Hybrid gradient smoothing technique with discrete shear gap method for shell structures

Li, Wei; Gong, Zhixiong; Cheng, Cong; Li, Tianyun; Zhang, Qifan; Wang, Mingsheng

doi:10.1016/j.camwa.2017.06.047

Cited by 51 publications

(11 citation statements)

References 72 publications

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“…In practical engineering applications, the geometries of the involved MEE structures are usually quite complicated. In these cases, the corresponding exact/analytical solutions are usually not available and we have to resort to the numerical approaches [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Chai,

Huang,

Wang

et al. 2024

Smart Mater. Struct.

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In this work, a carefully designed enriched finite element method (EFEM) is presented to improve the solution accuracy of the conventional FEM in analyzing the dynamic behaviors of the magnetic-electric-elastic (MEE) composite structures which are frequently used in designing various smart and intelligent devices. In formulating the proper EFEM with ideal numerical performance, different enrichment functions are considered and the corresponding solution quality of different versions of the EFEM are compared and examined in great detail. When the Lagrange polynomial basis functions together with the harmonic trigonometric functions are used as the enrichment functions, the obtained EFEM shows extremely powerful and ideal numerical performance, which are obviously better than the other versions of EFEM and the conventional FEM, in studying the free vibration and harmonic frequency responses of the MEE structures. The nearly exact numerical solutions for three-phase physical fields of MEE structures can be generated by the proposed EFEM even if very coarse mesh patterns are used. Intensive numerical studies are conducted to confirm and verify the excellent properties of the proposed EFEM in performing dynamic analysis of the MEE structures.

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Chai,

Huang,

Wang

et al. 2024

Smart Mater. Struct.

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“…In order to enhance the performance of the standard FEM in engineering computation, Liu et al proposed the smoothed FEM (S-FEM) [41][42][43][44][45][46] which combines traditional FEM with the generalized strain smoothing techniques with a mathematic base on the novel G space theory. By invoking the novel G space theory and strain smoothing operations, the "overly-stiff" stiffness matrices of the standard FEM can be properly softened and then a softened numerical model with appropriate system stiffness can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions

Dang

et al. 2022

Mathematics

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In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.

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“…In order to address the numerical dispersion error issue. Much research effort has been made and a variety of advanced or modified finite element schemes have been proposed (see, e.g., [28][29][30][31][32][33][34]), including the smoothed finite element method (S-FEM) (see, e.g., [35][36][37][38][39][40]). e S-FEM is developed by combining the classical finite element concepts and the generalized gradient smoothing technique (GGST) which is frequently employed in the meshless methods.…”

Section: Introductionmentioning

confidence: 99%

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

Chai

Zhang

2020

Mathematical Problems in Engineering

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In this work, the edge-based smoothed finite element method (ES-FEM) is incorporated with the Bathe time integration scheme to solve the transient wave propagation problems. The edge-based gradient smoothing technique (GST) can properly soften the “overly soft” system matrices from the standard finite element approach; then, the spatial numerical dispersion error of the calculated solutions for wave problems can be significantly reduced. To effectively solve the transient wave propagation problems, the Bathe time integration scheme is employed to perform the involved time integration. Due to the appropriate “numerical dissipation effects” from the Bathe time integration method, the spurious oscillations in the relatively large wave numbers (high frequencies) can be effectively suppressed; then, the temporal numerical dispersion error in the calculated solutions can also be notably controlled. A number of supporting numerical examples are considered to examine the capabilities of the present approach. The numerical results show that ES-FEM works very well with the Bathe time integration technique, and much more numerical solutions can be reached for solving transient wave propagation problems compared to the standard FEM.

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Hybrid gradient smoothing technique with discrete shear gap method for shell structures

Cited by 51 publications

References 72 publications

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the finite element method enriched by proper enrichment functions

Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

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