A Total Lagrangian Isogeometric Timoshenko Beam Formulation for Large Displacement Analysis of 2D Frames

Chorn, V.; Vo, Duy; Nanakorn, Pruettha

doi:10.1007/978-981-15-8079-6_90

Cited by 3 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this reason, other authors often consider Mattiasson's solutions as analytical ones. 25,26 Owing to symmetry, only a quarter of each frame needs to be analyzed. In our simulations, it is sufficient to use a mesh consisting of two elements for the square frame (Figure 7B) and a single-element mesh for the diamond frame (10b).…”

Section: Framesmentioning

confidence: 99%

See 1 more Smart Citation

Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

The article is focused on a two-dimensional geometrically nonlinear formulation of a Bernoulli beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

show abstract

Section: Framesmentioning

confidence: 99%

“…The elliptic integrals were numerically evaluated and presented in a tabulated form by Mattiasson 23 based on the procedure described by King, 24 which has shown excellent convergence properties and highly accurate results. For this reason, other authors often consider Mattiasson's solutions as analytical ones 25,26 …”

Section: Numerical Examplesmentioning

confidence: 99%

Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…The elliptic integrals were numerically evaluated and presented in a tabulated form by Mattiasson 13 based on the procedure described by King 14 , which has shown excellent convergence properties and highly accurate results. For this reason, other authors often consider Mattiasson's solutions as analytical ones 15,16 .…”

Section: Framesmentioning

confidence: 99%

Efficient formulation of a geometrically nonlinear beam element

Jirásek¹,

Ribolla²,

Hořák³

2021

Preprint

View full text Add to dashboard Cite

The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

show abstract

Geometrically Nonlinear Behavior of L-Shaped Frames Under Forces Applied at Different Positions

Duong¹,

Vo²,

Nanakorn³

2023

Lecture Notes in Civil Engineering

View full text Add to dashboard Cite

A Total Lagrangian Isogeometric Timoshenko Beam Formulation for Large Displacement Analysis of 2D Frames

Cited by 3 publications

References 10 publications

Efficient finite difference formulation of a geometrically nonlinear beam element

Efficient finite difference formulation of a geometrically nonlinear beam element

Efficient formulation of a geometrically nonlinear beam element

Geometrically Nonlinear Behavior of L-Shaped Frames Under Forces Applied at Different Positions

Contact Info

Product

Resources

About