On choice of optimal anisotropy of composite plates against buckling, with special attention to bending-twisting coupling

2019

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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].

mentioning

confidence: 99%

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

2019

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“…If the maximal post-buckling plate deflection value becomes lower (for the obtained solutions) compared to the maximal deflection of the known solutions, then the fact may implicitly require a decrease of edge junction forces. In the present paper, we watch the deflections from this viewpoint and demonstrate the decrease of the maximal plate deflection in the solutions obtained, as compared to the angle-ply or the "equal buckling" [29] solutions.…”

Section: Preliminary Considerationmentioning

confidence: 91%

“…It is interesting to mention that (see [29]) the lay-up of the maximal upper estimate of the first buckling value corresponds to the second item in (23)- (27). In the case of pre-buckling, the lay-up solution with maximal stiffness value corresponds to the first item in (23)- (27).…”

Section: Plate-wise Optimality Conditionsmentioning

confidence: 98%

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

2019

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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.

“…The value of 0 z is equal to zero. The relation ( 7) was obtained in the more simplified case in (Selyugin, 2013) using (Gibson, 1994) background on composites.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Analysis of Lay-Up Optimality Conditions for Buckling Optimization of Vat (Steered Fiber) Composite Plates

2020

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The present paper is devoted to the theoretical explanation of the known numerical results of other authors on re-distributing the pre-buckling stresses to supported regions for improving the buckling behavior. The analysis of the lay-up optimality conditions (derived earlier) for buckling optimization of VAT composite plates is performed. The plates have a symmetric lay-up and loaded along their contour by the in-plane forces. The consideration employs the von Karman approach. The lay-up optimality conditions correspond to the maximization of a single-mode (lowest) buckling eigenvalue. The order of magnitude of the items of the conditions is assessed and compared.