A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section

Peres, Nuno; Gonçalves, Rodrigo; Camotim, Dinar

doi:10.1016/j.cma.2021.113804

Cited by 21 publications

(3 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Even though a very large number of past works addressed developments concerning beam elements (see [8][9][10][11][12], to name a few), a posteriori estimates for errors caused by inexact representation of the flexural stiffness have not yet been proposed. This is the main novelty of this paper.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error estimates for beams with inexact flexural stiffness representation

Torii,

Gracite,

Miguel

et al. 2023

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement.

show abstract

Section: Introductionmentioning

confidence: 99%

A posteriori error estimates for beams with inexact flexural stiffness representation

Torii,

Gracite,

Miguel

et al. 2023

J. Appl. Math. Comput. Mech.

View full text Add to dashboard Cite

show abstract

“…It is used to analyse the free vibration of complex beam components such as different cross sections (Alshorbagy et al, 2011), support types (Villavicencio and Soares, 2011) and curve linear forms (Piovan et al, 2012). Peres et al used a geometrically accurate beam finite element to accurately predict the spatial displacement and distortion of curved beams (Peres et al, 2021). Parallel computation and adaptive algorithms of finite element methods have been developed by many researchers (Arndt et al, 2010(Arndt et al, , 2016Zhang, 2009;Liu and Zhang, 2009;Cheng and Zhang, 2012;Liu et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Peres et al . used a geometrically accurate beam finite element to accurately predict the spatial displacement and distortion of curved beams (Peres et al. , 2021).…”

Section: Introductionmentioning

confidence: 99%

Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes

Wang

2022

View full text Add to dashboard Cite

PurposeIn this paper, a superconvergent patch recovery method is proposed for superconvergent solutions of modes in the finite element post-processing stage of variable geometrical Timoshenko beams. The proposed superconvergent patch recovery method improves the solution speed and accuracy of the finite element analysis of a curved beam. The free vibration and natural frequency of the beam were considered for studying forced vibrations and structural resonance. Beam vibration mode analysis was performed for high-precision vibration mode solutions and frequency values. The proposed method can be used to compute beam vibration modes of beams with different shapes and boundary conditions as well as variable cross sections and curvatures. The purpose of this paper is to address these issues.Design/methodology/approachAn adaptive method was proposed to analyse the in-plane and out-of-plane free vibrations of the variable geometrical Timoshenko beams. In the post-processing stage of the displacement-based finite element method, the superconvergent patch recovery method and high-order shape function interpolation technique were used to obtain the superconvergent solution of mode (displacement). The superconvergent solution of mode was used to estimate the error of the finite element solution of mode in the energy form under the current mesh. Furthermore, an adaptive mesh refinement was proposed by mesh subdivision to derive an optimised mesh and accurate finite element solution to meet the preset error tolerance.FindingsThe results computed using the proposed algorithm were in good agreement with those computed using other high-precision algorithms, thus validating the accuracy of the proposed algorithm for beam analysis. The numerical analysis of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams helped verify that the solutions of frequencies were consistent with the results obtained using other specially developed methods. The proposed method is well suited for the mesh refinement analysis of a curved beam structure for analysing the changes in high-order vibration mode. The parts where the vibration mode changed significantly were locally densified; a relatively fine mesh division was adopted that validated the reliability of the mesh optimisation processing of the proposed algorithm.Originality/valueThe proposed algorithm can obtain high-precision vibration solutions of variable geometrical Timoshenko beams based on more optimized and reasonable meshes than the conventional finite element method. Furthermore, it can be used for vibration problems of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams. The proposed algorithm can be extended for application in superconvergent computation and adaptive analysis of finite element solutions of general structures and solid deformation fields and used for adaptive analysis of more complex plates, shells and three-dimensional structures. Additionally, this method can analyse the vibration and stability of curved members with crack damage to obtain high-precision vibration modes and instability modes under damage defects.

show abstract

Unveiling the Mechanism Behind the Asymmetric Bending Compliance of Thin-Walled U-Shaped Strips: A Study Inspired by Plant Leaves

Wei

Guo²,

Guo³

2022

Acta Mech. Solida Sin.

View full text Add to dashboard Cite

A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section

Cited by 21 publications

References 41 publications

A posteriori error estimates for beams with inexact flexural stiffness representation

A posteriori error estimates for beams with inexact flexural stiffness representation

Finite element mesh refinement for in-plane and out-of-plane vibration of variable geometrical Timoshenko beams based on superconvergent vibration modes

Unveiling the Mechanism Behind the Asymmetric Bending Compliance of Thin-Walled U-Shaped Strips: A Study Inspired by Plant Leaves

Contact Info

Product

Resources

About