Dynamic analysis of Euler–Bernoulli beam problems using the Generalized Finite Element Method

Shang, Helen; Machado, Roberto Dalledone; Filho, João Elias Abdalla

doi:10.1016/j.compstruc.2016.05.019

Cited by 26 publications

(17 citation statements)

References 34 publications

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“…The trigonometric enrichment function for enriched two nodes bar element shown by Table 2 is already employed in the previous work. 36,60…”

Section: Enrichment Strategy With Generalized Finite Element Methodsmentioning

confidence: 99%

“…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%

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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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“…The trigonometric enrichment function for enriched two nodes bar element shown by Table 2 is already employed in the previous work. 36,60…”

Section: Enrichment Strategy With Generalized Finite Element Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…According to the obtained outcomes, the projected computational method was adept of accurately catching the damage progress under complicated boundary conditions. Shang et al used FEM for solving Euler-Bernoulli beam problems [23]. They presented a dynamic analysis scheme.…”

Section: Introductionmentioning

confidence: 99%

Stress Analysis by Two Cuboid Isoparametric Elements

Rezaiee‐Pajand

Karimipour

2019

TECM

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The finite element method is a powerful tool for solving most of the structural problems. This technique has been used extensively, since the complexity of the elastic field equations does not allow the specialist to find analytical solutions, especially for the three-dimensional structures. It is well-known that the finite element formulation yields the approximate stress responses. To remedy this defect, the Airy stress function is utilized in this study. The stress function formulation leads to a valid solution since it satisfies equilibrium and compatibility equations simultaneously. Two cuboid isoparametric elements are formulated for solving three-dimensional elastic structures. To demonstrate the performance of the proposed technique, various benchmark problems are analyzed. The errors between the exact, displacement-based finite element and recommended scheme solution are also calculated. All the obtained outcomes show the good merit of the presented new elements.

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“…They approximated displacements and electric potential using Lagrange's polynomials. Shang et al [14] used Generalized FE Method to carry out the dynamic analyses of 1D bar and beam problems. They compared their results with conventional FE formulation to prove efficiency of the method.…”

Section: Introductionmentioning

confidence: 99%

Finite element modelling to assess the effect of surface mounted piezoelectric patch size on vibration response of a hybrid beam

Rahman¹,

Alam²

2018

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Vibration response analysis of a hybrid beam with surface mounted patch piezoelectric layer is presented in this work. A one dimensional finite element (1D-FE) model based on efficient layerwise (zigzag) theory is used for the analysis. The beam element has eight mechanical and a variable number of electrical degrees of freedom. The beams are also modelled in 2D-FE (ABAQUS) using a plane stress piezoelectric quadrilateral element for piezo layers and a plane stress quadrilateral element for the elastic layers of hybrid beams. Results are presented to assess the effect of size of piezoelectric patch layer on the free and forced vibration responses of thin and moderately thick beams under clamped-free and clamped-clamped configurations. The beams are subjected to unit step loading and harmonic loading to obtain the forced vibration responses. The vibration control using in phase actuation potential on piezoelectric patches is also studied. The 1D-FE results are compared with the 2D-FE results.

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Dynamic analysis of Euler–Bernoulli beam problems using the Generalized Finite Element Method

Cited by 26 publications

References 34 publications

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

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

Stress Analysis by Two Cuboid Isoparametric Elements

Finite element modelling to assess the effect of surface mounted piezoelectric patch size on vibration response of a hybrid beam

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