Refined beam elements with arbitrary cross-section geometries

Carrera, Erasmo; Giunta, Gaetano; Nali, Pietro; Petrolo, Marco

doi:10.1016/j.compstruc.2009.11.002

Cited by 224 publications

(108 citation statements)

References 25 publications

Supporting

Mentioning

105

Contrasting

Order By: Relevance

“…Third-order Lagrange polynomials are used as shape functions. For the sake of brevity, more details are not reported here, but can be found in Carrera et al [9,11]. This beam model can be easily extended to mixed theories.…”

Section: Finite Element Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

Varello¹,

Carrera²

2014

Proceedings of 10th World Congress on Computational Mechanics

Self Cite

View full text Add to dashboard Cite

Abstract. This paper presents an application of refined one-dimensional (1D) models to the static and free vibration analysis of thin-walled layered structures. Carrera Unified Formulation (CUF) is employed to easily introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the beam cross-section. Classical Euler-Bernoulli beam theory is obtained as a particular case of these variable kinematic models while a higher-order expansion permits the detection of the in-plane cross-section deformation. Finite element (FE) method is used to provide numerical results. In particular, the case of a deformable clamped-clamped thin-walled layered cylinder loaded by a non-uniform internal pressure is discussed. The static analysis reveals the model capabilities in accurately describing the three-dimensional deformation of the cylinder. The free vibration analysis provides results not detectable by typical 1D models in excellent agreement with a solid (3D) FE solution. The present models do not introduce additional numerical problems with respect to classical beam theories. Moreover, the results clearly show that finite elements which are formulated in the CUF framework offer shell-type capabilities in analyzing thin-walled structures with a remarkable reduction in the computational cost required.

show abstract

Section: Finite Element Formulationmentioning

confidence: 99%

“…CUF has been developed over the last decade for plate/shell models [6,3] and it has recently been extended to static and dynamic 1D modeling [7,9,12]. CUF is a hierarchical formulation which considers the order of the model as a free-parameter of the analysis.…”

Section: Introductionmentioning

confidence: 99%

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

Varello¹,

Carrera²

2014

Proceedings of 10th World Congress on Computational Mechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…1), contrary to what occurs in the CUF, thus enabling the definition of non-ambiguous generalised stress-resultants, reducing the coupling of equilibrium equations, and leading to more coherent BCs. Finally, it is noted that the present beam element includes only the two extremity nodes, while Carrera et al [25] developed elements with two, three and four nodes, respectively addressed as B2, B3 and B4.…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…The choice falls on the so-called ''Carrera's Unified Formulation'', or CUF, briefly discussed in the introductory section of the companion paper [1], due to its systematic approach and completeness (Carrera and Giunta [3]; Carrera et al [4,25]). …”

Section: Comparison With Other Refined Higher-order Beam Theoriesmentioning

confidence: 99%

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Almeida

Correia

Pinho

2015

Engineering Structures

View full text Add to dashboard Cite

a b s t r a c tThe specific features of the proposed force-based formulation derived in the companion paper, which is applied for the first time to higher-order beam theories, are herein thoroughly validated. Introductory numerical examples illustrate the influence of mesh refinement, boundary conditions, and slenderness ratios for isotropic linear elastic response. Specific higher-order effects-unique to the developed element-are then suitably interpreted, as well as the formulation appropriateness to consider distributed loads and to model three-dimensional behaviour, which is verified with solid finite element analyses. Extensive comparisons against existing proposals, namely other refined higher-order beam theories, emphasize the performance of the proposed approach. Finally, the nonlinear response of the element with a multiaxial J2 linear plasticity material model is analysed, highlighting its advantages in relation to a classical force-based Euler-Bernoulli beam using a one-dimensional plastic material model with kinematic hardening.

show abstract

“…The Taylor expansion (TE) or Lagrange expansion (LE) can be used to describe the displacement over the cross-section. When TE is adopted, as shown by Carrera and Giunta [20] and Carrera et al [21], the displacements are approximated using a global expansion around a point, which is usually the centroid of the crosssection. Static and dynamic analyses using TE models were presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Accurate Free Vibration Analysis of Launcher Structures Using Refined 1D Models

Carrera¹,

Zappino²,

Cavallo³

2015

International Journal of Aeronautical and Space Sciences

View full text Add to dashboard Cite

This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.

show abstract

Refined beam elements with arbitrary cross-section geometries

Cited by 224 publications

References 25 publications

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

Static and Dynamic Analysis of a Thin-Walled Layered Cylinder by Refined 1d Theories

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Accurate Free Vibration Analysis of Launcher Structures Using Refined 1D Models

Contact Info

Product

Resources

About