An isogeometric framework for the optimal design of variable stiffness shells undergoing large deformations

Liguori, Francesco S.; Zucco, Giovanni; Madeo, Antonio; Garcea, Giovanni; Leonetti, Leonardo; Weaver, Paul M.

doi:10.1016/j.ijsolstr.2020.11.003

Cited by 38 publications

(26 citation statements)

References 38 publications

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“…The test regards a curved panel under compression whose geometry, loads, and boundary conditions are represented in Fig.1. The postbuckling response of this panel has been optimised in [4,2]. Tables 1 and 2 show the convergence of the first 4 linearised buckling loads.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Alternatively, the constitutive matrix can be expressed as a function of lamination parameters that is useful in optimisation problems, as shown in [2].…”

Section: Modified Generalized Constitutive Matrixmentioning

confidence: 99%

“…Composite shells are nowadays employed as primary structural elements in a very wide range of applications [1,2]. Their success is mainly due to the high strength/weight ratio that is crucial for lightweight structures.…”

Section: Introductionmentioning

confidence: 99%

“…In this way, the response of the structure is defined by a reduced system of nonlinear equations where the unknowns are the load factor and m modal amplitudes and the coefficients correspond to 2nd, 3rd and 4th order energy variations. The most convenient aspect of the method is that the effects of geometrical imperfections can be included a posteriori in the reduced system of the perfect structure [1,2].…”

Section: Introductionmentioning

confidence: 99%

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An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies

Liguori¹,

Madeo²,

Leonetti³

et al. 2021

14th WCCM-ECCOMAS Congress

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The optimal design of shell structures undergoing buckling phenomena is nowadays an open problem, whose solution would provide interesting answers to both academy and industry. The main difficulty is represented by the high computational cost required for optimising a full-scale structure characterised by a relatively complex postbuckling behaviour. In this work, this topic is addressed by proposing an isogeometric solid-shell model. The equilibrium path is evaluated through a multimodal Koiter's method. The resulting postbuckling analysis turns out to be efficient and accurate, as shown by numerical examples.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Alternatively, the constitutive matrix can be expressed as a function of lamination parameters that is useful in optimisation problems, as shown in [2].…”

Section: Modified Generalized Constitutive Matrixmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies

Liguori¹,

Madeo²,

Leonetti³

et al. 2021

14th WCCM-ECCOMAS Congress

View full text Add to dashboard Cite

show abstract

“…A numerical example of optimal material design is also given, where the optimisation suppresses the snap-through instability leading a globally stable behaviour. Examples of applicability for actual engineering uses can be found in [ 27 , 35 ].…”

Section: Introductionmentioning

confidence: 99%

Material Design for Optimal Postbuckling Behaviour of Composite Shells

et al. 2021

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Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufacturing methods are enabling the realization of composite materials with spatially varying material properties. Variable angle tow fibre composites are a representative example, but also nanocomposites are opening new interesting possibilities. Taking advantage of these tunable materials requires the development of computational design methods. The failure of such structures is often dominated by buckling and can be very sensitive to material configuration and geometrical imperfections. This work is a review of the recent computational developments concerning the optimisation of the response of composite thin-walled structures prone to buckling, showing how baseline products with unstable behaviour can be transformed in stable ones operating safely in the post-buckling range. Four main aspects are discussed: mechanical and discrete models for composite shells, material parametrization and objective function definition, solution methods for tracing the load-displacement path and assessing the imperfection sensitivity, structural optimisation algorithms. A numerical example of optimal material design for a curved panel is also illustrated.

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Dragonfly‐Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams

et al. 2023

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This research is taking the first steps toward applying a 2D dragonfly wing skeleton in the design of an airplane wing using artificial intelligence. The work relates the 2D morphology of the structural network of dragonfly veins to a secondary graph that is topologically dual and geometrically perpendicular to the initial network. This secondary network is referred as the reciprocal diagram proposed by Maxwell that can represent the static equilibrium of forces in the initial graph. Surprisingly, the secondary graph shows a direct relationship between the thickness of the structural members of a dragonfly wing and their in‐plane static equilibrium of forces that gives the location of the primary and secondary veins in the network. The initial and the reciprocal graph of the wing are used to train an integrated and comprehensive machine‐learning model that can generate similar graphs with both primary and secondary veins for a given boundary geometry. The result shows that the proposed algorithm can generate similar vein networks for an arbitrary boundary geometry with no prior topological information or the primary veins' location. The structural performance of the dragonfly wing in nature also motivated the authors to test this research's real‐world application for designing the cellular structures for the core of airplane wings as cantilever porous beams. The boundary geometry of various airplane wings is used as an input for the design proccedure. The internal structure is generated using the training model of the dragonfly veins and their reciprocal graphs. One application of this method is experimentally and numerically examined for designing the cellular core, 3D printed by fused deposition modeling, of the airfoil wing; the results suggest up to 25% improvements in the out‐of‐plane stiffness. The findings demonstrate that the proposed machine‐learning‐assisted approach can facilitate the generation of multiscale architectural patterns inspired by nature to form lightweight load‐bearable elements with superior structural properties.

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An isogeometric framework for the optimal design of variable stiffness shells undergoing large deformations

Cited by 38 publications

References 38 publications

An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies

An Isogeometric Solid-Shell Model for Postbuckling Optimisation Strategies

Material Design for Optimal Postbuckling Behaviour of Composite Shells

Dragonfly‐Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams

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