Abstract Layered composite materials consisting of thin orthotropic layers offer for a designer many possibilities to tailor the structure: the behaviour and properties of the structure can be influenced not only by varying the geometry and thicknesses of the structure but also by varying the lay-up of the laminate. As new orthotropic materials having high specific strength and stiffness are used in structures, the tailoring is essential to utilize all the benefits of these materials. In this thesis tailoring and optimization of thermomechanical properties of layered composite structures are considered. The tailoring problemis formulated and solved as a constrained nonlinear optimization problem. Different types of global thermomechanical properties, such as stiffnesses, coefficients of thermal expansion and natural frequencies and buckling loads of composite plates, as well as layer-wise properties, such as stresses and strains in a certain lamina, are considered. Also, coupled thermalstructural problems are studied. When lay-up parameters, i.e. number of layers, and their orientations and thicknesses, are employed as design variables, global as well as layer-wise properties of the laminate can be considered. As relations between thermomechanical properties and lay-up parameters are highly nonlinear, optimization may suffer from various local optima. However, in tailoring the global minima or maxima are not the points of interest but rather the points of design space, where appropriate values for considered properties are achieved. In the thesis optimization of global thermomechanical properties is presented also by applying so-called lamination parameters as design variables. The lamination parameters are defined as integrals of the functions, which consist of sines and cosines of the lay-up angles of different layers multiplied by the powers of the thickness co-ordinate z, through the thickness of the laminate. Thus, information of the lay-up of the laminate can be compressed into these parameters and only twelve lamination parameters are needed to describe the behaviour of a common laminate. The use of these parameters as design variables is advantageous, because the number of parameters needed is small and often formulating a convex optimization problem is possible. After finding optimal lamination parameters, a procedure is needed to generate a lay-up corresponding to these parameters. Explicit equations are derived for generating lay-ups having optimal bending lamination parameters. For creating a laminate having both optimal in-plane and bending lamination parameters, a new optimization problem searching laminates having lamination parameters as close as possible to the optimal ones is formulated. In that problem, also layer-wise properties and restrictions of manufacturing are taken into account. Agenetic algorithmsearch is employed for solving that later problem as the value of the objective function can be computed efficiently. Also, often the thicknesses and orientations of different layers can have only discrete values, which can be handled easily in the GA search, where all design variables are discrete in character.

The growing number of applications of composite materials in aerospace and naval structures along with advancements in manufacturing technologies demand continuous innovations in the design of composite structures. In the traditional design of composite laminates, fiber orientation angles are constant for each layer and are usually limited to 0, 90, and ±45 degrees. To fully benefit from the directional properties of composite laminates, such limitations have to be removed. The concept of variable-stiffness laminates allows the stiffness properties to vary spatially over the laminate. Through tailoring of fiber orientations and laminate thickness spatially in an optimal fashion, mechanical properties of a part can be improved. In this thesis, the optimal design of variable-stiffness fiber-reinforced composite laminates is studied using an emerging numerical engineering optimization scheme based on the cellular automata paradigm. A cellular automaton (CA) based design scheme uses local update rules for both field variables (displacements) and design variables (lay-up configuration and laminate density measure) in an iterative fashion to convergence to an optimal design. In the present work, the displacements are updated based on the principle of local equilibrium and the design variables are updated according to the optimality criteria for minimum compliance design. A closed form displacement update rule for constant thickness isotropic continua is derived, while for the general anisotropic continua with variable thickness a numeric update rule is used. Combined lay-up and topology design of variable-stiffness flat laminates is performed under the action of in-plane loads and bending loads. An optimality criteria based formulation is used to obtain local design rules for minimum compliance design subject to a volume constraint. It is shown that the design rule splits into a two step application. In the first step an optimal lay-up configuration is computed and in the second step the density measure is obtained. The spatial lay-up design problem is formulated using both fiber angles and lamination parameters as design variables. A weighted average formulation is used to handle multiple load case designs. Numerical studies investigate the performance of the proposed design methodology. The optimal lay-up configuration is independent of the lattice density with more details emerging as the density is increased. Moreover, combined topology and lay-up designs are free of checkerboard patterns. The lay-up design problem is also solved using lamination parameters instead of the fiber orientation angles. The use of lamination parameters has two key features: first, the convexity of the minimization problem guarantees a global minimum; second, for both in-plane and bending problems it limits the number of design variables to four regardless of the actual number of layers, thereby simplifying the optimization task. Moreover, it improves the convergence rate of the iterative design scheme as compared to using fiber angles as design variables. Design parametrization using lamination parameters provides a theoretically better design, however, manufacturability of the designs is not certain. The cases of general, balanced symmetric, and balanced symmetric with equal thickness layers are studied separately. The feasible domain for laminates with equal thickness layers is presented for an increasing number of layers. A restricted problem is proposed that maintains the convexity of the design space for laminates with equal thickness layers. A recursive formulation for computing fiber angles for this case is also presented. On the computational side of the effort, a parallel version of the present CA formulation is implemented on message passing multiprocessor clusters. A standard parallel implementation does not converge for an increased number of processors. Detailed analysis revealed that the convergence problem is due to a Jacobi type iteration scheme, and a pure Gauss-Seidel type iteration through a pipeline implementation completely resolved the convergence problem. Timing results giving the speedup for the pipeline implementation were obtained for up to 260 processors. This work was supported by Grant NAG-1-01105 from NASA Langley Research Center. Special thanks to our project monitor Dr. Damodar R. Ambur for his technical guidance. / Ph. D.

The digital transformation of engineering design processes is essential for the aerospace industry to remain competitive in the global market. Multidisciplinary design optimization (MDO) frameworks play a crucial role in this transformation by integrating various engineering disciplines and enabling the optimization of complex spacecraft structures. Since the design team consists of multiple entities from different domains working together to build the final product, the design and analysis tools must be readily available and compatible. An integrated approach is required to handle the problem's complexity efficiently. Additionally, most aerospace structures are made from composite panels. It is challenging to optimize such panels as they require the satisfaction of constraints where the design ply thicknesses and orientations can only take discrete values prescribed by the manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient because they provide sub-optimal solutions when the number of design variables is large. They also are computationally expensive in handling the combinatorial nature of the problem. To overcome these challenges, this work proposes a two-fold solution that integrates multiple disciplines and efficiently optimizes composite spacecraft structures by building a rapid design framework. The proposed model-based design framework for spacecraft structures integrates commercially available software from Siemens packages such as NX and HEEDS and open-source Python libraries. The framework can handle multiple objectives, constraint non-linearities, and discrete design variables efficiently using a combination of black-box global optimization algorithms and Mixed Integer Programming (MIP)-based optimization techniques developed in this work. Lamination parameters and MIP are adopted to optimize composite panels efficiently. The framework integrates structural, thermal and acoustic analysis to optimize the spacecraft's overall performance while satisfying multiple design constraints. Its capabilities are demonstrated in optimizing a small spacecraft structure for required structural performance under various static and dynamic loading conditions when the spacecraft is inside the launch vehicle or operating in orbit. / Doctor of Philosophy / The design of new spacecraft takes several years and requires significant resources. The primary design objective is to minimize spacecraft mass/cost while satisfying the mission requirements. This is done by altering the structure's geometric and material properties. Most spacecraft panels are made from composite materials where the orientations of fiber paths and the thickness of the panel determine its strength and stiffness. Finding the best values for these parameters cannot be done efficiently using existing optimization algorithms, as several combinations of orientations can give a similar performance which can be subpar. In this dissertation, mathematical programming is adopted for fast evaluation of optimum panel properties, thereby saving a significant amount of resources compared to conventional techniques. Moreover, the requirements that govern the design process are handled one at a time in an organization. This leads to discrepancies in the various teams' designs that satisfy all requirements. A framework is built to integrate all requirements to account for their conflicting nature and quickly give the best possible spacecraft structural design configuration.