Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

Almeida, Cristiane Maria Galdino de; Albino, Juan Carlos Romero; Menezes, Ivan F. M.; Paulino, Gláucio H.

doi:10.1016/j.mechrescom.2011.07.006

Cited by 34 publications

(17 citation statements)

References 17 publications

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“…Hence, to obtain the final deformed configuration of a body under a given state of loading, the intermediate deformed states are captured and it is considered as the initial configuration for the next state of deformation coming from the corresponding incremental loading. This method is commonly known as incremental Lagrangian formulation [109][110][111][112][113][114][115][116][117]. The method is also used in applications, where the complicated body geometry calls for a nonlinear 'strain-displacement' relation.…”

Section: Analysis With Geometry Updationmentioning

confidence: 99%

“…Based on the configuration to which the reference is transformed, Lagrangian approach is classified into two categories and they are total Lagrangian [109][110][111][112][113][114][115][116] and updated Lagrangian [115,117] formulations. In total Lagrangian approach, all parameters involved in energy expressions are referred to the initial configuration ( 0 C ).…”

Section: Analysis With Geometry Updationmentioning

confidence: 99%

“…The expression, derived through Lagrangian approach, is highly nonlinear in incremental displacement and closed form solution based on continuum mechanics is rarely available in literature [112,113]. Generally, Lagrangian formulation is used as the basis of finite element analysis of nonlinear beam bending problem, which results element wise nonlinear governing equation [109][110][111][114][115][116][117]. These nonlinear equations are generally linearized using small incremental strain steps and solved using some iterative method [109-111, 113, 115, 116] to obtain element stiffness matrix.…”

Section: Analysis With Geometry Updationmentioning

confidence: 99%

“…Three major categories of loading are concentrated, uniformly or non-uniformly distributed and combined distributed and concentrated loads. In addition, a beam can also be subjected to couple or moment [58,63,73,87,92,111].…”

Section: Loading Conditionmentioning

confidence: 99%

See 3 more Smart Citations

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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Section: Analysis With Geometry Updationmentioning

confidence: 99%

Section: Analysis With Geometry Updationmentioning

confidence: 99%

Section: Analysis With Geometry Updationmentioning

confidence: 99%

Section: Loading Conditionmentioning

confidence: 99%

See 2 more Smart Citations

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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show abstract

“…However, FEM formulations based on Lagrangian formulations for studying geometric nonlinearity in dynamic problems, such as those presented by Almeida et al [35] and Polat and Calayir [36], could be also used. From this perspective, a nonlinear formulation for FEM dynamic analysis was employed by Shooshtari and Razavi [37] to analyze the free vibration of rectangular plates resting on an elastic foundation.…”

Section: 4 Finite Element Analysis 4fem Formulation Overviewmentioning

confidence: 99%

Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast

Wahrhaftig

Brasil

2016

J Braz. Soc. Mech. Sci. Eng.

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Geometrically Nonlinear Behaviour of Functionally Graded Beam and Frame Structures Under Mechanical Loading

Bui

Tran

Nguyen

2022

The AUN/SEED-Net Joint Regional Conference in Transportation, Energy, and Mechanical Manufacturing Engineering

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Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

Cited by 34 publications

References 17 publications

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Initial undamped resonant frequency of slender structures considering nonlinear geometric effects: the case of a 60.8 m-high mobile phone mast

Geometrically Nonlinear Behaviour of Functionally Graded Beam and Frame Structures Under Mechanical Loading

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