Higher‐order beam model with eigenstrains: theory and illustrations

Corre, Grégoire; Lebée, Arthur; Sab, Karam; Ferradi, Mohammed Khalil; Cespedes, Xavier

doi:10.1002/zamm.201700180

Cited by 9 publications

(27 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The displacement modes are computed by using the asymptotic expansion method. This model was first introduced for elastic beams loaded by external forces in [39] and extended to the case of elastic beams loaded by eigenstrains in [40] before its adaptation to elastoplasticity [1]. This higher-order elastoplastic beam model was presented with 2 -plasticity.…”

Section: The Aeld Beam Modelmentioning

confidence: 99%

“…The modes are computed on a transverse mesh of the crosssection S. The discretization used is the same as the one used in [40] and [1]: the modes are computed by using Lagrange quadratic triangle finite elements. Strain and stress are computed and integrated at the 3 Gauss points of each triangle element and the modes of displacement are computed at the nodes of the transverse mesh.…”

Section: Numerical Approximationmentioning

confidence: 99%

“…In order to preserve local accuracy of the element and to get a better description of macroscopic forces, the approach adopted in the present paper is to use a higher-order elastoplastic beam model. First developed for elasticity in [39], it has been extended to eigenstrains [40] before being adapted to the case of elastoplasticity [1]. The kinematics is enriched thanks to a systematic method with displacement modes computed on the 2D cross-section of the structure.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A new higher-order elastoplastic beam model for reinforced concrete

et al. 2019

View full text Add to dashboard Cite

The present paper introduces a new elastoplastic beam model for reinforced concrete based on a higher-order beam model previously developed [1]. Steel and concrete are both defined as elastoplastic materials. The beam model represents the concrete body whereas rebars are given a specific discretization. A Rankine criterion is used for concrete in both tension and compression, and a closed-form solution for the local projection of the trial stress on the yield surface is formulated. Steel rebars are modelled with 1D bar elements and added to the global stiffness of the concrete beam model. The kinematics of the higher-order beam model is enriched by a systematic method with displacement modes. This extension of the kinematics leads to local accuracy and yields results comparable to 3D computations. The present reinforced concrete model is validated through a set of case studies. Implemented within the software programs of the company Strains Engineering, the objective is to develop a fast computing and efficient model that can be directly used by engineers.

show abstract

Section: The Aeld Beam Modelmentioning

confidence: 99%

Section: Numerical Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new higher-order elastoplastic beam model for reinforced concrete

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Here on the contrary, the implementation of the asymptotic method will require that we reconstruct the asymptotic theory of plates and beams in a low frequency regime, as previously done for a single body in solid mechanics, see e.g. [43,44] for plates and [45,46,47,48] for beams. However, this classical theory has to be complemented with matched asymptotic expansions to link the behavior in the periodic set of bodies with that in the substrate.…”

Section: Introductionmentioning

confidence: 99%

“…The effective (partial) problem -Reflection of an elastic wave on the surface x 1 = 0 where effective boundary conditions (6) apply. The incident wave is defined by(48) and the solution by(49). The arrows show the wavevectors.…”

mentioning

confidence: 99%

Effective model for elastic waves propagating in a substrate supporting a dense array of plates/beams with flexural resonances

Marigo

Pham

Maurel

et al. 2020

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

We consider the effect of an array of plates or beams over a semi-infinite elastic ground on the propagation of elastic waves hitting the interface. The plates/beams are slender bodies with flexural resonances at low frequencies able to perturb significantly the propagation of waves in the ground. An effective model is obtained using asymptotic analysis and homogenization techniques, which can be expressed in terms of the ground alone with effective dynamic (frequencydependent) boundary conditions of the Robin's type. For an incident plane wave at oblique incidence, the displacement fields and the reflection coefficients are obtained in closed forms and their validity is inspected by comparison with direct numerics in a two-dimensional setting.

show abstract

The Asymptotic Expansion Load Decomposition elastoplastic beam model

Corre

Lebée

Sab

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

A new higher-order elasto-plastic beam model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher-order elastic beam model using the asymptotic expansion method. This model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the beam. In order to capture the effect of plasticity on the structure, the present elasto-plastic model considers the plastic strain as an eigenstrain imposed on the structure and new degrees of freedom are added on the fly into the kinematics during the incrementaliterative process. The radial return algorithm of 2 plastic flow is used. Because of the constant evolution of the beam kinematics, the Newton-Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever beam loaded at its free extremity is presented and compared to a 3D reference solution. The beam model shows satisfying results even at a local scale and for a computation time significantly reduced.

show abstract

Higher‐order beam model with eigenstrains: theory and illustrations

Cited by 9 publications

References 29 publications

A new higher-order elastoplastic beam model for reinforced concrete

A new higher-order elastoplastic beam model for reinforced concrete

Effective model for elastic waves propagating in a substrate supporting a dense array of plates/beams with flexural resonances

The Asymptotic Expansion Load Decomposition elastoplastic beam model

Contact Info

Product

Resources

About