Shijun Guo

Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping

Abstract It is known that an allowance for warping stiffness can change the natural frequencies of thin-walled open section beams substantially. The purpose of this paper is to investigate the magnitude of such changes by using an exact member theory. This is achieved by formulating an exact dynamic stiffness matrix for a typical beam member from established theory and linking this to a new and convenient procedure which extends the well-known Wittrick-Williams algorithm to ensure convergence upon any desired natural frequency. Numerical results are given for both single and continuous beams of the channel section for which some comparative results are available in the literature. The effect of warping stiffness on the natural frequencies is discussed and it is concluded that substantial error can be incurred if the effect is ignored.

Aeroelastic Tailoring of Composite Wing Structures by Laminate Layup Optimization

P REVIOUS research showed that elastic coupling and warping restraint might have a positive effect on aeroelastic stability of forward-swept composite wings [1–4]. The work encouraged subsequent investigation into the optimization of composite wing structures for desirable aeroelastic behavior [5–8]. The research has demonstrated that a significant increase of flutter speed can be achieved by optimizing the wing skin thickness or the laminate layups considering the effect of bending–torsion coupling [7,8]. However, the impact of wing geometry upon the influence of stiffness coupling on the aeroelastic optimization has received little attention. This current research is therefore aimed at investigating the effect of swept angle, taper ratio, andmass distribution on aeroelastic tailoring of a composite wing. Six aeroelastic tailoring cases of a composite wing by optimizing the wing box laminate layups have been considered. A classical gradient-based deterministic GD optimization method and a genetic algorithm GA have been employed for comparison purposes. It was noted that the optimized layup solution by using the GD method largely depends on the setting of initial design variables. Nevertheless, this method is efficient and normally produces an optimal result at each step of the optimization process before converging to the final optimal solution. Comparing with the GD method, the GA approach is more robust and produces optimal solutions with little influence from the initial layup despite the need for much more computational time. The example considered in this paper has shown that optimized layups resulting in a maximum increase of flutter speed can be achieved by employing either the GD or GA method. However, wing geometry and mass distribution have significant influence on aeroelastic tailoring results.

The effect of laminate lay-up on the flutter speed of composite wings

Abstract This paper presents an analytical study on optimization of a laminated composite wing structure for achieving a maximum flutter speed and a minimum weight without strength penalty. The investigation is carried out within the range of incompressible airflow and subsonic speed. In the first stage of the optimization, attention has been paid mainly to the effect on flutter speed of the bending, torsion and, more importantly, the bending-torsional coupling rigidity, which is usually associated with asymmetric laminate lay-up. The study has shown that the torsional rigidity plays a dominant role, while the coupling rigidity has also quite a significant effect on the flutter speed. In the second stage of the optimization, attention has been paid to the weight and laminate strength of the wing structure, which is affected by the variation in laminate lay-up in the first stage. Results from a thin-walled wing box made of laminated composite material show that up to 18 per cent increase in flutter speed and 13 per cent reduction in weight can be achieved without compromising the strength. The investigation has shown that a careful choice of initial lay-up and design variables leads to a desirable bending, torsional and coupling rigidities, with the provision of an efficient approach when achieving a maximum flutter speed with a minimum mass of a composite wing.

Aeroelastic optimisation of composite wings using the dynamic stiffness method

A computer program for use in the conceptual stage of aircraft design has been developed. The program obtains minimum mass designs for high aspect ratio, composite wings, subject to constraints on flutter speed, divergence speed and material stress. The wing is modelled as a series of composite beam elements and both flutter speed and divergence speed are calculated using a normal mode approach. Modal analysis is carried out by applying the Wittrick-Williams algorithm to the dynamic stiffness method, whereas unsteady aerodynamic loads are calculated from strip theory, although an option which uses lifting-surface theory is also presented. A previously published example is given to validate the analysis. Single level optimisation is carried out using a sequential quadratic programming strategy combined with the modified methods of feasible directions optimizer, for which flutter sensitivities are obtained by an efficient determinant interpolation technique. Design variables include topological variables such as spar and engine positions as well as layer thicknesses, which are modelled using quadratic functions. The wing of a regional turboprop aircraft is optimized to illustrate the use of the program. The problem was modelled using 10 elements and had 43 design variables, 162 constraints and required just over 20 minutes of CPU time on a workstation. This, coupled with the fact that a full three-dimensional FE model of the same wing would require over 1000 elements, illustrates the suitability of the dynamic stiffness method to the conceptual design stage.

Optimal design of an aeroelastic wing structure with seamless control surfaces

Abstract This article presents an investigation into the concept and optimal design of a lightweight seamless aeroelastic wing (SAW) structure for small air vehicles. Attention has been first focused on the design of a hingeless flexible trailing edge (TE) control surface. Two innovative design features have been created in the SAW TE section: an open sliding TE and a curved beam and disc actuation mechanism. This type of actuated TE section allows for the SAW having a camber change in a desirable shape and minimum control power demand. This design concept has been simulated numerically and demonstrated by a test model. For a small air vehicle of large sweep back wing, it is noted that significant structural weight saving can be achieved. However, further weight saving is mainly restricted by the aeroelastic stability and minimum number of carbon/epoxy plies in a symmetric layup rather than the structural strength. Therefore, subsequent effort was made to optimize the primary wing box structure. The results show that an initial structural weight can be reduced significantly under the strength criterion. The resulting reduction of the wing box stiffness and aeroelastic stability and control effectiveness can be improved by applying the aeroelastic tailoring. Because of the large swept angle and resulting lightweight and highly flexible SAW, geometrical non-linearity and large bending—torsion aeroelastic coupling have been considered in the analysis.

Development of piezoelectric actuated mechanism for flapping wing micro-aerial vehicle applications

Abstract Abstract A piezoelectric actuated two-bar two-flexure motion amplification mechanism for flapping wing micro-aerial vehicle application has been investigated. f r*A as an optimisation criterion has been introduced where f r is its fundamental resonant frequency of the system and A the vibration amplitude at the wing tip, or the free tip deflection at quasi-static operation. This criterion can be used to obtain the best piezoelectric actuation mechanism with the best energy transmission coefficient for flapping wing micro-aerial vehicle applications, and is a measurable quantity therefore can be compared with experimental results. A simplified beam model has been developed to calculate the fundamental resonant frequency for the full system consisted of piezoelectric actuator, motion amplification mechanism and the attached wing and the calculated values were compared with the measured results. A clear trend of the criteria f r*A varying with the two-flexure dimension, stiffness and setting angle have been obtained from the measured data and also the predicted results as a guideline for optimal design of the system.

Optimal Design of a Seamless Aeroelastic Wing Structure

This paper presents an investigation into the optimal design of a Seamless Aeroelastic Wing (SAW) structure for a light weight aircraft. Attention was firstly paid to a design concept of a hinge-less flexible trailing edge control surface and the actuation mechanism. By creating an innovative sliding trailing edge and improving an existing curved torque beam design, the SAW camber can be varied in a desirable shape with minimum control power demand. This design concept has been simulated numerically and demonstrated by a test model. Since the wing loading is relatively small for a small scale aircraft, strength and flutter are not the major design constraints for weight saving. Due to a large sweptback angle, significant bending-torsion coupling makes the bending stiffness play a very important role in the aeroelastic stability. As a result, the control efficiency becomes a main concern in the wing design. The subsequent effort was therefore made to optimise the wing structure configuration and aeroelastic tailoring. The results showed that an initial base line example structural weight was reduced by approximately 30% under the strength criteria. The resulting reduction of the wing box stiffness and aeroelastic stability were improved by applying aeroelastic tailoring.

Experimental study on the lift generated by a flapping rotary wing applied in a micro air vehicle

An experimental study was conducted to further validate whether the newly proposed flapping rotary wing is suitable for micro air vehicle design. First, the effects of two main kinematical parameters (flapping frequency and initial angle of attack) of flapping rotary wing on lift generation were discussed. It was found that a higher lift can be generated by flapping rotary wing through increasing flapping frequency at a proper initial angle of attack. Second, effect of coupled flapping motion with rotating motion on lift generation was analyzed. It is important that a larger lift was generated by flapping rotary wing than the superposition lifts from purely flapping and purely rotating motions when the initial angle of attack was less than a critical value. Finally, the comparison of the capability of lift generation from the flapping rotary wing and conventional rotary wing was given. It was indicated that the lift from flapping rotary wing was larger than that from conventional rotary wing in the range of Reynolds number from 2600 to 5000 as long as Strouhal number was determined appropriately. The present work suggests that flapping rotary wing may be a feasible and promising wing layout used in the design of micro air vehicle in terms of lift generation.

Modeling and nonlinear aeroelastic analysis of a wing with morphing trailing edge

An investigation was made into the nonlinear aeroelastic behavior of a composite wing with morphing trailing edge actuated by curved beams. Based on the design concept, an experimental wing model was built and a finite element model was created using MSC Patran/Nastran software. Impact test of the experimental model was carried out and the test data were used to validate the finite element models. In order to investigate the effect of freeplay nonlinearity between discs attached to the curved beams and wing skins, a nonlinear aeroelastic equation in modal coordinate was created. Generalized structural mass, damping, and stiffness matrixes were printed with DMAP language in Nastran. Doublet lattice method and Roger’s approximation were used to calculate unsteady aerodynamic influence coefficients matrix. In the analysis, the effect of morphing stiffness on critical flutter speed was studied. In addition, Hopf bifurcation and limit cycle oscillation were detected for the aeroelastic system with freeplay. The results show that the freeplay nonlinearity may reduce convergence speed and accelerate divergence of aeroelastic responses.

Simultaneous partial topology and size optimization of a wing structure using ant colony and gradient based methods

This article presents a methodology and process for a combined wing configuration partial topology and structure size optimization. It is aimed at achieving a minimum structural weight by optimizing the structure layout and structural component size simultaneously. This design optimization process contains two types of design variables and hence was divided into two sub-problems. One is structure layout topology to obtain an optimal number and location of spars with discrete integer design variables. Another is component size optimization with continuous design variables in the structure FE model. A multi city-layer ant colony optimization (MCLACO) method is proposed and applied to the topology sub-problem. A gradient based optimization method (GBOM) built in the MSC.NASTRAN SOL-200 module was employed in the component size optimization sub-problem. For each selected layout of the wing structure, a size optimization process is performed to obtain the optimum result and feedback to the layout topology process. The numerical example shows that the proposed MCLACO method and a combination with the GBOM are effective for solving such a wing structure optimization problem. The results also indicate that significant structural weight saving can be achieved.