Richard Butler

Morphing and shape control using unsymmetrical composites

Unsymmetrical carbon fiber/epoxy composites with bonded piezoelectric actuators are investigated as a means to shape or morph, the composite structures. Both a cantilever and unsupported laminate structure are examined along with their response to applied strains (from piezoelectric actuators) and applied mechanical load; with particular emphasis on the characterization of shape/deflection, the influence of externally applied mechanical loads and methods of reversing or promoting snap-through of these materials from one stable state to another. A variety of shape change/actuation modes for such structures have been identified namely, (i) reversible actuation by maintaining a constant stable state using piezoelectric actuation, (ii) an increased degree of shape change by irreversible snap-through using piezoelectric actuation and (iii) reversible snap-through using combined piezoelectric actuation and an externally applied load.

Compressive strength of delaminated aerospace composites.

An efficient analytical model is described which predicts the value of compressive strain below which buckle-driven propagation of delaminations in aerospace composites will not occur. An extension of this efficient strip model which accounts for propagation transverse to the direction of applied compression is derived. In order to provide validation for the strip model a number of laminates were artificially delaminated producing a range of thin anisotropic sub-laminates made up of 0°, ±45° and 90° plies that displayed varied buckling and delamination propagation phenomena. These laminates were subsequently subject to experimental compression testing and nonlinear finite element analysis (FEA) using cohesive elements. Comparison of strip model results with those from experiments indicates that the model can conservatively predict the strain at which propagation occurs to within 10 per cent of experimental values provided (i) the thin-film assumption made in the modelling methodology holds and (ii) full elastic coupling effects do not play a significant role in the post-buckling of the sub-laminate. With such provision, the model was more accurate and produced fewer non-conservative results than FEA. The accuracy and efficiency of the model make it well suited to application in optimum ply-stacking algorithms to maximize laminate strength.

Bilevel optimization and postbuckling of highly strained composite stiffened panels

The paper presents a bilevel strategy for the efficient optimum design of composite stiffened panels using VICONOPT, a fast-running optimization package based on linear eigenvalue buckling theory, and embracing practical composite design rules. Panel level optimization finds a minimum weight cross-sectional geometry based on a substitution of equivalent ortbotropic plates for laminated plates. Optimization at the laminate level finds stacking sequences satisfying laminate design rules. VICONOPT models are validated with ABAQUS finite element models, and with experimental compressive testing of two blade-stiffened panels. The buckling and postbuckling behavior of the two panels, with initial buckling in the stiffeners and skin, respectively, is investigated in a high load and high strain range. The bilevel strategy is evaluated by the design of a relatively short Z stiffened panel which has been manufactured and tested, and also by design of a long wing cover panel with combined loads. The weight saving from the wing cover panel is 13% compared with an existing datum design. This demonstrated that the strategy is efficient, reliable, and extendable into the long panel range.

Aeroelastic Response of a Flexible Delta Wing Due to Unsteady Vortex Flows

Aeroelastic response of a flexible delta wing due to the unsteady vortex flows was investigated in a wind tunnel. It was found that maximum rms buffeting occurs when vortex breakdown is close to the apex of the wing. The rms acceleration drops very rapidly in the vortex shedding regime at higher angles of attack. The dominant modes of vibration are the second and third modes when vortex breakdown is over the wing. In the case of the full-model delta wing, vortex breakdown produces the largest aeroelastic response, and the dominant mode is the second antisymmetric mode. Hence, there is evidence of a coupling between the wing structure and unsteady vortex pair interactions, which was surprising at this relatively low sweep angle of Λ=60°.

Buckling optimization of variable-angle-tow panels using the infinite-strip method

A minimum-mass optimization strategy for variable-angle-tow panels subject to buckling and manufacturing constraints is presented. The optimization is performed using a fast-running optimization package that employs infinite-strip analysis for buckling and a gradient-based optimization method. A new variable-angle-tow-panel manufacturing method, continuous tow shearing, providing good quality, is considered in the optimization strategy where variable thickness occurs due to the shear deformation of dry tows. Optimum designs of variable-angle-tow panels are obtained and compared with panels without thickness variation. Different panel boundary conditions are investigated and discussed. The results show that boundary conditions have dramatic effects on optimum fiber paths. Over 20% mass saving is obtained for the optimization strategy with thickness variation compared with the design without thickness variation. The buckling strains are reduced to a practical level when the thickness variation is considered...

LOCATING DELAMINATIONS IN COMPOSITE BEAMS USING GRADIENT TECHNIQUES AND A GENETIC ALGORITHM

This paper presents a method of locating delaminations within composite beams. The method compares the experimental natural frequencies and mode-shapes of a delaminated beam, with those predicted by an analytical model. The differences are quantified by an objective function, which is minimised using a numerical optimisation technique. When the difference between the analytically produced modal parameters, and those measured experimentally, is minimised, the damage is said to have been located. A simple model, based on the static deflection of a cantilever beam, is developed to obtain an estimate for the effective shear rigidity of the delaminated area, and this is incorporated into the Dynamic Stiffness Method (DSM). The damage is located using a two stage optimisation process. Firstly the differences in the analytical and experimental frequencies and modeshapes are minimised by altering the material properties and boundary conditions of the model. Once the differences have been minimised for an undamaged beam, damage is located by altering the number, size and location of delaminations within the beams. Results are obtained and compared using two different optimisation procedures; a gradientbased optimisation procedure and a genetic algorithm.

Analysis and testing of a postbuckled stiffened panel

The suitability of using the efficient, linear elastic design software VICONOPT for the analysis of a stiffened panel with a postbuckling reserve of strength is investigated. A longitudinally compressed panel, which initially buckled in a local skin mode, was analyzed with allowance being made for the effects of an initial overall imperfection. The panel was also analyzed using the nonlinear finite element package ABAQUS, and four laboratory specimens that represent the panel were tested to failure. The similarity of the experimental failure with the VICONOPT and ABAQUS predictions indicates that VICONOPT can give satisfactory analysis results for use in preliminary design.

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.

Optimum buckling design of composite wing cover panels with manufacturing constraints

A bi-level design method is used to provide practic al designs of composite stiffened panels subject to compression loads combined with lateral pressure. The bi-level method includes panel level optimization of the cross sectional pan el dimensions and laminate level design of the stacking sequence using a Genetic Algorithm (GA). A fast-running optimization package, VICONOPT, is used at the continuous optimization level where the buckling analysis is accurately and effectively performed. The beam-column analysis used to account for lateral loading for analysis during optimization is reporte d. Finite Element non-linear analyses within ABAQUS are performed for prediction of buckling of continuous wing cover panels with three rib bays to validate the beam-column approach. Practical design rules and manufacturing constraints are taken into account within the method. The continuity constraint is applied by selecting stacking sequenc es satisfying this constraint from a table listing sequences for different integer thickness o f laminates. Three blade stiffened panels are firstly designed using the GA for three typical compression loads on inboard wing sections without considering the continuity constra int. It is then shown that a small reduction in buckling capacity (typically less than 10%, resulting in less than 2% mass penalty) is incurred when the tabular laminate stac king sequences are used but that continuity is improved two fold compared with the GA designs. I. Introduction

Optimum buckling design of compression panels using VICONOPT

The structural efficiency of a range of panels under uniaxial compression is investigated using the optimum buckling design program VICONOPT. The design uses very efficient VIPASA analysis to guard against all possible modes of failure, together with a tailored sizing strategy. The panels all have nine blades, zed or hat stiffeners and between three and fifteen design variables, covering traditional design using one size of stiffener and more sophisticated design with five sizes of stiffener. Results show that using two stiffener sizes or two stiffener types in alternate positions across the panel width can produce mass savings of up to 30% compared with traditional design. Convergence on an optimum normally occurs within six sizing cycles, but up to twelve sizing cycles are required for sophisticated designs when the initial configuration is poorly chosen. Computational efficiency and material strength constraints are also considered.