Flutter of stiffened composite panels considering the stiffener’s base as a structural element

Castro, Saullo G.P.; Guimarães, Thiago A.; Rade, Domingos A.; Donadon, Maurício Vicente

doi:10.1016/j.compstruct.2015.12.056

Cited by 30 publications

(9 citation statements)

References 23 publications

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“…tween different semi-analytical domains [73,74,75,76], even for Koiter's asymptotic analysis. Such possibilities would allow one to apply semi-analytical methods for stiffened panels and shells using efficient displacement representations such as those provided by Legendre hierarchical polynomials [77,78,79,80].…”

Section: Resultsmentioning

confidence: 99%

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Castro¹,

Jansen²

2020

Preprint

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Koiter’s asymptotic method enables the calculation and deep understanding of the initial post-buckling behaviour of thin-walled structures. For the single-mode asymptotic analysis, Budiansky (1974) presented a clear and general formulation for Koiter’s method, based on the expansion of the total potential energy function. The formulation from Budiansky is herein revisited and expanded for the multimodal asymptotic analysis, of primordial importance in structures with clustered bifurcation modes. Given the admittedly difficult implementation of Koiter’s method, especially for multi-modal analysis and during the evaluation of the third– and fourth–order tensors involved in Koiter’s analysis; the presented study proposes a formulation and notation with close correspondence with the implemented algorithms. The implementation is based on state-of-the-art collaborative tools: Python, NumPy and Cython. The kinematic relations are specialized using von Kármán shell kinematics, and the displacement field variables are approximated using an enhanced Bogner-Fox-Schmit (BFS) finite element, modified to reach third-order interpolation also for the in-plane displacements, using only 4 nodes per element and 10 degrees-of-freedom per node, aiming an accurate representation of the second-order fields. The formulation and implementation are verified by comparing results for isotropic and composite plates against established literature. Finally, results for multi-modal displacement fields with up to 5 modes and corresponding post-buckling factors are reported for future reference.

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Section: Resultsmentioning

confidence: 99%

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Castro¹,

Jansen²

2020

Preprint

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“…The Legendre polynomials are chosen because they capture localised behaviour well due to the non-periodic nature of the successive polynomials with respect to trigonometric functions [12][13][14]. Moreover, with Legendre polynomials the choice between simply-supported, clamped or free boundary conditions is done by simply including or not the first terms in the series [12,15,16], in contrast with penalization-based approaches for linear [17][18][19] and non-linear semi-analytical approaches [20][21][22][23]. It has been mentioned that at the vertical edges, the Φ 0 functions only describe the 0 behaviour, i.e.…”

Section: Figmentioning

confidence: 99%

Semi-Analytical Modelling of Variable Stiffness Laminates with Cut-Outs

Janssens¹,

Castro²

2021

AIAA Scitech 2021 Forum

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Designs taking advantage of fibre-steered laminated manufacturing can optimally vary the stiffness and strength properties of high-performance structural components according to the geometry, loads and boundary conditions. For the stability behaviour of laminates with discontinuities such as local reinforcements and cut-outs, variable stiffness laminates have the additional ability to decrease stress concentration factors, increase buckling loads and decrease the negative effects of a cut-out; outperforming traditional straight-fibre designs. With the aim of finding closed-form analysis methods or methods with a reduced computational cost, the present study proposes a semi-analytical framework to analyze the stability behaviour of variable stiffness laminates with local reinforcements and cut-outs. Due to the discontinuous nature of the displacement field in these structures, the approximation functions are enriched to capture the behaviour near the discontinuity. In order to determine the energy functional derivatives across the laminate domain, Gauss-Legendre Quadrature numerical integration rules are applied to both rectangular and circular domains and the resultant energies are obtained by subtracting the integration of the cut-out domain from the full domain. A displacement-based formulation is used for the out-of-plane field variable, whereas a stress-based approach is used for the in-plane pre-buckling stress state. The model is set-up for balanced and symmetric laminates, thus decoupling the out-of-plane and the in-plane behaviours. A thorough verification is performed against existing models in the literature and against finite element results. The results for various plates and laminates with varying discontinuities and variable stiffness properties show a good agreement for both in-plane and out-of-plane field variables, ultimately leading to an accurate prediction of the stability behavior of structures with discontinuities.

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“…For the approximate solution of a simply supported immovable edges panel, the displacement field are evaluated using a set of Ritz functions as generalized coordinates [21], that is,…”

Section: Nonlinear Aeroelastic Modelmentioning

confidence: 99%

Nonlinear supersonic post-flutter motion of panels with adjacent bays and thermal effects

Guimarães

Sanches

Marques

2020

International Journal of Non-Linear Mechanics

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Aerospace vehicle structures in the supersonic regime flight have their outer skin subjected to unsteady aerodynamic and thermal loading, which may lead to aeroelastic instability. Typical aerospace structures are built as multiple adjacent panels, the so-called multi-bay configuration, but early efforts to predict the supersonic flutter were based on a single panel arrangement. This work evaluates the aeroelastic behavior of supersonic multi-bay fluttering panels under thermal effects, aiming to improve the understanding of adjacent panels interaction in the nonlinear regime. The aeroelastic model is established by using the first-order quasi-steady piston theory in conjunction with isotropic panel model using the von Kármán's assumptions to account for geometrical nonlinearities. The Newmark time-integration method is used to evaluate the resulting equations of motion. The Hopf bifurcation behavior that determines the flutter onset, thermo-buckling loading, phase portrait plots, and bifurcation diagrams for two adjacent panels are presented. The numerical results show the detrimental aspect of thermal loading in the aeroelastic behavior of fluttering panels, and the new findings corroborate with some recent studies that highlight the difference in the nonlinear flutter behavior between a single panel and multi-bay panels. Moreover, the existence of limit cycle oscillations amplitude jumps from a certain level of flow dynamic pressure is also observed. The multi-bay panels configuration also shows the anticipation of the buckled to the limit cycle oscillation solutions, when compared with a single panel analysis. Results indicate that simplified single bay panel assumptions can underestimate the post-flutter oscillations amplitudes of the adjacent bay. Such dynamic behavior may lead to a negative impact on aircraft structural design and fatigue life estimation.

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Flutter of stiffened composite panels considering the stiffener’s base as a structural element

Cited by 30 publications

References 23 publications

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Displacement-based formulation of Koiter’s method: application to multi-modal post-buckling finite element analysis of plates

Semi-Analytical Modelling of Variable Stiffness Laminates with Cut-Outs

Nonlinear supersonic post-flutter motion of panels with adjacent bays and thermal effects

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