variable of the governing coupled equations of porous media. This is in line with the well-known fact that higher-order shape functions can provide more stable solutions in porous problems. Some of the benchmark problems in deformable porous media are solved with the developed approach and the results are compared with available references.

关键词： maximum entropy FEM fully coupled multi-phase system porous media

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Flexural-torsional buckling behavior of aluminum alloy beams

Xiaonong GUO,Zhe XIONG,Zuyan SHEN

《结构与土木工程前沿（英文）》 2015年第9卷第2期页码 163-175 doi: 10.1007/s11709-014-0272-8

摘要： This paper presents an investigation on the flexural-torsional buckling behavior of aluminum alloy beams (AAB). First, based on the tests of 14 aluminum alloy beams under concentrated loads, the failure pattern, load-deformation curves, bearing capacity and flexural-torsional buckling factor are studied. It is found that all the beam specimens collapsed in the flexural-torsional buckling with excessive deformation pattern. Moreover, the span, loading location and slenderness ratio influence the flexural-torsional buckling capacity of beams significantly. Secondly, besides the experiments, a finite element method (FEM) analysis on the flexural-torsional buckling behavior of AAB is also conducted. The main parameters in the FEM analysis are initial imperfection, material property, cross-section and loading scheme. According to the analytical results, it is indicated that the FEM is reasonable to capture mechanical behavior of AAB. Finally, on the basis of the experimental and analytical results, theoretical formulae to estimate the flexural-torsional buckling capacity of AAB are proposed, which could improve the application of present codes for AAB.

关键词： flexural-torsional buckling aluminum alloy beams (AAB) finite element method (FEM) theoretical formula

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Special Column on Multiscale Stochastic Finite Element Method

《结构与土木工程前沿（英文）》 2015年第9卷第2期页码 105-106 doi: 10.1007/s11709-015-0297-7

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Numerical investigation of the ultimate lateral resistance of piles in soft clay

Konstantinos P. TZIVAKOS,Michael J. KAVVADAS

《结构与土木工程前沿（英文）》 2014年第8卷第2期页码 194-200 doi: 10.1007/s11709-014-0251-0

摘要： The paper presents a numerical study on the undrained lateral response of a single, free-head, reinforced concrete pile in soft clays. Soil conditions simulating normally consolidated clays are examined—undrained shear strength increasing with depth—and the pile-soil interaction under static lateral loading is analyzed. The nonlinear ? curves proposed in literature for soft clays are imported into a beam-on-nonlinear-Winkler-foundation simulation in order to predict the pile head lateral load—displacement curve and the distribution of the horizontal displacement and bending moment along the pile. The striking differences among these methods require further investigation via 3D finite element analyses. The determination of the ultimate soil resistance from the results of the finite element analyses aims at providing the estimation of a range of values for the ultimate soil resistance coefficient with depth and the comparison of the derived values to the corresponding ones proposed by existing methodologies.

关键词： laterally loaded pile soft clay p?y curves finite element method (FEM)

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Applying the spectral stochastic finite element method in multiple-random field RC structures

Abbas YAZDANI

《结构与土木工程前沿（英文）》 2022年第16卷第4期页码 434-447 doi: 10.1007/s11709-022-0820-6

摘要： This paper uses the spectral stochastic finite element method (SSFEM) for analyzing reinforced concrete (RC) beam/slab problems. In doing so, it presents a new framework to study how the correlation length of a random field (RF) with uncertain parameters will affect modeling uncertainties and reliability evaluations. It considers: 1) different correlation lengths for uncertainty parameters, and 2) dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete structures. To show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability, two examples of RC beams and slabs have been investigated. According to the results, the RF correlation length is effective in modeling uncertainties and evaluating reliabilities; the longer the correlation length, the greater the dispersion range of the structure response and the higher the failure probability.

关键词： uncertainty spectral stochastic finite element method correlation length reliability assessment reinforced concrete beam/slab

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Multiscale stochastic finite element method on random field modeling of geotechnical problems – a fast

Xi F. XU

《结构与土木工程前沿（英文）》 2015年第9卷第2期页码 107-113 doi: 10.1007/s11709-014-0268-4

摘要： The Green-function-based multiscale stochastic finite element method (MSFEM) has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.

关键词： multiscale finite element settlement perturbation random field geotechnical

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Structural characteristics of cement-stabilized soil bases with 3D finite element method

Yunfeng PENG, Yunlong HE,

《结构与土木工程前沿（英文）》 2009年第3卷第4期页码 428-434 doi: 10.1007/s11709-009-0059-5

摘要： Cement-stabilized soil bases have been widely used in expressways due to its high strength, appropriate stiffness, good water resistance, and frost resistance. So far, the structural characteristics and mechanical behaviors of cement-stabilized soil bases were not investigated so much. In this paper, the 3D elastic-plastic finite element method (FEM) was used to analyze the mechanical behaviors and structural characteristics of cement-stabilized soil bases from construction to operation. The pavement filling and the traffic loading processes were simulated, and a contact model was used to simulate the contact behavior between each layer of the pavement. Considering the construction process, the structural characteristics and mechanical behaviors of cement-stabilized soil bases were studied under asphalt-concrete pavement conditions. Furthermore, the general rules of deformations and stresses in cement-stabilized soil bases under different conditions were discussed, and some suggestions were put forward for the design and construction of cement-stabilized soil bases.

关键词： different strength asphalt-concrete pavement FEM appropriate stiffness