This dissertation investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The intent is to achieve a more efficient load-bearing mechanism and to passively control aeorelastic behavior of the structure under the flight loads. The use of SpaRibs broadens the design space and allows for the natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new MATLAB-based optimization framework referred to as EBF3SSWingOpt. This framework interfaces different analysis software to perform the tasks required. VisualDOC is used as optimizer; the generation of the SpaRibs geometry and of the structure Finite Element Model (FEM) is performed by MD.PATRAN; MD.NASTRAN is utilized to compute the weight of the structure, the linear static stress analysis and the linear buckling analysis required for the calculation of the response functions. EBF3SSWingOpt optimization scheme performs both the sizing and the shaping of the internal structural elements. Two methods are compared while optimizing the wing-box; a One-Step method in which sizing and topology optimization are carried out simultaneously and a Two-Step method, in which the sizing and topology optimization are carried out separately but in an iterative way. The optimization problem statements for the One-Step and the Two-Step methodologies are presented. Three methods to define the shape of the SpaRibs parametrically are described: (1) the Bounding Box and Base Curves method defines the shape of the SpaRibs based on the shape of two curves called Base Curves which are positioned into the Bounding Box, a rectangular region defined on the plane z=0 and containing the projection of the wing plan-form onto the same plane; (2) the Linked Shape method defines the shape of a set of SpaRibs in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique however, mathematical relations link their curvature in an effort to reduce the number of design variables; and (3) the Independent Shape parameterization is similar to the Linked Shape parameterization however, the shape of each curve is unique. The framework and parameterization methods described are applied to optimize different types of wing structures. Following results are presented and discussed: (1) a rectangular wing-box subjected to a chord-wise linearly varying load, optimized using SpaRibs parameterized with Bounding-Box and Base Curves method; (2) a rectangular wing-box subjected to a chord-wise linearly varying load, optimized using SpaRibs parameterized with Linked Shape method; (3) a generic fighter wing subjected to uniform distributed pressure load, optimized using SpaRibs parameterized with Bounding-Box and Base Curves method; (4) a general business jet wing subjected to pull-up maneuver loads computed using ZESt (ZONA Technology Inc. Steady Euler equations solver), optimized using SpaRibs parameterized with Independent Shape method; (5) a preliminary application of the Linked Shape parameterization to place SpaRibs into a high speed commercial transport aircraft wing-box characterized by high geometry layout complexity; and (6) an optimization of panels subjected to axial and shear loads using curvilinear stiffeners and grids of curvilinear stiffeners. The results for the optimization of the rectangular wing-box show 36.8% weight reduction from the baseline, when the Bounding Box and Base Curves parameterization is applied and the Two-Step framework is implemented. For the same structure the weight reduction amounts to 46.7% when the Linked Shape parameterization and the Two-Step framework are used. Similar results are obtained for the generic fighter wing-box structure. In this case, the weight saving is about 20%. Bounding Box and Base Curves parameterization and Two-Step framework are used. Finally, the weight reduction for the general business jet wing-box structure amounts to 17% of the baseline weight. In this case, the computation is carried out using the Independent Shape parameterization and the Two-Step framework. In general, the Two-Step optimization framework finds better optimal structure configurations as compared to the One-Step optimization framework. However, the computational time required to find to optimum with the Two-Step optimization is larger when a small number of particles are used in the particle swarm optimization method. For larger number of particles, the computational time for the two methods is comparable. Finally for very large number of particles the Two-Step optimization requires less computational time. It is also important to notice how the Two-Step framework consistently leads to a better optimum than the One-Step framework, for the same number of particles. / Ph. D.

In intelligent structures, structural deformation is generally controlled by either embedding or surface bonding the induced strain actuator to the structure. With bonded or embedded actuators used for inducing flexure, the developed in-plane force contributes indirectly through a locally-generated moment. Control authority in this configuration is thus limited by actuator offset distance. The focus of this research was to investigate a new concept in which the actuator, as opposed to being bonded, is attached to the structure at discrete points. This configuration is fundamentally different from the bonded/embedded configuration in that the actuator and the structure between the two discrete points can deform independently; and the in-plane force of the actuator, which contributes only indirectly in the case of bonded actuator, can directly influence out-of-plane displacements of the structure. Additionally, the actuator offset distance can be optimized with respect to actuator force/strain saturation for increased authority. Two implementations of this concept as applied to beam structures were investigated. In the first, the actuator (e.g., shape memory alloy actuator wire) does not possess any flexural stiffness; and therefore, remains straight between the two attachment points. In the second implementation, the actuator (PZT's and electrostrictive) possesses flexural stiffness, and bends with the structure. The formulation and experimental results for both implementations are presented. Enhanced authority is demonstrated by comparing the static response of the discretely attached actuator beam systems with their bonded counterpart systems. / Ph. D.

A global/local framework for multidisciplinary optimization of generalized aircraft wing structure has been developed. The concept of curvilinear stiffening members (spars, ribs and stiffeners) has been applied in the optimization of a wing structure. A global wing optimization framework EBF3WingOpt, which integrates the static aeroelastic, flutter and buckling analysis, has been implemented for exploiting the optimal design at the wing level. The wing internal structure is optimized using curvilinear spars and ribs (SpaRibs). A two-step optimization approach, which consists of topology optimization with shape design variables and size optimization with thickness design variables, is implemented in EBF3WingOpt. A local panel optimization EBF3PanelOpt, which includes stress and buckling evaluation criteria, is performed to optimize the local panels bordered by spars and ribs for further structural weight saving. The local panel model is extracted from the global finite element model. The boundary conditions are defined on the edges of local panels using the displacement fields obtained from the global model analysis. The local panels are optimized to satisfy stress and buckling constraints. Stiffened panel with curvilinear stiffeners is implemented in EBF3PanelOpt to improve the buckling resistance of the local panels. The optimization of stiffened panels has been studied and integrated in the local panel optimization. EBF3WingOpt has been applied for the optimization of the wing structure of the Boeing N+2 supersonic transport wing and NASA common research model (CRM). The optimization results have shown the advantage of curvilinear spars and ribs concept. The local panel optimization EBF3PanelOpt is performed for the NASA CRM wing. The global-local optimization framework EBF3GLWingOpt, which incorporates global wing optimization module EBF3WingOpt and local panel optimization module EBF3PanelOpt, is developed using MATLAB and Python programming to integrate several commercial software: MSC.PATRAN for pre and post processing, MSC.NASTRAN for finite element analysis. An approximate optimization method is developed for the stiffened panel optimization so as to reduce the computational cost. The integrated global-local optimization approach has been applied to subsonic NASA common research model (CRM) wing which proves the methodology's application scaling with medium fidelity FEM analysis. Both the global wing design variables and local panel design variables are optimized to minimize the wing weight at an acceptable computational cost. / Ph. D.

In order to perform structural optimization and/or modification on a structure, an analytical model which sufficiently describes the behavior of the structure must be developed. Analytical models can be generated for almost any structure, but such a model will generally not effectively predict the behavior of the structure unless the model is somehow reconciled with experimental data taken from the structure. Additionally, the model must also be complete, i.e., it must not only model the structure but also model any suspension system used to support the structure. If the suspension is not included in the model, any attempt to reconcile the model with experimental data will result in a incorrect model. Using this incorrect model to perform structural modification cannot be expected to give correct results. In this thesis, an approach for estimating the effects of a suspension system on the flexural vibration of a structure is developed. These effects are treated mathematically as variations in boundary conditions. Topics discussed include formulation of an analytical model that includes suspension effects, experimental methods for acquiring mode shapes which exhibit these effects, and reconciliation techniques for matching analytical mode shapes to experimental mode shapes to determine the effective boundary conditions. / Master of Science

Deployable structures serve a large number of space missions. They are vital since spacecraft are launched by placing them inside launch vehicle payload fairings of limited volume. Traditional spacecraft design often involves large components. These components could have power, communication, or optics applications and include booms, masts, antennas, and solar arrays. Different stowing methods are used in order to reduce the overall size of a spacecraft. Some examples of stowing methods include simple articulating, more complex origami inspired folding, telescoping, and rolling or wrapping. Wrapping of a flexible component could reduce the weight by eliminating joints and other components needed to enable some of the other mechanisms. It also is one of the most effective methods at reducing the compaction volume of the stowed deployable. In this study, a generic unfurlable structure is optimized for maximum natural frequency at its fully deployed configuration and minimal strain energy in its stowed configuration. The optimized stowed structure is then deployed in simulation. The structure consists of a rectangular panel that tightly wraps around a central cylindrical hub for release in space. It is desired to minimize elastic energy in the fully wrapped panel and hinge to ensure minimum reaction load into the spacecraft as it deploys in space, since that elastic energy stored at the stowed position transforms into kinetic energy when the panel is released and induces a moment in the connected spacecraft. It is also desired to maximize the fundamental frequency of the released panel as a surrogate for the panel having sufficient stiffness. Deployment dynamic analysis of the finite element model was run to ensure satisfactory optimization formulation and results. / Master of Science / Spacecraft, or artificial satellites, do not fly from earth to space on their own. They are launched into their orbits by placing them inside launch vehicles, also known as carrier rockets. Some parts or components of spacecraft are large and cannot fit in their designated space inside launch vehicles without being stowed into smaller volumes first. Examples of large components on spacecraft include solar arrays, which provide power to the spacecraft, and antennas, which are used on satellite for communication purposes. Many methods have been developed to stow such large components. Many of these methods involve folding about joints or hinges, whether it is done in a simple manner or by more complex designs. Moreover, components that are flexible enough could be rolled or wrapped before they are placed in launch vehicles. This method reduces the mass which the launch vehicle needs to carry, since added mass of joints is eliminated. Low mass is always desirable in space applications. Furthermore, wrapping is very effective at minimizing the volume of a component. These structures store energy inside them as they are wrapped due to the stiffness of their materials. This behavior is identical to that observed in a deformed spring. When the structures are released in space, that energy is released, and thus, they deploy and try to return to their original form. This is due to inertia, where the stored strain energy turns into kinetic energy as the structure deploys. The physical analysis of these structures, which enables their design, is complex and requires computational solutions and numerical modeling. The best design for a given problem can be found through numerical optimization. Numerical optimization uses mathematical approximations and computer programming to give the values of design parameters that would result in the best design based on specified criterion and goals. In this thesis, numerical optimization was conducted for a simple unfurlable structure. The structure consists of a thin rectangular panel that wraps tightly around a central cylinder. The cylinder and panel are connected with a hinge that is a rotational spring with some stiffness. The optimization was solved to obtain the best values for the stiffness of the hinge, the thickness of the panel, which is allowed to vary along its length, and the stiffness or elasticity of the panel's material. The goals or objective of the optimization was to ensure that the deployed panel meets stiffness requirement specified for similar space components. Those requirements are set to make certain that the spacecraft can be controlled from earth even with its large component deployed. Additionally, the second goal of the optimization was to guarantee that the unfurling panel does not have very high energy stored while it's wrapped, so that it would not cause large motion the connected spacecraft in the zero gravity environments of space. A computer simulation was run with the resulting hinge stiffness and panel elasticity and thickness values with the cylinder and four panels connected to a structure representing a spacecraft. The simulation results and deployment animation were assessed to confirm that desired results were achieved.

The objectives of the research presented in this thesis are the development of a seven degree-of-freedom morphing airplane and the design and integration of a variable camber compliant tail. The morphing airplane was designed and manufactured to study the benefits of large planform changes and flight control morphing. Morphing capabilities of each wing consist of 8 in. wing extension and contraction, 40° of wing sweep and ±20.25° of outboard wing twist in addition to 6 in. of tail extension and contraction. Initial wind-tunnel tests proved that for a large range of lift coefficients, the optimal airplane configuration changes to minimize the drag. Another portion of this research deals with the development of a structural optimization program to design a variable camber compliant tail. The program integrates ANSYS, aerodynamic thin airfoil theory and the Method of Moving Asymptotes to optimize the shape of an airfoil tail for maximum trailing edge deflection. An objective function is formulated to maximize the trailing edge tip deflection subject to stress constraints. The optimal structure needs to be flexible to maximize the tip deflection, but stiff enough to minimize the deflection of the tip due to aerodynamic loading. The results of the structural optimization program created a compliant tail mechanism that can deflect the trailing edge tip with a single actuator ±4.27°. / Master of Science

A significant improvement can be achieved in the performance of transonic transport aircraft using Multidisciplinary Design Optimization (MDO) by implementing truss-braced wing concepts in combination with other advanced technologies and novel design innovations. A considerable reduction in drag can be obtained by using a high aspect ratio wing with thin airfoil sections and tip-mounted engines. However, such wing structures could suffer from a significant weight penalty. Thus, the use of an external strut or a truss bracing is promising for weight reduction. Due to the unconventional nature of the proposed concept, commonly available wing weight equations for transport aircraft will not be sufficiently accurate. Hence, a bending material weight calculation procedure was developed to take into account the influence of the strut upon the wing weight, and this was coupled to the Flight Optimization System (FLOPS) for total wing weight estimation. The wing bending material weight for single-strut configurations is estimated by modeling the wing structure as an idealized double-plate model using a piecewise linear load method. Two maneuver load conditions 2.5g and -1.0g factor of safety of 1.5 and a 2.0g taxi bump are considered as the critical load conditions to determine the wing bending material weight. From preliminary analyses, the buckling of the strut under the -1.0g load condition proved to be the critical structural challenge. To address this issue, an innovative design strategy introduces a telescoping sleeve mechanism to allow the strut to be inactive during negative g maneuvers and active during positive g maneuvers. Also, more wing weight reduction is obtained by optimizing the strut force, a strut offset length, and the wing-strut junction location. The best configuration shows a 9.2% savings in takeoff gross weight, an 18.2% savings in wing weight and a 15.4% savings in fuel weight compared to a cantilever wing counterpart. / Master of Science

This dissertation addresses the ultimate strength analysis of nonlinear beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on nonlinear beam theory with material and geometric nonlinearities. Nonlinear constitutive law is developed for elastic-perfectly-plastic beam cross-section consisting of base plate and T-bar stiffener. The analysis method is validated using commercial nonlinear finite element analysis. A new direct solving method is developed, which combines the original governing equations with their derivatives with respect to deformation matric and solves for the ultimate strength directly. Structural optimization and reliability analysis use a gradient-based algorithm and need accurate sensitivities of the ultimate strength to design variables. Semi-analytic sensitivity of the ultimate strength is calculated from a linear set of analytical sensitivity equations which use the Jacobian matrix of the direct solving method. The derivatives of the structural residual equations in the sensitivity equation set are calculated using complex step method. The semi-analytic sensitivity is more robust and efficient as compared to finite difference sensitivity. The design variables are the cross-sectional geometric parameters. Random variables include material properties, geometric parameters, initial deflection and nondeterministic load. Failure probabilities calculated by ultimate strength reliability analysis are validated by Monte Carlo Simulation. Double-loop RBDO minimizes structural weight with reliability index constraint. The sensitivity of reliability index with respect to design variables is calculated from the gradient of limit state function at the solution of reliability analysis. By using the ultimate strength direct solving method, semi-analytic sensitivity and gradient-based optimization algorithm, the RBDO method is found to be robust and efficient for nonlinear beam-columns. The ultimate strength direct solving method, semi-analytic sensitivity, structural optimization, reliability analysis, and RBDO method can be applied to more complicated engineering structures including stiffened panels and aerospace/ocean structures. / Ph. D. / This dissertation presents a Reliability-Based Design Optimization (RBDO) procedure for nonlinear beam-columns. The beam-column cross-section has asymmetric I shape and the nonlinear material model allows plastic deformation. Structural optimization minimizes the structural weight while maintaining an ultimate strength level, i.e. the maximum load it can carry. In reality, the geometric parameters and material properties of the beam-column vary from the design value. These uncertain variations will affect the strength of the structure. Structural reliability analysis accounts for the uncertainties in structural design. Reliability index is a measurement of the structure’s probability of failure by considering these uncertainties. RBDO minimizes the structural weight while maintaining the reliability level of the beam-column. A novel numerical method is presented which solves an explicit set of equations to obtain the maximum strength of the beam-column directly. By using this method, the RBDO procedure is found to be efficient and robust.

To meet the requirements for the next generation of space missions, a paradigm shift is required from current structures that are static, heavy and stiff, to innovative structures that are adaptive, lightweight, versatile, and intelligent. This work proposes the use of a novel morphing structure, the thermally actuated anisogrid morphing boom, to meet the design requirements by making the primary structure actively adapt to the on-orbit environment. The proposed concept achieves the morphing capability by applying local and global thermal gradients and using the resulting thermal strains to introduce a 6 Degree of Freedom (DOF) morphing control. To address the key technical challenges associated with implementing this concept, the work is broken into four sections. First, the capability to develop and reduce large dynamic models using the Data Based Loewner-SVD method is demonstrated. This reduction method provides the computationally efficient dynamic models required for evaluation of the concept and the assessment of a vast number of loading cases. Secondly, a sensitivity analysis based parameter ranking methodology is developed to define parameter importance. A five parameter model correlation effort is used to demonstrate the ability to simplify complex coupled problems. By reducing the parameters to only the most critical, the resulting morphing optimization computation and engineering time is greatly reduced. The third piece builds the foundation for the thermal morphing anisogrid structure by describing the concept, defining the modeling assumptions, evaluating the design space, and building the performance metrics. The final piece takes the parameter ranking methodology, developed in part two, and the modeling capability of part three, and performs a trust-region optimization to define optimal morphing geometric configuration. The resulting geometry, optimized for minimum morphing capability, is evaluated to determine the morphing workspace, the frequency response capability, and the minimum and maximum morphing capability in 6 DOF. This work has demonstrated the potential and provided the technical tools required to model and optimize this novel smart structural concept for a variety of applications. / Ph. D. / To meet the requirements for the next generation of space missions, a paradigm shift is required from current structures that are static, heavy and stiff, to innovative structures that are adaptive, lightweight, versatile, and intelligent. This work proposes the combination of a unique structure with a new control method to provide a novel way to achieve smart structural adaptive (morphing) capability. This concept takes advantage of the natural expansion and contraction of materials caused by temperature changes (Coefficient of Thermal Expansion) to bend and twist the structure of interest into the desired configuration. By applying local heat (thermal energy) to induce temperature differences in the structure, the temperature induced material expansion (thermal strain) can be used to control and direct the structure into all different planes and rotations(X, Y, and Z displacements as well as the rotations in the X, Y, and Z axis). This structure is called an anisogrid boom. The potential applications of model range from passive thermal mitigation system to an active precision low frequency vibration control system. The anisogrid boom is a low mass and efficient structural configuration with a long history in aerospace applications. The thermally morphing anisogrid structure is made up of helical members (these members are heated and cooled to actively bend and twist the structure) and circumferential members (these members provide stability and rigidity to the structure). This work details the methods used to move and control the structure as well as the development of the technical capabilities required to effectively demonstrate the limits of the concept. To address the key technical challenges associated with implementing this concept, the work is broken into four sections. First, the method is detailed that is used to generate the large dynamic computer models and the method to reduce them using a model reduction method, Data Based Loewner-SVD. This reduction method provides the computationally-efficient dynamic models required for evaluation of the concept. Secondly, a novel methodology is discussed identifying the impact of an input parameter change on the resulting output, such that the parameters of importance can be ranked. This ranking provides insight into what parameters should be the focus for further evaluation and optimization. The last two sections address how these tools are used to demonstrate the performance of this novel morphing structure as a function of the geometric input parameters relative to multiple developed performance metrics. Finally, the structure is optimized to achieve the most accurate morphing possible so that the limits of the capability can be better understood. This work has demonstrated the potential and provided the technical tools required to model and optimize this novel smart structural concept for a variety of applications.

Designing structures for lightness is an intelligent and responsible way for engineers and architects to conceive structural systems. Lightweight structures are able to bridge wide spans with a least amount of material. However, the quest for lightness remains an utopia without the driving constraints that give sense to contemporary structural design.<p><p>Previously proposed computational methods for designing lightweight structures focused either on finding an equilibrium shape, or are restricted to fairly small design applications. In this work, we aim to develop a general, robust, and easy-to-use method that can handle many design parameters efficiently. These considerations have led to truss layout optimization, whose goal is to find the best material distribution within a given design domain discretized by a grid of nodal points and connected by tentative bars. <p><p>This general approach is well established for topology optimization where structural component sizes and system connectivity are simultaneously optimized. The range of applications covers limit analysis and identification of failure mechanisms in soils and masonries. However, to fully realize the potential of truss layout optimization for the design of lightweight structures, the consideration of geometrical variables is necessary. <p><p>The resulting truss geometry and topology optimization problem raises several fundamental and computational challenges. Our strategy to address the problem combines mathematical programming and structural mechanics: the structural properties of the optimal solution are used for devising the novel formulation. To avoid singularities arising in optimal configurations, the present approach disaggregates the equilibrium equations and fully integrates their basic elements within the optimization formulation. The resulting tool incorporates elastic and plastic design, stress and displacements constraints, as well as self-weight and multiple loading.<p><p>Besides, the inherent slenderness of lightweight structures requires the study of stability issues. As a remedy, we develop a conceptually simple but efficient method to include local and nodal stability constraints in the formulation. Several numerical examples illustrate the impact of stability considerations on the optimal design.<p><p>Finally, the investigation on realistic design problems confirms the practical applicability of the proposed method. It is shown how we can generate a range of optimal designs by varying design settings. In that regard, the computational design method mostly requires the designer a good knowledge of structural design to provide the initial guess. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished