Geometrically nonlinear analysis of sandwich FGM and laminated composite degenerated shells using the isogeometric finite strip method

Shahmohammadi, Mohammad Amin; Azhari, Mojtaba; Saadatpour, M.M.; Sarrami-Foroushani, Saeid

doi:10.1016/j.cma.2020.113311

Cited by 32 publications

(5 citation statements)

References 40 publications

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“…• The 2D von Kármán strain approximation can be adopted for the analysis of pinched cylindrical shells and hinged cylindrical panels under transverse loads, but the 3D full geometrically nonlinear model should be employed for structures subjected to compressive loads. The same considerations made for the snap-through instability case are also valid for the snap-back one, already studied in the works of Wu et al [30] and Shahmohammadi et al [64].…”

Section: Discussionmentioning

confidence: 62%

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: Discussionmentioning

confidence: 62%

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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“…Some other studies have been conducted by combining the different numerical solutions in a unit formulation. For instance, in the Shahmohammadi et al [57][58][59][60] a new version of finite strip method was developed by combining the isogeometric analysis and finite element method. Also in Shahmohammadi et al, 61 a coupled FEM-DQM formulation was developed to assess the nonlinear behavior of sandwich nanoplates.…”

Section: Introductionmentioning

confidence: 99%

An analytical closed-form solution for free vibration and stability analysis of curved sandwich panels made of porous metal-foam core and nanocomposite reinforced face-sheets

Badarloo,

Salehipour

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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This paper aims to obtain an analytical solution for free vibration and stability analysis of shallow curved sandwich panels made of a porous metal-foam core and nanocomposites reinforced sheets resting on a Winkler-Pasternak elastic foundation. In this regard, two nanocomposites, carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) are considered for reinforcing the face-sheets. The governing equations are developed by considering the transversal shear strains based on the first-order shear deformation theory (FSDT). The obtained system of differential equations representing the dynamic equilibrium and compatibility of the proposed curved sandwich panels are solved analytically, using the principal of Galerkin method. In order to examine the results of developed formulation, some benchmark examples are adopted from the existing literature and the obtained results corresponding to the considered examples are compared with those are presented in the references. Using the achieved numerical results in the framework of a comprehensive parametric study, the effects of various material and geometrical factors and also various boundary conditions on the natural frequencies and buckling loads of the proposed sandwich panels are assessed. By performing the extensive parametric study it was observed that several results corresponding to the free vibration and stability of the proposed sandwich panels can be achieved by the present method without spending much time for computations. On the contrary, in order to achieve the similar results using the numerical methods, a time-consuming process is required which can justify the novelty of the present work.

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“…Studies and employment of FSM have been extensive in recent decades. However, some research works are recently carried out to use this approach for various problems; for example, see References 58–63. More detailed information on FSM can be found in the books by Cheung 57 and Cheung and Tham 64 …”

Section: Introductionmentioning

confidence: 99%

Finite strip method based on Carrera unified formulation for the free vibration analysis of variable stiffness composite laminates

Shojaee

Hamzehei‐Javaran

2022

Numerical Meth Engineering

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This work presents a refinement of the finite strip method (FSM) based on the Carrera unified formulation (CUF) and is applied to free vibration analysis of variable stiffness composite laminated (VSCL) plates. VSCL plates considered here are composed of layers with curvilinear fibers in which their orientation angle changes linearly with respect to one of the in‐plane coordinates. The FSM permits the plate to be divided into some finite strips connected along the so‐called nodal lines. The conventional finite strip method involves an approximation of the solution of a plate problem by using continuously harmonic series in the longitudinal direction along the nodal lines and simple polynomial shape functions (the usual beam shape functions) in the transverse direction of the plate. However, refined finite strip model that presented in this paper allows one to express the unknown variables as a set of thickness functions that only depend on the thickness coordinate and the corresponding variable that depends on the in‐plane coordinates which involve continuously harmonic series and polynomial shape functions. Thanks to this new finite strip model, the shape functions used in the transverse direction can be chosen as 1D bar shape functions, and also, all three components of the displacement field are considered in each nodal line. Moreover, based on this approach, three‐dimensional displacement field is approximated in a compact form as a generic N‐order expansion. Therefore, explicit expressions of fundamental nuclei of finite strip matrices are obtained in a compact form and presented here. The results obtained by the present formulation for VSCL plates are compared with those obtained from published data. The results show that this kind of strip is efficient and useful. Further, several numerical examples are presented, and the effect of the order of expansion, the number of strips, curvilinear fiber angle, and various boundary conditions are examined.

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Geometrically nonlinear analysis of sandwich FGM and laminated composite degenerated shells using the isogeometric finite strip method

Cited by 32 publications

References 40 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

An analytical closed-form solution for free vibration and stability analysis of curved sandwich panels made of porous metal-foam core and nanocomposite reinforced face-sheets

Finite strip method based on Carrera unified formulation for the free vibration analysis of variable stiffness composite laminates

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