Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models

Carrera, Erasmo; Kaleel, Ibrahim; Petrolo, Marco

doi:10.1080/15376494.2017.1378780

Cited by 35 publications

(12 citation statements)

References 22 publications

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“…The Newton-Raphson incremental linearized scheme is employed as in Pagani and Carrera 26 and Carrera et al 29 The linearized strain-displacement operators and stress-strain relations are…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

“…The Carrera Unified Formulation (CUF) can generate any-order structural theory and, recently, has been extended to nonlinear problems. [26][27][28][29][30][31] Pagani and Carrera formulated a refined beam model based on the CUF to solve geometrically nonlinear problems. They presented the Fundamental Nucleus (FN) of the secant and tangent stiffness matrix and used the Newton-Raphson linearization scheme along with a path-following method.…”

Section: Introductionmentioning

confidence: 99%

“…27 The same authors investigated the large deflection and post-buckling of composite beams using the CUF, and layer-wise kinematics. 26 Carrera et al 29 carried out a nonlinear analysis on the elastoplastic thin-walled structures using the isotropically work-hardening von Mises constitutive model for the material nonlinearity. Petrolo et al 28 presented a global-local approach based on the CUF considering physical nonlinearities to analyze elastoplastic thin-walled structures.…”

Section: Introductionmentioning

confidence: 99%

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Static analysis of thin-walled beams accounting for nonlinearities

Petrolo

Nagaraj

Daneshkhah

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom.

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“…The Newton-Raphson incremental linearized scheme is employed as in Pagani and Carrera 26 and Carrera et al 29 The linearized strain-displacement operators and stress-strain relations are…”

Section: Nonlinear Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Static analysis of thin-walled beams accounting for nonlinearities

Petrolo

Nagaraj

Daneshkhah

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…In particular, their introduction could be essential when these innovative constituents are included in the stacking sequences of multilayered or sandwich structures [ 20 , 21 , 22 , 23 , 24 , 25 ]. These aspects have been clearly emphasized in the works by Carrera [ 26 , 27 , 28 ], Carrera and Giunta [ 29 ], and Carrera et al [ 30 ]. In these works, accurate and effective higher-order structural models based on a unified formulation have been presented.…”

Section: Introductionmentioning

confidence: 99%

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

Bacciocchi

Tarantino

2021

Materials

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The aim of the paper is the development of a third-order theory for laminated composite plates that is able to accurately investigate their bending behavior in terms of displacements and stresses. The starting point is given by the corresponding Reddy’s Third-order Shear Deformation Theory (TSDT). This model is then generalized to consider simultaneously the Classical Laminated Plate Theory (CLPT), as well as the First-order Shear Deformation Theory (FSDT). The constitutive laws are modified according to the principles of the nonlocal strain gradient approach. The fundamental equations are solved analytically by means of the Navier methodology taking into account cross-ply and angle-ply lamination schemes. The numerical applications are presented to highlight the nonlocal effects on static behavior.

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“…UF has been extended to large deflections and postbuckling analysis of beam structures in recent works by Pagani and Carrera [20,21], where the capability of such approach to investigate global and local deformations in solid and thin-walled beam structures was demonstrated by using Lagrange polynomials as approximating functions for the cross-section kinematics within a layer-wise approach. An elastoplastic analysis via UF-based one-dimensional finite elements has been carried out by Carrera et al [22], showing that such formulation can lead to a 3D-like accuracy in terms of displacements and stresses for compact and thin-walled structures subjected to localized loadings. Applications of the UF approach for the investigation of multiphysics problems, vibration analyses, and static structural analyses of composite structures can be found in Carrera et al [23], Biscani et al [24], Koutsawa et al [25], and Giunta et al [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

Hui

Pietro

Giunta

et al. 2018

Mathematical Problems in Engineering

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models

Cited by 35 publications

References 22 publications

Static analysis of thin-walled beams accounting for nonlinearities

Static analysis of thin-walled beams accounting for nonlinearities

Third-Order Theory for the Bending Analysis of Laminated Thin and Thick Plates Including the Strain Gradient Effect

Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements

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