Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

Yoon, Kyungho; Lee, Phill-Seung; Kim, Do-Nyun

doi:10.1016/j.compstruct.2015.07.024

Cited by 33 publications

(9 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A formulation of a 3D beam element for computation of transversal and warping eigenmodes is presented in [16]. In [17], a new 3D finite element for geometrically nonlinear analysis of beams, made of Functionally Graded Material (FGM) with transversally varying material properties, is presented. The warping displacements are accurately predicted.…”

Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

View full text Add to dashboard Cite

In this paper, the influence of the variable axial force and of the Secondary Torsion-Moment Deformation-Effect (STMDE) on the deformations of beams due to torsional warping is investigated. The investigation is based on the second-order torsional warping theory of doubly symmetric beams with thin-walled open or closed cross-sections. The effect of the axial force on the torsional stiffness of thinwalled beams is considered according to the second-order torsional warping theory. The solutions of the underlying differential equations are used for setting up the relations, needed for application of the transfer matrix method. They are derived, considering both static and dynamic action. This enables stablishing the local

show abstract

Section: Introductionmentioning

confidence: 99%

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Aminbaghai

Muŕın

Balduzzi

et al. 2017

Engineering Structures

View full text Add to dashboard Cite

show abstract

“…Niknam et al [23] considered the nonlinear bending behaviour of tapered FG beams based on two different numerical approaches namely; Galerkin method and Generalized Differential Quadrature method (GDQ). Yoon et al [24] presented a continuum based 3D beam finite element for geometrically nonlinear analysis of FG beam structures considering cross-sectional warping. Pascon [25] proposed a plane beam finite element to solve bending problem of FG beams assuming moderate strains and variable Poisson's ratio.…”

Section: Introductionmentioning

confidence: 99%

“…However, except for the work of Yoon et al [24], all of the works on the large deflection analysis of FG beams are restricted to 2D plane problems and the main focus of all of these works has been mostly on the chemical composition gradient functionally graded materials by the micro-structural mixture of metals and ceramics. Moreover, the important problem of non-conservative (follower) loads for FG beams has received little attention and as apparent from the above literature review, the 3D large deflection behaviour of functionally graded beams with porous structure has not yet been appropriately addressed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation

Masjedi

Maheri

2019

Applied Mathematical Modelling

View full text Add to dashboard Cite

Porous graded materials found in nature can be regarded as variable stiffness optimized load carrier elements that exhibit beneficial properties for real-life engineering designs. In order to investigate the nonlinear behaviour of variable stiffness bioinspired materials, the large deflection of functionally graded beams made from porous materials is considered in this work. Our purpose is to present an efficient and accurate methodology capable of capturing spatially large deflections of these structures with different types of loading conditions and porosity distributions. A geometrically exact beam model with fully intrinsic formulation is employed for the first time to study the large deflection behaviour of functionally graded beams under conservative and non-conservative (follower) loading scenarios. An orthogonal Chebyshev collocation method is used for the discretisation of the fully intrinsic formulation. Two types of porosity distributions, namely cross-sectional and span-wise, are considered and the effect of porosity distribution has been investigated for various benchmark classical test cases. It is shown that to obtain a given level of accuracy, the span-wise functionally graded beam is computationally more demanding compared to the cross-sectional functionally graded beam. In addition to classical problems, two examples demonstrating 3D deflections of a highly flexible structures made from porous material subject to combined loads are investigated. It is shown that the current paradigm, while being computationally efficient, can effectively capture the large deflections of functionally graded beams with excellent accuracy.

show abstract

“…The numerical assessment of the mechanical or multiphysical behaviour is a critical issue in the product development process and new and enhanced strategies have to be developed. Accurate and efficient structural finite elements like beams, plates and shells require suitable homogenization procedures to arrive effective stiffness quantities for the membrane, bending, transverse and torsional shear properties accompanied with a suitable warping stiffness regarding non-uniform torsion [1][2][3]. In the literature, a huge amount of papers can be found, which deal with modelling and simulation of static and dynamic problems of FGM beams.…”

Section: Introductionmentioning

confidence: 99%

Extension of the FGM Beam Finite Element by Warping Torsion

Muŕın

Hrabovský

Aminbaghai

et al. 2019

Strojnícky Časopis - Journal of Mechanical Engineering

View full text Add to dashboard Cite

In the contribution, our 3D FGM Timoshenko beam finite element with 12x12 stiffness and mass matrices for doubly symmetric open and closed cross-section [1] is extended by warping torsion effect (non-uniform torsion) to 14x14 finite element matrices. A longitudinal continuous variation of effective material properties is considered by the finite element equations derivation, which can be obtained by homogenization of the spatial varying material properties in real FGM beam. Results of numerical elastostatic non-uniform torsional analysis of the FGM cantilever beam of I-cross-section are presented and the accuracy and effectiveness of the new FGM beam finite element is discussed and evaluated.

show abstract

Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

Cited by 33 publications

References 40 publications

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Second-order torsional warping theory considering the secondary torsion-moment deformation-effect

Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation

Extension of the FGM Beam Finite Element by Warping Torsion

Contact Info

Product

Resources

About