Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

Carrera, Erasmo; Azzara, R.; Daneshkhah, Ehsan; Pagani, Alfonso; Wu, Bin

doi:10.1016/j.ijnonlinmec.2021.103716

Cited by 29 publications

(5 citation statements)

References 52 publications

(75 reference statements)

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“…A comparison between the 3D full Green-Lagrange nonlinear strains and the classical von Kármán strains is reported. For completeness, readers are referred to [62] for a comparison between the linear buckling results and those obtained by incremental solutions.…”

Section: Numerical Resultsmentioning

confidence: 99%

Effect of different geometrically nonlinear strain measures on the static nonlinear response of isotropic and composite shells with constant curvature

Pagani

Azzara

et al. 2021

Preprint

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The structural analysis of ultra-lightweight flexible shells and membranes may require the adoption of complex nonlinear strain-displacement relations. These may be approximated and simplified in some circumstances, e.g., in the case of moderately large displacements and rotations, in some others may be not. In this paper, the effectiveness of various geometrically nonlinear strain approximations such as the von Kármán strains is investigated by making use of refined shell formulations based on the Carrera Unified Formulation (CUF). Furthermore, geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton-Raphson method. Test cases include the study of shells subjected to pinched loadings, combined flexure and compression, and post-buckling including snap-through problems. It is demonstrated that full geometrically nonlinear analysis accounting for full Green-Lagrange strains shall be performed whenever displacements are higher than the order of magnitude of the thickness and if compressive loads are applied.

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Section: Numerical Resultsmentioning

confidence: 99%

Effect of different geometrically nonlinear strain measures on the static nonlinear response of isotropic and composite shells with constant curvature

Pagani

Azzara

et al. 2021

Preprint

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“…Note that the vectors 𝒖, 𝜸 and 𝝈 ⟨ℓ ⟩ represent the eigenfunction associated with the eigenvector 𝜆 and have a different meaning than the vectors appearing in Eq. (19). Eventually, the smallest value of 𝜆 represents the critical multiplicative factor to be applied to the external loads in order for the structure to buckle.…”

Section: F Buckling Problemmentioning

confidence: 99%

“…The most widely employed numerical method is the Finite Element Method (FEM), which is at the base of many commercial software libraries featuring a buckling solver and is still employed in current research studies focused on buckling analysis, see e.g. [19,20].…”

Section: Introductionmentioning

confidence: 99%

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

2022

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A novel formulation for the linear buckling analysis of multilayered shells is presented. High-order equivalent-single-layer shell theories based on the through-the-thickness expansion of the covariant components of the displacement field are employed. The novelty of the formulation regards the governing equations solution via implicit-mesh discontinuous Galerkin method. It is a high-order accurate numerical technique based on a discontinuous representation of the solution among the mesh elements and on the use of suitably defined boundary integrals to enforce the continuity of the solution at the inter-element interfaces as well as the boundary conditions. Owing to its discontinuous nature, it can be naturally employed with nonconventional meshes. In this work, it is combined with the implicitly defined mesh technique, whereby the mesh of the shell modeling domain is constructed by intersecting an easy-to-generate background grid and a level set function implicitly representing the cutouts. Several numerical examples are considered for the buckling loads of plates and shells modeled by different theories and characterized by various materials, geometry, boundary conditions, and cutouts. The obtained results are compared with literature and finite-element solutions, and they demonstrate the accuracy and the robustness of the proposed approach.

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“…In CUF, the accuracy of the model can be fine-tuned straightforwardly since the order of the structural model is treated as input of the analysis. CUF has been adopted to obtain 2D theories, which have been then extended to the analysis of multilayered, composite plates and shells, and later for beam models [ 30 , 31 , 32 ]. In recent years, CUF has also been employed in the analysis of VAT composites.…”

Section: Introductionmentioning

confidence: 99%

Accurate Stress Analysis of Variable Angle Tow Shells by High-Order Equivalent-Single-Layer and Layer-Wise Finite Element Models

et al. 2021

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New concepts of lightweight components are conceived nowadays thanks to the advances in the manufacture of composite structures. For instance, mature technologies such as Automatic Fibre Placement (AFP) are employed in the fabrication of structural parts where fibres are steered along curvilinear paths, namely variable angle tow (VAT), which can enhance the mechanical performance and alleviate the structural weight. This is of utmost importance in the aerospace field, where weight savings are one of the main goals. For that reason, shell structures are commonly found in the aerospace industry because of their capabilities of supporting external loadings. Straight-fibre composite shell structures have been studied in recent decades and, now, spatially varying composite shells are attracting the attention of manufacturers. This work analyses the mechanical behaviour of VAT composite shells subjected to different external loadings and boundary conditions. The Carrera Unified Formulation (CUF) is employed to obtain the different structural models in a systematic and hierarchic manner. The outcomes of such numerical models are discussed and compared with commercial software Abaqus.

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Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

Cited by 29 publications

References 52 publications

Effect of different geometrically nonlinear strain measures on the static nonlinear response of isotropic and composite shells with constant curvature

Effect of different geometrically nonlinear strain measures on the static nonlinear response of isotropic and composite shells with constant curvature

Accurate Multilayered Shell Buckling Analysis via the Implicit-Mesh Discontinuous Galerkin Method

Accurate Stress Analysis of Variable Angle Tow Shells by High-Order Equivalent-Single-Layer and Layer-Wise Finite Element Models

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