Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams

Maqueda, Luis G.; Shabana, Ahmed A.

doi:10.1007/s11044-007-9077-z

Cited by 50 publications

(25 citation statements)

References 17 publications

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“…(12) assume that material is fully incompressible, that is, J is equal to one. This condition must be fulfilled by using additional techniques, such as Lagrange multipliers or penalty method [23]. In the current paper, the penalty method is used, due to simplicity and efficiency.…”

Section: Standard Mooney-rivlin Polynomial Modelsmentioning

confidence: 99%

“…A similar pendulum was examined in [23]. In the undeformed state, beam has a length of 1 m and a uniform square cross section of dimension 20 mm.…”

Section: Physical Pendulummentioning

confidence: 99%

“…The isotropic and hyperelastic material models (including incompressible models) were introduced into ANCF by Maqueda and Shabana [23]. Moreover, the applications of the incompressible materials to the rubber chains build with ANCF beam elements were presented [22].…”

Section: Introductionmentioning

confidence: 99%

“…While this objective was addressed in previous publications [23], the main contribution of this paper is to show the importance of volumetric locking elimination in the applications when bending-dominated models are considered. For a detailed overview of the locking phenomena occurring within ANCF framework as well as general review of developments in ANCF, consult [14,26].…”

Section: Introductionmentioning

confidence: 99%

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Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Orzechowski

Frączek

2015

Nonlinear Dyn

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Many modern applications of the flexible multibody systems require formulations that can effectively solve problems that include large displacements and deformations having the ability to model nonlinear materials. One method that allows dealing with such systems is continuum-based absolute nodal coordinate formulation (ANCF). The objective of this study is to formulate an efficient method of modeling nonlinear nearly incompressible materials with polynomial Mooney-Rivlin models and volumetric energy penalty function in the framework of the ANCF. The main part of this paper is dedicated to the examination of several ANCF fully parameterized beam elements under incompressible regime. Moreover, two volumetric suppression methods, originating in the finite element analysis, are proposed: a well-known selective reduced integration and F-bar projection. It is also presented that the use of these methods is crucial for performing reliable analysis of models with bending-dominated loads when lower-order elements are employed. The results of the simulations carried on with considered elements and proposed methods are compared with the results obtained from commercial finite element package and existing ANCF implementation. The results

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Section: Standard Mooney-rivlin Polynomial Modelsmentioning

confidence: 99%

“…A similar pendulum was examined in [23]. In the undeformed state, beam has a length of 1 m and a uniform square cross section of dimension 20 mm.…”

Section: Physical Pendulummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Orzechowski

Frączek

2015

Nonlinear Dyn

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“…Compressible and incompressible hyperelastic and isotropic material models were firstly used within the ANCF by Maqueda and Shabana (2007). Furthermore, Maqueda et al (2010) presented the application of the ANCF beams with incompressible materials to rubber chains systems.…”

Section: Introductionmentioning

confidence: 99%

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Orzechowski

Frączek

2017

jtam

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The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F -bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

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Dynamic Modelling and Analysis of Flexible Structure Actuated by Dielectric Elastomer

Guo,

Li,

et al. 2024

Lecture Notes in Mechanical Engineering

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Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams

Cited by 50 publications

References 17 publications

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Dynamic Modelling and Analysis of Flexible Structure Actuated by Dielectric Elastomer

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