The meshless analysis of wave propagation based on the Hermit-type RRKPM

Jian, Ma; Gao, Hongfen; Wei, Gaofeng; Qiao, Jinwei

doi:10.1016/j.soildyn.2020.106154

Cited by 9 publications

(6 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To eliminate the adverse effects of the different kernel functions on computational accuracy, the radial basis function (RBF) is introduced into RKPM, and the radial basis reproducing kernel particle method (RRKPM) is proposed by Liu et al [30]. Ma et al [31] introduced the normal derivative of RBF into RKPM and proposed a Hermit-type RKPM. This method is applied to elastic mechanics problems, and its advantages and development potential in terms of accuracy and convergence rate are tested.…”

Section: High-accuracy Sph Algorithmsmentioning

confidence: 99%

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Wang

Yang

et al. 2023

Acta Mech. Sin.

View full text Add to dashboard Cite

Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has broad prospects in modeling a wide range of problems in engineering and science, including extremely large deformation problems such as explosion and high velocity impact. This paper aims to provide a comprehensive overview on the recent advances of SPH method in the fields of fluid, solid, and biomechanics. First, the theory of SPH is described, and improved algorithms of SPH with high accuracy are summarized, such as the finite particle method (FPM). Techniques used in SPH method for simulating fluid, solid and biomechanics problems are discussed. The δ -SPH method and Godunov SPH (GSPH) based on the Riemann model are described for handling instability issues in fluid dynamics. Next, the interface contact algorithm for fluid-structure interaction is also discussed. The common algorithms for improving the tensile instability and the framework of total Lagrangian SPH are examined for challenging tasks in solid mechanics. In terms of biomechanics, the governing equations and the coupling forces based on SPH method are exemplified. Then, various typical engineering applications and recent advances are elaborated. The application of fluid mainly depicts the interaction between fluid and rigid body as well as elastomer, while some complicated fluid-structure interaction ocean engineering problems are also presented. In the aspect of solid dynamics, galaxy, geotechnical mechanics, explosion and impact, and additive manufacturing are summarized. Furthermore, the recent advancements of SPH method in biomechanics, such as hemodynamically and gut health, are discussed in general. In addition, to overcome the limitations of computational efficiency and computational scale, the multiscale adaptive resolution, the parallel algorithm and the automated mesh generation are addressed. The development of SPH software in China and abroad is also summarized. Finally, the challenging task of SPH method in the future is summarized. In future research work, the establishment of multi-scale coupled SPH model and deep learning technology in solid and biodynamics will be the focus of expanding the engineering applications of SPH methods.

show abstract

Section: High-accuracy Sph Algorithmsmentioning

confidence: 99%

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Wang

Yang

et al. 2023

Acta Mech. Sin.

View full text Add to dashboard Cite

show abstract

“…Meshless methods have been successfully applied to a wide range of problems, such as free surface [38][39][40][41], impact magnetohydrodynamics [42][43], explosion phenomena [44][45], heat conduction [46][47], fracture and crack propagation [48][49], wave propagation [50][51], acoustics and fluid flow [52][53], vibration analysis [54][55][56], beams [57][58], plates and shells [59][60], and nanoscale mechanics [61][62][63][64][65][66]. A methodological study on possible and existing meshfree methods is presented in G. R. Liu [67] to solve the partial differential equations governing solid mechanics problems.…”

Section: Introductionmentioning

confidence: 99%

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

Marius,

Jacques,

MINSILI

2023

Numerical Methods in Civil Engineering

View full text Add to dashboard Cite

In this paper, the computational design of box culverts are compared using Kleinlogel's formulas and three-dimensional models based on Winkler and Modified Vlasov Foundation (MVF) by Radial Point Interpolation method (RPIM). In order to extend the RPIM to the study of box culverts, a method of decomposition is made by subdomain and creation of a fictitious rotation. Similar results are observed between the RPIM_Winkler and STAAD PRO (FEM software), with fewer nodes in the case study. Kleinlogel's formulas or the Winkler model gives a maximal increase in stresses at the middle of the raft of 5% and 12 times increased displacement. Finally, it emerges that for the same type of soil and a single structure, the reaction and shear modulus of the soil is highly depends on the distribution of loads on the structure.

show abstract

“…The FEM is highly mesh dependent, and its disadvantages of mesh refinement and mesh distortion are difficult to avoid when dealing with the crack propagation and nonlinear deformation problems. The BEM needs the basic solutions in establishing the boundary integral equations and it is difficult to solve the singular integral (Ma et al, 2020a; Wang et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

“…Then, Arefi et al (2018) researched the free vibration of a functionally graded piezoelectric laminate nanoplate by the Hamilton’s principle and nonlocal elastic theory. The electromechanical response of a piezoelectric composite beam was analyzed by Ma et al (2020b) using the load simulation method. Based on the Ritz-Lagrange formulation, Arefi and Najafitabar (2021) studied the buckling and free vibration of a functionally graded sandwich beam.…”

Section: Introductionmentioning

confidence: 99%

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Zhou

Xue

2022

Journal of Intelligent Material Systems and Structures

View full text Add to dashboard Cite

Piezoelectric materials have played an important role in industry due to a number of beneficial properties. However, most numerical methods for the piezoelectric materials need mesh, in which the mesh generation and remeshing are prominent difficulties. This paper proposes a Hermite interpolation element-free Galerkin method (HIEFGM) for piezoelectric materials, where the Hermite approximate approach and interpolation element-free Galerkin method (IEFGM) are combined. Based on the constitutive equation, geometric equation, and Galerkin integral weak form, the HIEFGM formulation for piezoelectric materials is established. In the proposed method, the problem domain is discretized by many nodes rather than the meshes, so the pre-processing of numerical computation is simplified. Furthermore, a new approximation technique based on the moving least squares method and Hermite approximate approach is used to derive the approximation function of field quantities. The derived approximation function has the Kronecker delta property and considers the field quantity normal derivatives of boundary nodes, which avoids the problem of imposing the essential boundary conditions and improves the accuracy of meshless approximation. The effects of the scaling factor, node density, and node arrangement on the accuracy of the proposed method are investigated. Numerical examples are given for assessing the proposed method and the results uniformly demonstrate the proposed method has excellent performance in analyzing piezoelectric materials.

show abstract

The meshless analysis of wave propagation based on the Hermit-type RRKPM

Cited by 9 publications

References 38 publications

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Meshless Analysis of a box culvert resting on Modified Vlasov Foundation

A Hermite interpolation element-free Galerkin method for piezoelectric materials

Contact Info

Product

Resources

About