Optimal laminate configurations with symmetric lay-ups for maximum postbuckling stiffness

Adali, Sarp; Verijenko, V.E.; Walker, Mark

doi:10.1016/0961-9526(95)91286-p

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…Among papers considering a description of the postbuckling stiffness, the paper [6] should be indicated. In the paper, the compressed post-buckled orthotropic laminated plates are considered.…”

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confidence: 99%

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Selyugin¹

2019

Preprint

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The present paper deals with the optimization of post-buckled composite plates. The plates have a symmetric lay-up. The layer orientation angles vary in the point-wise or in the platewise ways. The von Karman theory is employed. The boundary conditions are the simple support ones or the clamped ones. The structural potential energy is treated as a measure of structural stiffness. For the plate stiffness maximization problem, the first-order necessary conditions of the local optimality are derived. The mathematical treatment of the conditions is performed. The conditions contain two terms. One of them corresponds to the mid-plane strains; another one corresponds to the plate curvatures. The optimality conditions may lead to a co-axiality of some structural tensors. An illustration of the optimality conditions is presented.-2 - INTRODUCTIONPostbuckling of thin composite plates attracts the attention of numerous researchers, working in various modern application areas. Among these applications, there are the aerospace, the automotive, the marine, and the civil ones. According to design practice in composite structures, the account of the load-carrying capability "above buckling" gives an opportunity of extra weight saving, as compared to existing traditional design.Composite plates are a part of a considerable number of structures in the above applications. The loading applied to the plates is a combination of compression and shear. The compression dominates for the structures similar to the upper panels of an airplane wing structure. As the examples of known structures designed for pure shear, one may indicate airplane wing ribs and spars, as well as some fuselage panels. As a rule, the shear-loaded plates have the so-called angle-ply symmetric lay-up. For example, buckling is not allowed in airplane structures in the case of loading up to the so-called limit loads (LL) and may be allowed for the loading level between the limit loads and the so-called ultimate loads (UL).The latter loads are 1.5 times higher than the limit loads.When optimizing the composite plate, an engineer, in fact, does his best to save the structural weight, the material cost, and the production time. Due to that, the optimization problems for the composite plates attract considerable attention at the design phase. The layup optimization problem is one of them requiring a solution at the beginning of the design process. Since the last decade of the previous century, numerous papers dealt with the lay-up optimization of composite plates. The non-exhaustive list [1]-[22] contains the important publications devoted to the postbuckling analysis and optimization. The foundations of the postbuckling theory are described in [23].

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confidence: 99%

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Selyugin¹

2019

Preprint

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“…The first item in (16) is equal to zero due to (6). Hence, from the second item we obtain a relation for the orientation angle of k-th layer at a current point:…”

Section: Determination Of Ijmentioning

confidence: 99%

“…Among papers considering a description of the post-buckling stiffness, the paper [6] should be indicated. In the paper, the compressed post-buckled orthotropic laminated plates are considered.…”

Section: Introductionmentioning

confidence: 99%

Composite Plates and Their Lay-Up Solutions Leading to High Buckling and Post-Buckling Resistance

Selyugin¹

2019

Preprint

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At the beginning of the present paper, the post-buckled composite plates are examined. The plates have a symmetric lay-up. The layer orientation angles vary in a point-wise way or in a plate-wise way. The von Karman theory describes a plate behavior. For a plate stiffness maximization problem the first-order optimality conditions are derived. In the conditions, the essential roles play the mid-plane principal strains and the principal curvatures. The optimality conditions may lead to a co-axiality of some structural tensors. Analytical examples illustrate the solutions of such types. Further, several numerical examples are presented. In the examples, the plates are loaded by shear and have the high buckling-resisting ability also. A significant conclusion of the paper is that in the properly designed lay-up the outermost layers and the innermost layers play different roles. The former ones withstand mainly buckling, and the latter ones withstand mainly post-buckling. The innermost layers have the orientation angle rather close to 0°. The weight reduction opportunities are demonstrated.

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“…Typical examples are the works of Adali et al [3], Haftka and Walsh [4], Le Riche and Hafka [5], Aymerich and Serra [6], Irisarri et al [7,8], Bisagni and Vescovini [9]. Most of these works deal with the problem of the buckling load and/or post-buckling stiffness maximisation with an assigned mass [3][4][5][6]8], or the dual problem of minimisign the mass under constraints on the buckling strength [4,7,9], being the buckling phenomenon a main concern when dealing with the optimisation of thin-walled structures. Due to the discrete nature of the design variables and to the non-convexity of the problem, gradient-based algorithms cannot be used for the solution search and researchers have investigated and compared different meta-heuristics, including Genetic Algorithms (GAs), Integer Programming, Ant Colony Optimisation, Evolutionary Algorithms, searching for the most efficient choice, finally finding comparable results.…”

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A multi-scale two-level optimisation strategy integrating a global/local modelling approach for composite structures

Izzi

Montemurro

Catapano

et al. 2020

Composite Structures

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In this work, a multi-scale optimisation strategy for the preliminary design of composite structures involving design requirements at different scales, is presented. Such a strategy, denoted as GL-MS2LOS, has been formulated by integrating a dedicated global-local (GL) modelling approach into the multi-scale two-level optimisation strategy (MS2LOS). The GL-MS2LOS aims at proposing a very general formulation of the design problem, without introducing simplifying hypotheses and by considering, as design variables, the full set of geometric and mechanical parameters defining the behaviour of the composite structure at each pertinent scale. By employing a GL modelling approach, most of the limitations of well-established design strategies based on analytical or semi-empirical models are overcome. The effectiveness of the presented GL-MS2LOS is proven on a meaningful study case: the least-weight design of a composite fuselage barrel of a wide-body aircraft undergoing various loading conditions and subject to requirements of different nature. Fully parametric global and local FE models are interfaced with an in-house metaheuristic algorithm to perform the optimisation. Refined local FE models are created only for critical regions of the structure, automatically detected during the global analysis, and linked to the global one thanks to the implementation of a sub-modelling approach. The whole process is completely automated and, once set, it does not need any further user intervention. The general nature of the GL-MS2LOS allows finding an optimised configuration characterised by a weight saving of 40% when compared to an optimised aluminium solution obtained through a similar GL optimisation strategy.

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Optimal laminate configurations with symmetric lay-ups for maximum postbuckling stiffness

Cited by 6 publications

References 7 publications

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Composite Plates and Their Lay-Up Solutions Leading to High Buckling and Post-Buckling Resistance

A multi-scale two-level optimisation strategy integrating a global/local modelling approach for composite structures

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