Heng Cheng¹, Yichen Yang¹, Yumin Cheng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.3, pp. 2853-2894, 2025, DOI:10.32604/cmes.2025.073178 - 23 December 2025

Abstract The element-free Galerkin (EFG) method, which constructs shape functions via moving least squares (MLS) approximation, represents a fundamental and widely studied meshless method in numerical computation. Although it achieves high computational accuracy, the shape functions are more complex than those in the conventional finite element method (FEM), resulting in great computational requirements. Therefore, improving the computational efficiency of the EFG method represents an important research direction. This paper systematically reviews significant contributions from domestic and international scholars in advancing the EFG method. Including the improved element-free Galerkin (IEFG) method, various interpolating EFG methods, four distinct More >

Wenna He, Yichen Yang, Dongqiong Liang, Heng Cheng^*

CMC-Computers, Materials & Continua, Vol.83, No.1, pp. 1415-1414, 2025, DOI:10.32604/cmc.2025.059839 - 26 March 2025

Abstract In this paper, we develop an advanced computational framework for the topology optimization of orthotropic materials using meshless methods. The approximation function is established based on the improved moving least squares (IMLS) method, which enhances the efficiency and stability of the numerical solution. The numerical solution formulas are derived using the improved element-free Galerkin (IEFG) method. We introduce the solid isotropic microstructures with penalization (SIMP) model to formulate a mathematical model for topology optimization, which effectively penalizes intermediate densities. The optimization problem is defined with the numerical solution formula and volume fraction as constraints. The… More >

Alireza Moradi, Alireza Shaterzadeh^*

CMC-Computers, Materials & Continua, Vol.82, No.1, pp. 223-257, 2025, DOI:10.32604/cmc.2024.059441 - 03 January 2025

Abstract For the first time, the linear and nonlinear vibrations of composite rectangular sandwich plates with various geometric patterns of lattice core have been analytically examined in this work. The plate comprises a lattice core located in the middle and several homogeneous orthotropic layers that are symmetrical relative to it. For this purpose, the partial differential equations of motion have been derived based on the first-order shear deformation theory, employing Hamilton’s principle and Von Kármán’s nonlinear displacement-strain relations. Then, the nonlinear partial differential equations of the plate are converted into a time-dependent nonlinear ordinary differential equation… More >

Yuxiang Peng^1,*, Pengnan Sun¹, Niannian Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.31, No.3, pp. 1-1, 2024, DOI:10.32604/icces.2024.011902

Abstract Immersed boundary method (IBM) has been widely applied in the simulation of fluid-structure interaction problems. The traditional direct force model is less accurate, and the sharp-interface approaches involve complex topological operations which are not conducive to dealing with complex structures. The boundary data immersion method (BDIM) is a new fluid-structure coupling scheme that does not need to cut the mesh and can be extended to reach second-order accuracy. However, the traditional boundary data immersion method needs special treatment to deal with the sharp corners of the structure. In the present work, the volume fraction of More >

Biao Wang¹, Yuxiang Peng^1,*, Wenhua Xu²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.3, pp. 1-2, 2024, DOI:10.32604/icces.2024.012061

Abstract The damage process of ship structures under near-field underwater explosions involves strong nonlinear coupling effects of multiple media, and its numerical simulation poses a serious challenge to traditional numerical algorithms. Based on previous research, this article first establishes a highly compressible multiphase flow numerical calculation model based on the high-precision Discontinuous Galerkin Method (DGM) and a ship elastic-plastic damage dynamic model based on the meshless Reproducing Kernel Particle Method (RKPM). Furthermore, we develop an algorithm for grid-independent dynamic expansion of cracks. Based on this, the Boundary Data Immersion Method (BDIM) is used to couple the More >

Zhaoxu Lian¹,Wenbin Wu^2,*, Moubin Liu^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.011054

Abstract The underwater explosion (UNDEX) could cause the fatal damage of naval ships and submarines in the naval battle, and seriously threaten their combat capability [1]. The UNDEX process is very complicated, including the propagation and reflection of the shock wave, formation and collapse of cavitation zone, trainset dynamic structural response and so on [2]. In this paper, we develop the three-dimensional Discontinuous Galerkin method (DGM) model for simulating the propagation of incident shock loading in fluid domain. The pressure cutoff model is employed to deal with the cavitation effect due to the reflection of the More >

Qifa Lang, Yuqiao Zheng^*, Tiancai Cui, Chenglong Shi, Heyu Zhang

Energy Engineering, Vol.121, No.2, pp. 483-498, 2024, DOI:10.32604/ee.2023.042437 - 25 January 2024

Abstract This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle. We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory (NREL), to research the effects of the nonlinear flap-wise vibration characteristics. The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam, and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first. Then, the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the… More >

Jiaqun Wang^1,2, Guanxu Pan², Youhe Zhou², Xiaojing Liu^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.1, pp. 297-318, 2024, DOI:10.32604/cmes.2023.030622 - 30 December 2023

Abstract In this study, a wavelet multi-resolution interpolation Galerkin method (WMIGM) is proposed to solve linear singularly perturbed boundary value problems. Unlike conventional wavelet schemes, the proposed algorithm can be readily extended to special node generation techniques, such as the Shishkin node. Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients. All the shape functions possess the Kronecker delta property, making the imposition of boundary conditions as easy as that in the finite element method. Four numerical examples are studied to demonstrate the validity More >

Jufeng Wang¹, Yong Wu¹, Ying Xu¹, Fengxin Sun^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 341-356, 2023, DOI:10.32604/cmes.2022.023140 - 29 September 2022

Abstract By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system More >

Heng Cheng¹, Zebin Xing¹, Miaojuan Peng^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.3, pp. 945-964, 2022, DOI:10.32604/cmes.2022.020755 - 27 June 2022

Abstract In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steady-state heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical More >