A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

Liguori, Francesco S.; Madeo, Antonio

doi:10.1002/nme.6714

Cited by 27 publications

(9 citation statements)

References 51 publications

(73 reference statements)

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“…In this section, we shortly introduce the shell model and its discrete approximation through the MISS‐4 FE. The FE quantities are only reported to introduce the notation, while we refer elsewhere for further insights 22,26 …”

Section: Linear‐elastic Formulationmentioning

confidence: 99%

“…These features are preserved in large‐deformation problems 24 even for constant and variable‐stiffness composite materials 25 . In addition, an enhanced variant, called MISS‐4c, improves the performance of MISS‐4 26 by using assumed stress fields that a‐priori satisfy also compatibility equations for symmetric composite materials.…”

Section: Introductionmentioning

confidence: 99%

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A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

Liguori

Madeo

Garcea

2022

Numerical Meth Engineering

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Mixed assumed stress finite elements (FEs) have shown good advantages over traditional displacement‐based formulations in various contexts. However, their use in incremental elasto‐plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic‐perfectly plastic materials and small deformation problems, the integration of the constitutive equation furnishes a closest point projection (CPP) involving all the element stress parameters. In this work, a dual decomposition strategy is adopted to split this problem into a series of CPPs at the integration points level and in a nonlinear system of equations over the element, in order to simplify its solution. The strategy is tested with a four nodes mixed shell FE, named MISS‐4, characterized by an equilibrated stress interpolation which improves the accuracy. Two decomposition strategies are tested to express the plastic admissibility either in terms of stress resultants or point‐wise Cauchy stresses. The recovered elasto‐plastic solution preserves all the advantages of MISS‐4, namely it is accurate for coarse meshes in recovering the equilibrium path and evaluating the limit load showing a quadratic rate of convergence, as demonstrated by the numerical results.

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Section: Linear‐elastic Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

Liguori

Madeo

Garcea

2022

Numerical Meth Engineering

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“…Recently, Koiter's method has been employed to analyze the postbucking behavior using a specialized hybrid-Trefftz FE for composite structures. 55 Moreover, the reduction technique gives remarkable advantages in optimal design strategies of composite structures. 4,5,[56][57][58] The Koiter ROM can be also employed in standard incremental-iterative strategies as an accurate nonlinear predictor 59,60 followed by Newton's iterations on the full model.…”

Section: Introductionmentioning

confidence: 99%

“…Also, an accurate and efficient sensitivity analysis to geometrical imperfections can be obtained, 52 with the imperfection considered directly through additional coefficients in the reduced system of the perfect structure, thereby avoiding the ROM re‐evaluation. Recently, Koiter's method has been employed to analyze the postbucking behavior using a specialized hybrid‐Trefftz FE for composite structures 55 . Moreover, the reduction technique gives remarkable advantages in optimal design strategies of composite structures 4,5,56‐58 .…”

Section: Introductionmentioning

confidence: 99%

A Koiter reduction technique for the nonlinear thermoelastic analysis of shell structures prone to buckling

Liguori

Magisano

Madeo

et al. 2021

Numerical Meth Engineering

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The multi-modal Koiter method is a reduction technique for estimating quickly the nonlinear buckling response of structures under mechanical loads requiring a fine discretization. The reduced model is based on a quadratic approximation of the full model using a few linear buckling modes and their second order corrections, followed by the projection of the equilibrium equations onto the modal subspace. In this article, the method is reformulated for geometrically nonlinear thermoelastic analyses of shell structures. The starting point is an isogeometric solid-shell discretization with an accurate modeling of thermal strains, temperature-dependent materials and general temperature distributions. The equilibrium path is defined as a displacement versus temperature amplifier curve, while mechanical loads are kept constant. The strain energy nonlinearity with respect to the temperature amplifier is the main obstacle in the definition of an accurate reduced model. This task is achieved by coherent asymptotic expansions in mixed form using independent stress variables at the integration points and accurate linear buckling modes obtained by a two-point mixed eigenvalue problem. Structures made of isotropic and multi-layered composite materials, including variable angle tow laminates, are considered to show the accuracy of the proposed method.

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“…3,4 Finite element simulation is a broadly used method for analysing composite structures. Liguori et al 5 developed a corotational mixed flat shell element for the geometrically nonlinear analysis of laminated composite structures. Chiu et al 6 established a composite damage model to address intralaminar damage and delamination, for modelling crushing of laminated composites.…”

Section: Introductionmentioning

confidence: 99%

Lightweight cylindrical composite shell structures to support optical instruments in extremely large telescopes: A case study

Zheng

Zhang

Wang³

et al. 2021

Science Progress

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Aiming at the issues of heavy weight and insufficient structural performance of optical instrument supporting structures in extremely large telescopes, the Wide-Field Optical Spectrograph (WFOS) of the Thirty Meter Telescope (TMT) was taken as a case to study. In order to develop lightweight structures which satisfies the design requirements for mass and stiffness, a design scheme of cylindrical composite shells supporting structure was proposed and their finite element models were developed. A size optimisation and a ply sequence optimisation of the composite structure were carried out. The structures before and after optimisation were evaluated from the aspects of mass, displacement, failure index and fundamental frequency. After the optimised design, the mass of the optimised WFOS cylindrical composite shell structure is reduced to approximately 50%, but its maximum displacement (0.513 mm) and fundamental frequency (8.275 Hz) are nearly unchanged. The study indicates that a cylindrical composite shell structure is an efficient structural form for large optical instruments.

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A corotational mixed flat shell finite element for the efficient geometrically nonlinear analysis of laminated composite structures

Cited by 27 publications

References 51 publications

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element

A Koiter reduction technique for the nonlinear thermoelastic analysis of shell structures prone to buckling

Lightweight cylindrical composite shell structures to support optical instruments in extremely large telescopes: A case study

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