Finite beam elements based on Legendre polynomial expansions and node-dependent kinematics for the global-local analysis of composite structures

Li, G.; Miguel, A. G. de; Pagani, Alfonso; Zappino, Enrico; Carrera, Erasmo

doi:10.1016/j.euromechsol.2018.11.006

Cited by 14 publications

(3 citation statements)

References 73 publications

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“…Since the Finite Element Method (FEM) is used for the beam axis approximation, no problems about coupling different expansion functions arise. NDK was used and validated in the past years by Carrera and Zappino [34] and applied to composite struc-tures [35,36], 2D plate [37,38] and shell problems [39]. The geometrical nonlinear 1D governing equations of the beam theory are obtained by means of the so-called fundamental nuclei, which allow the automatic employment of low-to higher-order theories, arbitrarily.…”

Section: Introductionmentioning

confidence: 99%

Large deflection of composite beams by finite elements with node-dependent kinematics

2022

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In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis.

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Section: Introductionmentioning

confidence: 99%

Large deflection of composite beams by finite elements with node-dependent kinematics

2022

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“…They can change along the beam, and no problems about joining different expansion functions arise since the finite element method (FEM) is used between the two domains. NDK was used and validated in the past years by Carrera and Zappino [34] and applied to composite structures [35,36], a two-dimensional (2D) plate [37,38] and shell problems [39]. An application of NDK to the fluid-structure interaction can be found in [40].…”

Section: Introductionmentioning

confidence: 99%

Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

2020

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In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

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“…The numerical efficiency of the hierarchical elements has been reported by many researchers [34,35,40,41]. In the framework of CUF, this type of hierarchical functions has been used on refined beam [42], plate [43], and shell [12] finite element models for multi-layered structures. Via refined hierarchical 2D elements, the FE models can be mathematically enriched on both the kinematic and shape function levels, leading to an adaptable refinement FE approach with optimal numerical efficiency.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of shear and membrane locking in refined hierarchical shell finite elements for laminated structures

Carrera

Cinefra

et al. 2019

Adv. Model. and Simul. in Eng. Sci.

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Shear and membrane locking phenomena are fundamental issues of shell finite element models. A family of refined shell elements for laminated structures has been developed in the framework of Carrera Unified Formulation, including hierarchical elements based on higher-order Legendre polynomial expansions. These hierarchical elements were reported to be relatively less prone to locking phenomena, yet an exhaustive evaluation of them regarding the mitigation of shear and membrane locking on laminated shells is still essential. In the present article, numerically efficient integration schemes for hierarchical elements, including also reduced and selective integration procedures, are discussed and evaluated through single-element p-version finite element models. Both shear and membrane locking are assessed quantitatively through the estimation of strain energy components. The numerical results show that the fully integrated hierarchical shell elements can overcome the shear and membrane locking effectively when a sufficiently high polynomial degree is reached. Reduced and selective integration schemes can help with the mitigation of locking on lower-order hierarchical shell elements.

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Finite beam elements based on Legendre polynomial expansions and node-dependent kinematics for the global-local analysis of composite structures

Cited by 14 publications

References 73 publications

Large deflection of composite beams by finite elements with node-dependent kinematics

Large deflection of composite beams by finite elements with node-dependent kinematics

Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

Evaluation of shear and membrane locking in refined hierarchical shell finite elements for laminated structures

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