Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: In this paper, the meshless local Petrov-Galerkin (MLPG) method is implemented for mesh-free integration and numerical tests show the mesh-based integration method to be accurate and robust.
Abstract: In meshless methods based on weak formulation, the governing integral equation is obtained from the weak form of elasticity over global or local domains. Many of the so-called meshless methods, such as the element-free Galerkin (EFG) method [Belytschko T, Lu YY, Gu L. Element-free Galerkin methods. Int J Numer Methods Eng 1994;37:229–56], are based on the global weak form over the entire domain. The local weak forms are the basis of the meshless local Petrov–Galerkin (MLPG) [Atluri SN, Shen S. The meshless local Petrov–Galerkin (MLPG) method. Stuttgart: Tech Science Press; 2002] method. The integration of the resulting discrete set of algebraic equations are complex and require strategies using a large number of integration points, and may, therefore, be time-consuming. A possible improvement is the use of the Monte Carlo integration technique. The technique is straightforward and efficient, and is simpler and easier compared with other global or local integration methods. The method is implemented for MLPG and EFG methods. Numerical tests show the mesh-free integration method to be accurate and robust. Various Quasi-Monte Carlo sequences are performed and compared. These sequences are examined for three-dimensional elasticity problems. The numerical results prove the efficiency of the integration techniques for both meshless formulations tested.
16 citations
TL;DR: The historical development of Meshless method is outlined, shortcomings of the SPH method, it’s solution, and recent development has been reviewed for different applications.
16 citations
TL;DR: The meshless local Petrov-Galerkin method with a mixed formulation to impose Dirichlet boundary conditions is investigated and results show that the proposed technique leads to a good tradeoff between computational time and precision.
Abstract: The meshless local Petrov-Galerkin method (MLPG) with a mixed formulation to impose Dirichlet boundary conditions is investigated in this paper. We propose the use of Shepard functions for inner nodes combined with the radial point interpolation method with polynomial terms (RPIMp) for nodes over the Dirichlet boundaries. Whereas the Shepard functions have lower computational costs, the RPIMp imposes the essential boundary conditions in a direct manner. Results show that the proposed technique leads to a good tradeoff between computational time and precision.
16 citations
TL;DR: A review of recent progress made towards the applications of the meshfree particle methods (MPMs) for solving coupled fluid-structure interaction (FSI) problems and suggest potential avenues to explore the full potential of MPM capabilities for the solution of coupled problems.
Abstract: This paper presents a review of recent progress made towards the applications of the meshfree particle methods (MPMs) for solving coupled fluid-structure interaction (FSI) problems. Meshfree methods are categorized based on their mathematical formulation and treatment of computational data points. The advantages and limitations of these methods, particularly related to FSI applications, have been identified. A detailed account of salient work related to the FSI problems involving complex geometries, viscous flows, and large structural deformations has been presented and the benchmark solutions are identified for future research. Compared to their mesh-based counterparts, MPMs are found better suited in negotiating moving boundaries and complex geometries, features that are the hallmark of FSI problems. However, the biggest challenge to their wider acceptability is their implementation and programming complexity, higher computational cost, and lack of commercial software packages. So far, meshfree methods have mostly been limited to applications, where conventional methods show limited performance. Owing to its promising growth potential, partitioned FSI is the prime emphasis of this paper. Various aspects of partitioned FSI have been identified and classified for meshfree FSI problems, which include problem formulation strategies, domains discretization approaches, solver coupling methodology, interface treatment, benchmark problems, computational load, and availability of commercial software. Furthermore, various challenges involved in employing MPMs for FSI have also been identified and discussed along with the state-of-the-art techniques used in meshfree methods and FSI applications, and a future way forward has been proposed. In essence, this paper is an effort to identify and classify key aspects of MPM applications for FSI and suggest potential avenues to explore the full potential of MPM capabilities for the solution of coupled problems.
16 citations
TL;DR: As B-spline basis functions pose favorable properties such as easy to construct to any arbitrary order/degree, can be easily designed to pose the Kronecker delta property, the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method.
16 citations