Meshfree Methods: Progress Made after 20 Years

Chen, Jiun Shyan; Hillman, Michael; Wei, Sheng

doi:10.1061/(asce)em.1943-7889.0001176

Cited by 353 publications

(123 citation statements)

References 300 publications

(537 reference statements)

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“…To the authors' knowledge, the only application of an S‐PIM to problems with physical nonlinearities is that in a paper by Zhang et al, where the NS‐PIM was used to investigate elastoplastic models. However, the nodal integration strategy, which the NS‐PIM is based on, had already been applied to nonlinear elasticity, elastoplasticity, and damage problems . Here, attention is focused on the application of both the NS‐PIM and ES‐PIM strategies to problems of continuum damage mechanics , represented in terms of the scalar‐isotropic damage models .…”

Section: Weakened Weak Form For Scalar Damagementioning

confidence: 99%

Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models

Gori

Penna

Pitangueira

2018

Numerical Meth Engineering

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Summary The nonlocal character embedded in the formulation of smoothed point interpolation methods is exploited, in order to regularize the behavior of the simulations of scalar damage problems affected by strain localization. The use of these methods is made possible by the extension of the weakened weak form that they are based on to the case of elastic‐degrading media, with specific focus on the scalar damage case. The provided numerical simulations emphasize the regularization effects of this class of meshfree methods and the improved mesh objectivity with respect to the standard finite element method. Different strategies for support node selection are considered, pointing out the role played by the size of the support domains regarding the regularization effects.

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Section: Weakened Weak Form For Scalar Damagementioning

confidence: 99%

Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models

Gori

Penna

Pitangueira

2018

Numerical Meth Engineering

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“…Crack modelling in 3‐dimensions (3D) is a challenging problem in computational fracture mechanics. The majority of the literature, as reviewed in the works of Nguyen et al and Chen et al, to date on computational fracture mechanics focuses on 2‐dimensional (2D) problems with assumptions of plane strain or plane stress to reduce complexity and for ease of comparison with analytical solutions. However, for any of these methods to be of real industrial use, robust 3D formulations are needed.…”

Section: Introductionmentioning

confidence: 99%

An adaptive cracking particle method providing explicit and accurate description of 3D crack surfaces

Augarde

2018

Numerical Meth Engineering

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Summary Cracks in 3‐dimensions (3D) have arbitrary shapes and therefore present difficulties for numerical modelling. A novel adaptive cracking particle method with explicit and accurate description of 3D cracks is described in this paper. In this meshless method, crack surfaces are described by a set of discontinuous segments, which are associated with particles. This group of particles are assumed all to be “cracked” and split into 2 subparticles with modified support domains. Compared to the original method where the spherical supports at particles are equally divided, the proposed method makes use of nonplanar segments to account for changes in crack face direction. The orientations of those segments and the angular changes of cracks during crack propagation steps are recorded using triangular meshes. Supports of weight functions are modified according to those changes so that quasi‐continuous crack surfaces can be obtained, avoiding the spurious cracking seen in earlier cracking particle methods. An adaptive approach in 3D is then introduced to capture stress gradients around crack fronts. Several 3D crack problems with reference results have been tested to validate the proposed method with good agreement being achieved using the new method, showing it to be potentially a significant advance for 3D fracture prediction problems.

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“…Trying to alleviate mainly the tedious meshing of the traditional element methods (especially FEM), meshfree methods do not require connection between nodes and the approximation of unknowns in the partial differential equations (PDEs) is constructed based on scattered points, within the problem domain and on its boundaries, without mesh connectivity (Chen et al, 2017). The earliest development of a meshfree method was the Smoothed Particle Hydrodynamics (SPH) introduced by Gingold and Monaghan (1977) and Lucy (1977) initially for astrophysical problems, while for solid mechanics the method has been applied by Libersky et al (1993).…”

mentioning

confidence: 99%

“…On the other hand, the collocation meshfree methods (see e.g., Kansa, 1990a,b;Chi et al, 2013) are classified in the strong form category, suffering from very ill-conditioned systems. For more information on meshfree methods, the interested reader can consult the excellent review paper by Chen et al (2017).…”

mentioning

confidence: 99%

Computational Structural Engineering: Past Achievements and Future Challenges

Plevris

Tsiatas

2018

Front. Built Environ.

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PAST ACHIEVEMENTS AND CURRENT TRENDSComputational methods are computer-based methods used to numerically solve mathematical models that describe physical phenomena. The purpose of computational modeling is to study the behavior of complex systems by means of computer simulations and it can be used to make predictions of the system's behavior under different conditions, often for cases in which intuitive analytical solutions are not available (Nature, 2018). Computational methods have emerged in engineering during the 1960s. Since then, structural engineers have been leaders in technological solutions to engineering analysis and design problems. The evolution of electronic computers together with the tremendous increase of computational power has triggered the continuous development of computational methods. Rapid advances in computer hardware have had a profound effect on various engineering disciplines. The applications are numerous and cover a broad field of engineering branches including civil, mechanical, naval, electrical, aerospace, material, biomolecular, among others. Computational structural engineering has evolved as an insightful blend combining both structural analysis and computer science.Among all computational methods, the Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most prevalent ones. Both methods exhibit unique characteristics as well as advantages and disadvantages. The FEM, as a simulation tool, enables sophisticated methods of computational mechanics, computer technology and applied mathematics. It has been broadly adopted in scientific research and engineering applications and it can be considered as the most popular method used for structural analysis, tackling linear and nonlinear problems of systems with various geometries, material properties and loads (Reddy, 2005). In FEM, the solution domain is subdivided into a finite number of elements. Each element approximately reproduces the behavior of a small region of the body it represents, but continuity between the elements is only enforced in an overall minimum energy sense. The FEM is especially suitable for problems with complex geometries, but the whole-body discretization scheme that is utilized inevitably leads to a large number of finite elements and, thus, increased computational cost. Although Professor R. Clough coined the term "Finite Element Method" in his pioneer work dated back in 1960 (Clough, 1960), the answer to the question "who invented FEM in everyday use?" is possibly M. Jonathan (Jon) Turner at Boeing who generalized and perfected the Direct Stiffness Method, and convinced his company to commit resources to it, over the period 1952 -1964(Felippa, 2017. The FEM obtained its real impetus in the 1960s and 1970s by the developments of pioneers J. H. Argyris, R. W. Clough, H. C. Martin, O. C. Zienkiewicz and their co-workers who evolved the method and applied it to a wide range of structural problems and applications.In the years since its first use, FEM has grown and developed into a standard...

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Meshfree Methods: Progress Made after 20 Years

Cited by 353 publications

References 300 publications

Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models

Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models

An adaptive cracking particle method providing explicit and accurate description of 3D crack surfaces

Computational Structural Engineering: Past Achievements and Future Challenges

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