C.B. York

Unified Approach to the Characterization of Coupled Composite Laminates: Benchmark Configurations and Special Cases

Benchmark stacking sequence configurations with up to 21 plies are presented for laminates with properties similar to conventional materials, and against which new forms of coupled laminate behavior can be assessed. The benchmark configurations include fully uncoupled extensionally isotropic laminates and fully isotropic laminates, together with a special class of uncoupled laminate, possessing matching elastic properties in both extension and bending; more commonly referred to as a quasi-homogeneous orthotropic laminate. The concept of an equivalent isotropic laminate is also introduced as a universally applicable datum, useful for characterization of ply number groupings for which no benchmark configurations exist. Most of the benchmark configurations are found to possess nonsymmetric stacking sequences, which also serves to demonstrate that stacking sequence symmetry is neither sufficient nor necessary for fully uncoupled laminate designs. Finally, dimensionless parameters are provided for each stackin...

Unified approach to the characterization of coupled composite laminates

Purpose – The purpose of this paper is to demonstrate new design concepts for 24 classes of laminate, which have been derived as part of an ongoing study on the development of a unified approach to the characterization of coupled laminates. The paper presents a description of each class of coupled laminate.Design/methodology/approach – The paper gives an overview of the desired performance and requirements of a smart leading edge device, its aerodynamic design for the wind tunnel tests and the structural pre‐design and sizing of the full‐scale leading edge section which will be tested in the wind tunnel.Findings – Coupled laminates have potential applications in the design of aero‐elastic compliant rotor blades or aircraft wing structures, by introducing tailored extension‐twist and/or shear‐extension coupling at the laminate level; or in the design of thermally activated morphing structures, by exploiting more complex coupling behaviour.Practical implications – These laminates contain standard cross‐ply ...

Buckling analysis of skew plate assemblies: Classical plate theory results incorporating Lagrangian multipliers

A procedure is presented for the buckling analysis of prismatic skew plate assemblies subject to invariant in-plane stresses. Based on the exact solution of the plate differential equations, the method of Lagrangian multipliers is used to enforce the transverse skew boundaries by a sufficient number of point constraints. Analysis assumes that the plate is infinitely long and that supports repeat at bay length intervals, typifying the continuity found in aircraft wing construction. Following a brief derivation of the formulation adopted, results are presented and comparisons are made with other analyses for an unstiffened isotropic skew plate, subject to pure compression loading with both simply supported and clamped boundary conditions. Results for four benchmark stiffened panels, i.e. plate assemblies, incorporating composite material and combined loading are also given for a range of skew angles.

A parametric study of optimum designs for benchmark stiffened wing panels

Results are presented for the most heavily and lightly loaded of eight benchmark stiffened laminated wing panels defined from a Dornier wing by a GARTEUR (Group for Aeronautical Research and Technology in Europe) working party. These benchmark panels had three identical and equally spaced blade stiffeners. The results were chosen to help designers to understand many important aspects of the choice of design variables, and of the effects of changing the sophistication of modelling and theory used, for a wide range of wing panels. The percentage changes of (global) optimum mass are presented, along with the final values of the design variables. Some examples of mass histories and of (rejected) local optimum masses are also given. The principal design variables are skin and blade ply thicknesses and blade height. Additional factors considered include the effects of adding flanges to the blades whose plies either matched those of the blades or were allowed to vary independently, varying the number of stiffeners, allowing the stiffeners to differ from each other, varying stiffener spacing, varying some ply angles, including the stiffening effect of adjacent spars, including the effects of continuity with laterally adjacent panels, including through thickness shear deformation in the panel analysis and analysing the panel with its true skewed shape rather than approximating it as rectangular in plan.

Buckling Analysis and Minimum-Mass Design Procedures for Composite Wing-Box Structures

This study investigates the minimum-mass design of composite wing-box structures employing a syntactic film core (SynCore™) as a partial replacement for carbon-fiber material. Special attention is given to the balance between buckling strength and the limiting strain constraints of the two materials. Symmetric and antisymmetric angle-ply stacking sequences, with specially orthotropic properties, are combined to form the special orthotropic laminate skin of the wing box. Computer modeling accounts for continuity of the skin over composite curved root-channel-section spars, which are assumed to be connected by a single line of closely spaced bolts. Emphasis is also placed on the level of sophistication of the modeling and the level to which modeling approximations may be safely applied. The effects of analyzing a panel with its true skewed shape, rather than approximating it as rectangular in plan, are compared with the infinitely long panel representation on which the optimization study is based. Two design strategies are adopted in the study whereby either skin-ply thickness is the independent variable and the outer mold line of the wing box is maintained by linking the spar depth (dependant variable) or the spar pitch is the independent variable and all plies are held at their correct physical thicknesses.

Influence of continuity and aspect-ratio on the buckling of skew plates and plate assemblies

Abstract New buckling interaction results are presented for skew plates and prismatic assemblies of plates, which illustrate the influence of continuity over supports for a range of aspect-ratio and loading combinations. The work follows from initial comparisons (York and Williams, 1995, Buckling analysis of skew plate assemblies: classical plate theory results incorporating Lagrangian multipliers. Comput. Struct. 56, 625–635) with those in the literature for isolated plates and stiffened benchmark panels, consisting of prismatic assemblies of plates. The analysis method, which is an enhancement to the existing computer program VICONOPT, is based on an “exact” analytical solution using Classical Plate Theory. This accounts for an infinitely long prismatic plate assembly supported at regular intervals over supports with general skew angle α, forming a series of skew plates or plate assemblies joined end to end. This modelling can be described as exhibiting uni-axial continuity . The enhancement relates to a recent modification of the recurrence equations, which now accounts for infinitely wide skew plate assemblies supported at regular transverse intervals. This modelling possesses bi-axial continuity .

Theory and buckling results for infinitely wide, stiffened skew plate assemblies

Abstract Existing theory and the associated computer program VICONOPT deal with infinitely wide plate assemblies given that boundary conditions on all sides of each panel form a rectangle. They also deal with cases when the four supports form a parallelogram so that the plate is a skew plate. This is true provided the panel is of finite width, i.e. isolated from any adjacent panels, which is the case commonly modelled in practice. It does not represent what happens in the real structure, however, where normally there is continuity with the adjacent panel. The present paper shows how the theory and the computer program VICONOPT can be modified so that skewed plate assemblies that are infinitely wide and repeat at transverse intervals can now be modelled exactly. The paper also shows that the theory can be used, if a small measure of approximation is accepted, to model this situation by analysing only one of the identical stiffeners with associated panel skin in the common situations where the panel has equally spaced, identical, longitudinal stiffeners between each adjacent pair of longitudinal lines of support. Illustrative results are given.

Balanced and symmetric laminates: new perspectives on an old design rule

Stacking sequence listings are presented for bend-twist coupled laminates (ASB0DF), with up to 21 plies. The study demonstrates that the common design rule of balanced and symmetric stacking sequences predominantly gives rise to bend-twist coupling; all exceptions are presented in AIAA-2007-2083. However, the symmetry rule is shown to be a constraint that serves only to restrict the number of possible configurations to a very small proportion of the total design space for this laminate designation. This is demonstrated through a definitive list of laminate configurations, which are characterized in terms of angle- and cross-ply sub-sequence symmetries. Each stacking sequence configuration is presented together with dimensionless parameters from which the extensional and bending stiffness terms are readily calculated. Expressions relating the dimensionless parameters to the well-known lamination parameters are also given, together with graphical representations of feasible domains for all sub-sequence symmetries containing standard ply angle combinations i.e. ±45, 0 and 90 degrees. Quasi-isotropic (AIB0DF) laminates are also presented as an important sub-set of ASB0DF laminates. Finally, bounds on buckling performance under shear and compression are presented.

On composite laminates with extensional anisotropy

*The definite list of extensionally (membrane) anisotropic composite laminates with up to 21 plies is presented. The listings comprise of individual stacking sequences of entirely nonsymmetric laminates, which are characterized in terms of angle- and cross-ply sub-sequence relationships as well as the blend-ratio of unbalanced angle-plies. Dimensionless parameters, including lamination parameters, are provided, from which the extensional and bending stiffness terms are readily calculated and an assessment of the bending stiffness efficiency made for angle- and cross-ply sub-sequences. Comparisons are made between the structural response of extensionally-anisotropic laminates and laminates with both extensional- and bending-anisotropy, which can often be achieved in practice using symmetric configurations. This new class of coupled non-symmetric laminate can also be manufactured flat under a standard elevated temperature curing process, which is contrary to current understanding.

Elastic buckling design curves for isotropic rectangular plates with continuity or elastic edge restraint against rotation

Elastic buckling design curves are presented for flat isotropic rectangular plates, which are either isolated or form part of a larger continuous plate structure. The design curves illustrate the effect of introducing combinations of elastic rotational restraints to the edges of simply supported isolated plates, which are subject to uniform in-plane compression or shear. Results for infinitely long and/or wide plates, with rectangular bays, are superimposed for comparison.