The interpolating element-free Galerkin method for elastic large deformation problems

Wu, Qiang; Peng, Piaopiao; Cheng, Yumin

doi:10.1007/s11431-019-1583-y

Cited by 44 publications

(14 citation statements)

References 26 publications

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“…Yu et al studied the virtual hybrid simulation method for underground structures subjected to seismic loadings [26,27]. Based on the Least Square Method, some scholars have analyzed different cases [28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Chai

2021

Mathematics

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Based on the basic principle of thermodynamics, an elastoplastic damage constitutive model of concrete is constructed in this paper. The model is realized and verified in FLAC3D, which provides a solid foundation for the study of dynamic response and fatigue damage to the base structure of a heavy haul railway tunnel. The dynamic response and damage distribution of the base structure of a heavy-duty railway tunnel with defects were numerically simulated by the concrete elastic-plastic damage constitutive model. Then, by analyzing the response characteristics of the tunnel basement structure under different surrounding rock softening degrees, different foundation suspension range and different foundation structure damage degree are determined. The results show the following: (1) The elastoplastic damage constitutive model of concrete can well describe the stress–strain relationship of materials, especially with the simulation results of post peak softening being in good agreement with the test results, and the simulation effect of the unloading–reloading process of the cyclic loading and unloading test also meet the requirements. (2) The initial stress field and dynamic response of the tunnel basement structure under the action of train vibration load are very different from the ideal state of the structure design when the surrounding rock of the base is softened, the base is suspended, or the basement structure is damaged. With the surrounding rock softening, basement hanging, or basement structure damage developing to a certain extent, the basement structure will be damaged. (3) The horizontal dynamic stress amplitude increases with the increase in the softening degree of the basement surrounding rock. The horizontal dynamic stress of the measuring point increases with the increase in the width of the hanging out area when the hanging out area is located directly below the loading line. When the degree of damage to the basement structure is aggravated, the horizontal dynamic tensile stress of each measuring point gradually decreases. (4) The maximum principal stress increment increases with the increase in the fracture degree of the basement structure, while the minimum principal stress increment decreases with the increase in the fracture degree of the basement structure, but the variation range of the large and minimum principal stress increments is small. The research results have important theoretical and practical significance for further analysis of the damage mechanism and control technology of the foundation structure of a heavy haul railway tunnel with defects.

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Section: Introductionmentioning

confidence: 99%

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Chai

2021

Mathematics

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“…Numerical calculations are widely used in scientific research and engineering applications [23][24][25], which can realize optimal design and high-precision analysis of structures. A new and effective numerical method developed in recent years is the meshless method, including diffuse element method [26], smoothed particle method [27], reproducing kernel particle method [28][29][30][31], elementfree Galerkin method [32][33][34][35][36][37][38][39][40][41], finite point method [42], natural element method [43], radial basis function method [44], mesh-free kp-Ritz method [45], complex variable meshless method [46][47][48], and all kinds of meshless boundary integral equation method [49][50][51]. In addition, numerical methods also include weighted residual method, finite difference method, finite element method, and boundary element method.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Optimization of Pulling Point Position of Luffing Jib on Portal Crane

Jiao

Qin

Han³

et al. 2021

Mathematical Problems in Engineering

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Portal crane is the most commonly used equipment for cargo handling of large mixed loading ships with its advantages of flexible and convenient operation, wide adaptability, and high loading and unloading efficiency. The reasonable modeling and optimization of the pulling point position of luffing jib of portal crane can reduce the rack force of portal crane and the power consumption output of the rack and pinion during the luffing process. Based on penalty function optimization, the interior point method is used to optimize the pulling point position of luffing jib. Compared with the initial design, the race force of the luffing jib is reduced to a certain extent. In addition, the consistency between the finite element analysis results and the optimization results can be verified, and the effectiveness of the optimization design is also proved through the finite element analysis of portal crane.

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“…Based on MLS, the element-free Galerkin method has been viewed as one of the predominant meshless methods. Cheng et al proposed the improved moving least-squares (IMLS) approximation to develop the improved element-free Galerkin (IEFG) method [33][34][35] and the interpolating element-free Galerkin method [36][37][38]. By introducing the dimension splitting method into the reproducing kernel particle method, a new meshless method was developed to solve three-dimensional potential problems [39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

Guo

Boldbaatar

et al. 2020

Mathematical Problems in Engineering

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This paper develops a local Kriging meshless solution to the nonlinear 2 + 1-dimensional sine-Gordon equation. The meshless shape function is constructed by Kriging interpolation method to have Kronecker delta function property for the two-dimensional field function, which leads to convenient implementation of imposing essential boundary conditions. Based on the local Petrov–Galerkin formulation and the center difference method for time discretization, a system of nonlinear discrete equations is obtained. The numerical examples are presented and the numerical solutions are found to be in good agreement with the results in the literature to validate the ability of the present meshless method to handle the 2 + 1-dimensional sine-Gordon equation related problems.

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The interpolating element-free Galerkin method for elastic large deformation problems

Cited by 44 publications

References 26 publications

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Research on Dynamic Response Characteristics for Basement Structure of Heavy Haul Railway Tunnel with Defects

Modeling and Optimization of Pulling Point Position of Luffing Jib on Portal Crane

Numerical Solution of Sine-Gordon Equation with the Local Kriging Meshless Method

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