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

Gui-Rong Liu

Frontiers of Structural and Civil Engineering 2019, Volume 13, Issue 2,   Pages 456-477 doi: 10.1007/s11709-019-0519-5

Abstract:

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.

Keywords： method     finite element method     smoothed finite element method     strain smoothing technique     smoothing domain     weakenedweak form     solid mechanics     softening effect     upper bound solution    

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Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics

A. SHAFIEI

Frontiers of Structural and Civil Engineering 2018, Volume 12, Issue 4,   Pages 527-535 doi: 10.1007/s11709-018-0450-1

Abstract: Peridynamics is a theory in solid mechanics that uses integral equations instead of partial differential equations as governing equations. It can be applied to fracture problems in contrast to the approach of fracture mechanics. In this paper by using peridynamics, the crack path for inclined crack under dynamic loading were investigated. The peridynamics solution for this problem represents the main features of dynamic crack propagation such as crack bifurcation. The problem is solved for various angles and different stress values. In addition, the influence of geometry on inclined crack growth is studied. The results are compared with molecular dynamic solutions that seem to show reasonable agreement in branching position and time.

Keywords： peridynamics     inclined crack     dynamic fracture     crack branching    

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Analysis and stabilization control of a voltage source controlled wind farm under weak grid conditions

Frontiers in Energy 2022, Volume 16, Issue 6,   Pages 943-955 doi: 10.1007/s11708-021-0793-5

Abstract: This paper investigates and discusses the interaction stability issues of a wind farm with weak gridHowever, when it is applied to multiple WTs within a wind farm, its weak-grid performance regarding theof a stability margin quantification index, not only the interactions between the wind farm and the weak

Keywords： weak grids     voltage source (VS) control     wind turbine (WT)     stabilization control     wind farm     inertial    

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Enhancement of sludge gravitational thickening with weak ultrasound

Panyue ZHANG, Tian WAN, Guangming ZHANG

Frontiers of Environmental Science & Engineering 2012, Volume 6, Issue 5,   Pages 753-760 doi: 10.1007/s11783-011-0368-5

Abstract: of sonication on enhancing the sludge gravitational thickening with very low energy dose, so called “weakResults showed that weak sonication significantly changed the sludge settlability and the main mechanismWeak sonication (<680 kJ·kg DS) improved the sludge gravitational thickening while high ultrasonic energyWeak sonication could substitute expensive polyelectrolyte coagulant for sludge thickening.Combination of weak sonication and polyelectrolyte could further reduce the settling time to 6 h.

Keywords： activated sludge     sonication     settlability     dry weight     extracellular polymeric substances     polyelectrolyte    

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Modeling and analysis of magnetic dipoles in weak magnetic field

WANG Zhaoxia, ZHANG Weimin, LIU Hongguang

Frontiers of Mechanical Engineering 2008, Volume 3, Issue 2,   Pages 222-225 doi: 10.1007/s11465-008-0028-z

Abstract: The formula to compute the normal component of the weak magnetic field is deduced based on the spatial

Keywords： geomagnetic     theory     important criterion     magnetic leakage     normal component    

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Stability analysis on Tingzikou gravity dam along deep-seated weak planes during earthquake

Weiping HE, Yunlong HE

Frontiers of Structural and Civil Engineering 2012, Volume 6, Issue 1,   Pages 69-75 doi: 10.1007/s11709-012-0146-x

Abstract: The stability of a gravity dam against sliding along deep-seated weak planes is a universal and importantThere is no recommended method for stability analysis of the dam on deep-seated weak planes under earthquakesearching a proper way to evaluate the seismic safety of the dam against sliding along deep-seated weakplanes and the probable failure modes of dam on deep-seated weak planes during earthquake.While there is no geological structure planes to form the second slip surface, the intersection of the

Keywords： gravity dam     deep-seated weak planes     stability against sliding     earthquake    

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Combination form analysis and experimental study of mechanical properties on steel sheet glass fiber

Frontiers of Structural and Civil Engineering 2021, Volume 15, Issue 4,   Pages 834-850 doi: 10.1007/s11709-021-0743-7

Abstract: An optimization plan was proposed in the combined form of SSGCB.Three-dimensional finite element analysis was adopted to perform the combination form optimization of

Keywords： steel sheet GFRP composite bar     combination form     numerical modeling     mechanical properties test     strength    

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Experimental study on the progressive failure and its anchoring effect of weak-broken rock vertical slope

Hehua ZHU, Qianwei XU, Wenqi DING, Feng HUANG

Frontiers of Structural and Civil Engineering 2011, Volume 5, Issue 2,   Pages 208-224 doi: 10.1007/s11709-011-0111-0

Abstract: To improve the understanding on the failure behavior and its anchoring effect of weak-broken rock slope

Keywords： progressive failure     weak-broken rock     slope     model test     bolt    

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General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

Frontiers of Mechanical Engineering 2022, Volume 17, Issue 2, doi: 10.1007/s11465-022-0681-7

Abstract: The novel algebraic geometric (NAG) methods that obtain the general closed-form inverse kinematics forindicating that the inverse solutions are consistent with the given joint angles validate the general closed-formAdditionally, the mean and maximum of the master–slave tracking experiment for the closed-form solutionThe experiments results demonstrate that the closed-form solution is superior to the compensation methodThe results verify the proposed general closed-form inverse kinematics based on the NAG methods.

Keywords： inverse kinematics     Paden–Kahan subproblems     three-joint subproblems     product of exponential     closed-form    

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Feedback linearization based control for weak grid connected PV system under normal and abnormal conditions

Rahul SHARMA,Sathans SUHAG

Frontiers in Energy 2020, Volume 14, Issue 2,   Pages 400-409 doi: 10.1007/s11708-017-0459-5

Abstract: This paper proposes a control strategy for interface of distributed energy sources into the weak gridThe controller proposed has been implemented on the PV system connected with the weak grid using the

Keywords： PV system     grid interface     feedback linearization     inverter     LCL filter    

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Wavelet design for extracting weak fault feature based on lifting scheme

JIANG Hong-kai, WANG Zhong-sheng, HE Zheng-jia

Frontiers of Mechanical Engineering 2006, Volume 1, Issue 2,   Pages 199-203 doi: 10.1007/s11465-006-0009-z

Abstract: Weak fault features of mechanical signals are usually immersed in noisy signals.A new wavelet method based on lifting scheme to match weak fault characteristics is proposed.engineering results confirm that the proposed method is better than other wavelet methods for extracting weakModulus maxima of the detail signal in every operation cycle are extracted, the position and time that weak

Keywords： misalignment     imbalance     particular     position     mechanical    

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Extended stochastic resonance (SR) and its applications in weak mechanical signal processing

Niaoqing HU, Min CHEN, Guojun QIN, Lurui XIA, Zhongyin PAN, Zhanhui FENG,

Frontiers of Mechanical Engineering 2009, Volume 4, Issue 4,   Pages 450-461 doi: 10.1007/s11465-009-0072-3

Abstract: This paper presents a method based on stochastic resonance (SR) to detect weak fault signal.Then, the frequency range of the weak signals that the SR model can detect is extended through a typeFinally, the method is applied to extract the weak characteristic component from heavy noise to indicate

Keywords： extended stochastic resonance (SR)     stability analysis of SR     scale transform     weak signal detection     incipient    

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Weak characteristic information extraction from early fault of wind turbine generator gearbox

Xiaoli XU, Xiuli LIU

Frontiers of Mechanical Engineering 2017, Volume 12, Issue 3,   Pages 357-366 doi: 10.1007/s11465-017-0423-4

Abstract:

Given the weak early degradation characteristic information during early fault evolution in gearboxA weak characteristic information extraction based on µ-SVD and local mean decompositionExperimental results show that this method can significantly weaken signal noise, effectively extract the weak

Keywords： wind turbine generator gearbox     µ-singular value decomposition     local mean decomposition     weak characteristic    

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New form of geodetic coordinate system taking two length quantity as coordinate parameters

Yimin SHI, Ziyang ZHU, Yeming FAN

Frontiers of Structural and Civil Engineering 2009, Volume 3, Issue 1,   Pages 105-110 doi: 10.1007/s11709-009-0014-5

Abstract: A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitudeThe first fundamental form on the ellipsoidal surface and its three coefficients were deduced by theconsequently, it is convenient and accurate enough to operate on the ellipsoidal surface in this new form

Keywords： geodetic coordinate system     meridian and parallel circle     coordinate parameter     the first fundamental form    

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Subcellular distribution and chemical form of Pb in hyperaccumulator

Yanqun ZU,Yuan LI,Huan MIN,Fangdong ZHAN,Li QIN,Jixiu WANG

Frontiers of Environmental Science & Engineering 2015, Volume 9, Issue 2,   Pages 250-258 doi: 10.1007/s11783-014-0643-3

Abstract: Solution culture was conducted in order to understand accumulation characteristics and chemical forms of Pb in ( ) and the response of root exudates to Pb addition. The results showed that: 1) Pb contents in the shoot and root of increased with increasing in Pb concentrations in solution. 2) The contents of Pb chemical forms under Pb addition followed as: HAc extractable fraction (F )>HCl extractable fraction (F )>NaCl extractable fraction (F )>ethanol-extractable fraction (F )>water extractable fraction (F ). 3) Increased Pb level in the medium caused increases in Pb contents in the four subcellular fractions of shoots and roots, with most accumulation in FIV (Fraction IV, soluble fraction) in shoots and FI (Fraction I, cell wall fraction) in roots. 4) Contents of soluble sugar and free amino acid of root exudates increased with increasing Pb concentration in solution. Significantly positive correlations between Pb and contents of soluble sugar and free amino acid were observed. 5) With Pb concentrations in solution, low molecular weight organic acids (LMWOAs) contents followed the tendency: tartaric acid>acetic acid>malic acid>citric acid. Significantly positive correlation was observed between Pb and citric acid contents. The results indicate that soluble sugars, free amino acid and citric acid in root exudates of facilitate the absorption and accumulation of Pb, which exist in NaCl-, HCl- and HAc- extractable Pb forms, FI and FIV fractions, resulting in tolerance of to Pb.

Keywords： Pb     Arenaria orbiculata     chemical forms     subcellular distribution     root exudates     hydroponic culture    

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Title Author Date Type Operation

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

Gui-Rong Liu

Journal Article

Dynamic crack propagation in plates weakened by inclined cracks: an investigation based on peridynamics

A. SHAFIEI

Journal Article

Analysis and stabilization control of a voltage source controlled wind farm under weak grid conditions

Journal Article

Enhancement of sludge gravitational thickening with weak ultrasound

Panyue ZHANG, Tian WAN, Guangming ZHANG

Journal Article

Modeling and analysis of magnetic dipoles in weak magnetic field

WANG Zhaoxia, ZHANG Weimin, LIU Hongguang

Journal Article

Stability analysis on Tingzikou gravity dam along deep-seated weak planes during earthquake

Weiping HE, Yunlong HE

Journal Article

Combination form analysis and experimental study of mechanical properties on steel sheet glass fiber

Journal Article

Experimental study on the progressive failure and its anchoring effect of weak-broken rock vertical slope

Hehua ZHU, Qianwei XU, Wenqi DING, Feng HUANG

Journal Article

General closed-form inverse kinematics for arbitrary three-joint subproblems based on the product of

Journal Article

Feedback linearization based control for weak grid connected PV system under normal and abnormal conditions

Rahul SHARMA,Sathans SUHAG

Journal Article

Wavelet design for extracting weak fault feature based on lifting scheme

JIANG Hong-kai, WANG Zhong-sheng, HE Zheng-jia

Journal Article

Extended stochastic resonance (SR) and its applications in weak mechanical signal processing

Niaoqing HU, Min CHEN, Guojun QIN, Lurui XIA, Zhongyin PAN, Zhanhui FENG,

Journal Article

Weak characteristic information extraction from early fault of wind turbine generator gearbox

Xiaoli XU, Xiuli LIU

Journal Article

New form of geodetic coordinate system taking two length quantity as coordinate parameters

Yimin SHI, Ziyang ZHU, Yeming FAN

Journal Article

Subcellular distribution and chemical form of Pb in hyperaccumulator

Yanqun ZU,Yuan LI,Huan MIN,Fangdong ZHAN,Li QIN,Jixiu WANG

Journal Article