On the performance of GFEM with trigonometric enrichment in bidimensional dynamic elastoplastic modelling

Hsu, Yang Shang; Machado, Roberto Dalledone; Filho, João Elias Abdalla

doi:10.1016/j.euromechsol.2018.10.007

Cited by 7 publications

(5 citation statements)

References 54 publications

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“…Other recent studies involving FEM in two-dimensional problems analyze in-plane vibration of plates in curvilinear domains, which includes curved triangular p-element, a differential quadrature hierarchical finite element method, and the isogeometric approach (Houmat, 2008;Liu et al, 2017;Chen, Jin, Ye, & Zhang, 2017;Ren & Zhao, 2017;Qin, Jin, Chen, & Yin, 2018). Further, other procedures are also employed for vibration analysis of plane structures such as the h-hierarchical adaptive scaled boundary finite element method (Yang, Zhang, Liu, & Ooi, 2011), finite element method based on the consecutive-interpolation procedure (CIP) (Bui, Nguyen, Zhang, Hirose, & Batra, 2016), generalized finite element method with trigonometric enrichment (Shang, Machado, & Abdalla Filho, 2019), time-discontinuous finite element method (TD-FEM) based on complex Fourier shape functions (Izadpanah, Shojaee, & Hamzehei-Javaran, 2018) and generalized / eXtended finite element method (Cittadin, Corrêa, Arndt, & Machado, 2022). Regarding the applications of in-plane vibrations, we find relevant studies on the seismic behavior of shear walls (El-Kashif, Adly, & Abdalla Filho, 2019;Sepehrnia, Rahami, Mirhosseini, & Zeighami, 2020) and the use of plane elements with drilling rotation in vibration analysis (Rebiai & Belounar, 2013;Rebiai, 2018;Fortas et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

Bortoli,

Abdalla Filho

2024

Acta Sci Technol

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In this work, plane stress free vibration is performed using four-node elements formulated using strain gradient notation. Accurate results are sought, and the effects of parasitic shear are investigated. By applying strain gradient notation, which is a physically interpretable notation, parasitic shear terms are identified a priori in the shear strain expressions of the four-node plane element. Parasitic shear is the source of shear locking in that element, and the a priori removal of the parasitic shear terms corrects the element for locking. Several studies in the literature show that this modeling error causes improper behavior of the element in bending, which affects the computed results of stress and displacements of the structure. Based on this, this work applies strain gradient notation to examine the effects of parasitic shear on the natural frequencies and corresponding mode shapes of plane stress structures. The results are compared with literature results, and with the isoparametric FEM formulation modeled by ANSYS software. It is observed that parasitic shear has a higher preponderance in coarse meshes of flexural vibration modes. Furthermore, the deleterious effects are emphasized as bending deformation becomes more important in the model. Strain gradient notation shows advantages in the numerical aspect and successfully eliminates the parasitic shear terms from the four-node element. The problems studied here display accurate results.

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Section: Introductionmentioning

confidence: 99%

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

Bortoli,

Abdalla Filho

2024

Acta Sci Technol

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“…The enriched element formulated by these methods are applied to several different applications. Such as plane frame analyses, 14 free vibration analysis, 15,16 transient elastoplastic analysis, 17,18 and error estimator. 19 The swarm techniques, such as the particle swarm optimization (PSO) and genetic algorithms (GA), are widely used in engineering applications.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical approach based on particle swarm technique for optimization of nonlinear buried pipeline on tensionless foundation

Shang,

Deitos,

Ulrich

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work aims to contribute to the development of numerical approach for optimization of buried pipeline by using finite element (FE) method and particle swarm optimization (PSO), considering static analysis and material hardening. The buried pipeline is discretized by finite element approach, constituted by Euler-Bernoulli three nodes beam element, while the soil-structure interaction is modeled by Winker-type tensionless foundation. Moreover, the tensionless foundation is discretized by spring element in the numerical model. The material nonlinearity behavior is analyzed by Von Mises isotropic hardening model. In the numerical approach, this model is solved by stress increment procedure. Furthermore, the critical loading and optimum wall thickness, that leads to optimized condition, are determined using swarm techniques. The cost function is formulated using evaluated stress and target stress, more, the calculated error is minimized by using swarm techniques for single-variable and two-variable optimization. Several applications are carried out by considering several soil conditions, boundary conditions and loading types. As a novelty, the soil random stiffness is included in the numerical model, where the optimum wall thickness and critical loading are evaluated considering material nonlinearity. The performance of finite element particle swarm technique is also compared to finite element genetic algorithms technique. The results demonstrate the effectiveness of proposed numerical approach for nonlinear buried pipeline optimization.

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“…31,33–35 Recently, developments of enriched finite element (FE) approach, such as the generalized finite element method (GFEM), have gained the interest of several researchers in the dynamic elastoplastic analyses, due to its efficiency and competitiveness in comparison to other numerical formulations. 36–39 Other applications of GFEM include fracture mechanics and crack propagation. Moreover, the GFEM is also successfully applied in other field of engineering.…”

Section: Introductionmentioning

confidence: 99%

“…This enriched FE formulation is successfully employed in the previous works of author and shows competitiveness in comparison to other FE formulation in the context of dynamic elastoplastic analysis. 36,39 In addition, for the structure elastoplastic behavior, the von Mises isotropic hardening model is employed and solved by the Newton–Raphson algorithm. Moreover, the time increment procedure adopts an unconditionally stable HHT algorithm.…”

Section: Introductionmentioning

confidence: 99%

Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads

Hsu

Deitos

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work contributes to the generalized finite element approach in free vibration, dynamic elastic, and elastoplastic analysis of plane frame subjected to random excitation generated by the wind action. The wind velocity is modeled mathematically by using power spectral density method in combination with Shinozuka’s model, along with the commonly employed wind spectra. From these spectra, the dynamic wind loading is determined from the sum of the mean and floating wind velocities. The governing equation is formulated by Euler–Bernoulli beam theory, and it is discretized by using the enriched beam element. The enrichment is done by employing enriched finite element shape function to construct the enriched mathematical space. This strategy is constituted by the enrichment space, which is constructed by trigonometric functions, and the conventional space, which is constructed by conventional two-node Lagrange–Hermite shape function. The time increment procedure is carried out by Hilber-Hughes-Taylor algorithm and the material nonlinearity is modeled by von Mises isotropic hardening model, solved by the Newton–Raphson algorithm. A flowchart is presented to summarize the proposed numerical modeling procedure. Finally, several applications are presented, and the results obtained by the generalized finite element method are compared with those obtained by conventional beam element. Natural frequencies are determined in a one-story plane frame and are compared with reference results. The relative error in displacement is determined in h-refine strategy for quadratic beam element (FEM3), while the generalized finite element method adopts the enrichment increment strategy. The results demonstrate the competitiveness and numerical stability of generalized finite element method in this type of application. Even in comparison to the quadratic beam element, the generalized finite element method presents good performance and accuracy in numerical modeling.

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On the performance of GFEM with trigonometric enrichment in bidimensional dynamic elastoplastic modelling

Cited by 7 publications

References 54 publications

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

Free vibration analysis employing strain gradient notation four-node plane elements and considering the effects of parasitic shear

Numerical approach based on particle swarm technique for optimization of nonlinear buried pipeline on tensionless foundation

Enriched finite element modeling in the dynamic analysis of plane frame subject to random loads

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