The hybrid complex variable element-free Galerkin method for 3D elasticity problems

Cheng, Heng; Peng, Miaojuan; Cheng, Yumin; Meng, Zhijuan

doi:10.1016/j.engstruct.2020.110835

Cited by 51 publications

(16 citation statements)

References 50 publications

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“…To improve the computational efficiency, by using the theory of complex variables, Liew and Cheng et al proposed the complex variable moving least-squares (CVMLS) method [38]. The meshless method based on the CVMLS method can improve calculation efficiency and accuracy [39,40].…”

Section: Introductionmentioning

confidence: 99%

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

2021

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By introducing the dimension splitting method (DSM) into the improved interpolating moving least-squares (IMLS) method with nonsingular weight function, a dimension splitting–interpolating moving least squares (DS–IMLS) method is first proposed. Since the DSM can decompose the problem into a series of lower-dimensional problems, the DS–IMLS method can reduce the matrix dimension in calculating the shape function and reduce the computational complexity of the derivatives of the approximation function. The approximation function of the DS–IMLS method and its derivatives have high approximation accuracy. Then an improved interpolating element-free Galerkin (IEFG) method for the two-dimensional potential problems is established based on the DS–IMLS method. In the improved IEFG method, the DS–IMLS method and Galerkin weak form are used to obtain the discrete equations of the problem. Numerical examples show that the DS–IMLS and the improved IEFG methods have high accuracy.

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Section: Introductionmentioning

confidence: 99%

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

2021

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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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“…In recent times, Meng et al [24] presented a hybrid element-free Galerkin (HEFG) method for solving three dimensional wave propagation problem. Also Liu and Cheng [16], Liu et al [17] and Cheng et al [3] employed element-free Galerkin method in the study of some problems involving swelling of polymer gels, elastoplastic deformation problems and 3D elasticity problems. Gupta and Gayen [10] used multi-term Galerkin approximation in terms of Chebyshev polynomials to analyse the effect of two submerged unequal permeable plates in the propagation of water waves and also Roy et al [29] used multi-term Galerkin approximation technique with Chebyshevs polynomials for water wave scattering by unequal partially immersed vertical barriers in water of uniform finite depth.…”

Section: Introductionmentioning

confidence: 99%

Use of Galerkin Technique to the Rolling of a Plate in Deep Water

Ray

Mandal

2021

Mathematical Modelling and Analysis

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The classical problems of surface water waves produced by small oscillations of a thin vertical plate partially immersed as well as submerged in deep water are reinvestigated here. Each problem is reduced to an integral equation involving horizontal component of velocity across the vertical line outside the plate. The integral equations are solved numerically using Galerkin approximation in terms of simple polynomials multiplied by an appropriate weight function whose form is dictated by the behaviour of the fluid velocity near the edge(s) of the plate. Fairly accurate numerical estimates for the amplitude of the radiated wave at infinity due to rolling and also for swaying of the pate in each case are obtained and these are depicted graphically against the wave number for various cases.

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The hybrid complex variable element-free Galerkin method for 3D elasticity problems

Cited by 51 publications

References 50 publications

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

A Dimension Splitting-Interpolating Moving Least Squares (DS-IMLS) Method with Nonsingular Weight Functions

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

Use of Galerkin Technique to the Rolling of a Plate in Deep Water

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