Development of an explicit smoothed particle finite element method for geotechnical applications

Yuan, Wei‐Hai; Wang, Bin; Zhang, Wei; Jiang, Quan; Feng, Xia‐Ting

doi:10.1016/j.compgeo.2018.10.010

Cited by 71 publications

(61 citation statements)

References 23 publications

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“…For a large deformation calculation in geotechnical engineering, especially using an explicit time integration method, this numerical error is acceptable. The obtained result is also compared with various reference solutions (da Silva et al, Prandtl , and Meyerhof ) and other numerical solutions (PFEM , MPM , ALE , iSPFEM , and eSPFEM using a node integration scheme). All results are located between the analytical solution obtained by Prandtl (( π +2) c u = 5.14 c u ) and the limit load obtained by Meyerhof ((2 π +2) c u = 8.28 c u ).…”

Section: Numerical Examplessupporting

confidence: 58%

“…Since the SPFEM adopts the explicit integration scheme rather than the standard PFEM using the implicit integration scheme, it is reasonable that oscillations of the blue curve by SPFEM seem larger with respect to the oscillations of the curve of the standard PFEM. This can also be found in various calculations and comparisons . For a large deformation calculation in geotechnical engineering, especially using an explicit time integration method, this numerical error is acceptable.…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Furthermore, the obtained curve is higher than the eSPFEM and iSPFEM solutions, which is attributed to the difference of adopted strain smoothing techniques. In eSPFEM and iSPFEM , the node‐based strain smoothing method is adopted, which is known as “overly soft” or underestimation property and thus offers an upper bound solution . In the proposed SPFEM, the edge‐based strain smoothing method is used, which has a close‐to‐exact stiffness and often offers super‐convergent and very accurate solutions .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…For SPH, EFG, MPM, and CEL, applying boundary conditions is difficult and, moreover, is always inaccurate when solving small-deformation problems or during the early stages of large-deformation problems. By contrast, PFEM that is developed to solve fluid-structure interaction problems (Oñate et al 17,21,22 ) and fluid only problems 23,24 can be employed as an ideal method for avoiding the aforementioned problems and has recently been used to solve problems in geomechanics [25][26][27][28][29][30][31][32][33] . The key feature of PFEM is that nodes are regarded as "particles" and the continuum medium as a cloud of these particles, which transport all the information of the continuum medium (eg, displacements, strains, stresses, material properties, and state variables), allow free movement and even separation from the continuum to which they originally belong.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

Jin

Yuan

Yin

et al. 2020

Num Anal Meth Geomechanics

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Summary To solve large deformation geotechnical problems, a novel strain‐smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge‐based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node‐based smoothed PFEM when lower‐order triangular element is used. Compared with the node‐based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super‐convergent and very accurate solutions due to the implementation of edge‐based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.

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Section: Numerical Examplessupporting

confidence: 58%

Section: Numerical Examplesmentioning

confidence: 98%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

Jin

Yuan

Yin

et al. 2020

Num Anal Meth Geomechanics

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“…Recently [56,124,126] proposed to use nodal integration rather than the Gaussian one to improve the preservation of historical variables. In nodal integration schemes, all variables (including stresses and strains) are stored at the nodes.…”

Section: Historical Variable Recoverymentioning

confidence: 99%

A State of the Art Review of the Particle Finite Element Method (PFEM)

Cremonesi

Franci

Idelsohn

et al. 2020

Arch Computat Methods Eng

116

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The particle finite element method (PFEM) is a powerful and robust numerical tool for the simulation of multi-physics problems in evolving domains. The PFEM exploits the Lagrangian framework to automatically identify and follow interfaces between different materials (e.g. fluid–fluid, fluid–solid or free surfaces). The method solves the governing equations with the standard finite element method and overcomes mesh distortion issues using a fast and efficient remeshing procedure. The flexibility and robustness of the method together with its capability for dealing with large topological variations of the computational domains, explain its success for solving a wide range of industrial and engineering problems. This paper provides an extended overview of the theory and applications of the method, giving the tools required to understand the PFEM from its basic ideas to the more advanced applications. Moreover, this work aims to confirm the flexibility and robustness of the PFEM for a broad range of engineering applications. Furthermore, presenting the advantages and disadvantages of the method, this overview can be the starting point for improvements of PFEM technology and for widening its application fields.

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Development of an explicit time integration algorithm based on optimal integration parameter updating

Fu,

Li,

2023

Earthq Engng Struct Dyn

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Integration algorithm is an important mean to solve the discrete time equations of structural dynamics in earthquake engineering. In this paper, a new model‐based explicit integration algorithm, featured by optimization‐based integration parameter updating, is developed for a more accurate and efficient solution of structural dynamic problems. The new integration algorithm is designed to yield minimum error and controllable numerical dispersion under the premise of stability by defining objective functions and constraints. Numerical properties of the new integration algorithm are investigated in details using the amplification matrix method for a linear elastic single degree‐of‐freedom system. Meanwhile, representative numerical examples and complex structure examples are analyzed and compared with other representative algorithms. As a result, the proposed algorithm yields comparable numerical characteristics with other methods, but exhibits pronounced superiority in controllable algorithmic dissipation, higher precision, and better efficiency. Therefore, the new integration algorithm possesses extensive application prospect in solving complicated linear and nonlinear structural dynamic problems.

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Development of an explicit smoothed particle finite element method for geotechnical applications

Cited by 71 publications

References 23 publications

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

An edge‐based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

A State of the Art Review of the Particle Finite Element Method (PFEM)

Development of an explicit time integration algorithm based on optimal integration parameter updating

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