The usefulness of supplementary energy dissipation devices is now quite well-known in the earthquake structural engineering community for reducing the earthquake-induced response of structural systems. However, systematic design procedures for optimal sizing and placement of these protective systems in structural systems are needed and are not yet available. The main objective of this study is, therefore, to formulate a general framework for the optimal design of passive energy dissipation systems for seismic structural applications. The following four types passive energy dissipation systems have been examined in the study: (1) viscous fluid dampers, (2) viscoelastic dampers, (3) yielding metallic dampers and, (4) friction dampers. For each type of energy dissipation system, the study presents the (a) formulation of the optimal design problem, (b) consideration of several meaningful performance indices, (c) analytical and numerical procedures for seismic response and performance indices calculations, (d) procedures for obtaining the optimal design by an appropriate optimization scheme and, (e) numerical results demonstrating the effectiveness of the procedures and the optimization-based design approach. For building structures incorporating linear damping devices, such as fluid and solid viscoelastic dampers, the seismic response and performance evaluations are done by a random vibration approach for a stochastic characterization of the earthquake induced ground motion. Both the gradient projection technique and genetic algorithm approach can be conveniently employed to determine the required amount of damping material and its optimal distribution within a building structure to achieve a desired performance criterion. An approach to evaluate the sensitivity of the optimum solution and the performance function with respect to the problem parameters is also described. Several sets of numerical results for different structural configurations and for different performance indices are presented to demonstrate the effectiveness and applicability of the approach. For buildings installed with nonlinear hysteretic devices, such as yielding metallic elements or friction dampers, the computation of the seismic structural response and performance must be performed by time history analysis. For such energy dissipation devices, the genetic algorithm is more convenient to solve the optimal design problem. It avoids the convergence to a local optimal solution. To formulate the optimization problem within the framework of the genetic algorithm, the study presents the discretization procedures for various parameters of these nonlinear energy dissipation devices. To include the uncertainty about the seismic input motion in the search for optimal design, an ensemble of artificially generated earthquake excitations are considered. The similarities of the optimal design procedure with yielding metallic devices and friction devices are clearly established. Numerical results are presented to illustrate the applicability of the proposed optimization-based approach for different forms of performance indices and types of building structures. / Ph. D.

A method for the incorporation of continuum modeling in the optimization of large discrete structures is presented. The use of a continuum model facilitates decomposition of optimization problems and augments the scope and applicability of the multilevel decomposition method. This new concept is demonstrated by the optimization of slender, multi-bay, beam-like trusses with large numbers of members. An algorithm for the continuum model optimization of the truss is developed and tested against a traditional algorithm that might be used to solve the problem. Data are presented that reflect the advantages of the continuum model method over the traditional in the areas of computational efficiency and robustness. Additionally, design results for the beam-like truss are presented. / Master of Science

Artificial intelligence (AI) has progressed significantly during the last several decades, along with the rapid advancements in computational power. This advanced technology is currently being employed in various engineering fields, not just in computer science. In aerospace engineering, AI and machine learning (ML), a major branch of AI, are now playing an important role in various applications, such as automated systems, unmanned aerial vehicles, aerospace optimum design structure, etc. This dissertation mainly focuses on structural engineering to employ AI to develop lighter and safer aircraft structures as well as challenges involving structural optimization and analysis. Therefore, various ML applications are studied in this research to provide novel frameworks for structural optimization, analysis, and design. First, the application of a deep-learning-based (DL) convolutional neural network (CNN) was studied to develop a surrogate model for providing optimum structural topology. Typically, conventional structural topology optimization requires a large number of computations due to the iterative finite element analyses (FEAs) needed to obtain optimal structural layouts under given load and boundary conditions. A proposed surrogate model in this study predicts the material density layout inputting the static analysis results using the initial geometry but without performing iterative FEAs. The developed surrogate models were validated with various example cases. Using the proposed method, the total calculation time was reduced by 98 % as compared to conventional topology optimization once the CNN had been trained. The predicted results have equal structural performance levels compared to the optimum structures derived by conventional topology optimization considered ``ground truths". Secondly, reinforcement learning (RL) is studied to create a stand-alone AI system that can design the structure from trial-and-error experiences. RL application is one of the major ML branches that mimic human behavior, specifically how human beings solve problems based on their experience. The main RL algorithm assumes that the human problem-solving process can be improved by earning positive and negative rewards from good and bad experiences, respectively. Therefore, this algorithm can be applied to solve structural design problems whereby engineers can improve the structural design by finding the weaknesses and enhancing them using a trial and error approach. To prove this concept, an AI system with the RL algorithm was implemented to drive the optimum truss structure using continuous and discrete cross-section choices under a set of given constraints. This study also proposed a unique reward function system to examine the constraints in structural design problems. As a result, the independent AI system can be developed from the experience-based training process, and this system can design the structure by itself without significant human intervention. Finally, this dissertation proposes an ML-based classification tool to categorize the vibrational mode shapes of tires. In general, tire vibration significantly affects driving quality, such as stability, ride comfort, noise performance, etc. Therefore, a comprehensive study for identifying the vibrational features is necessary to design the high-performance tire by considering the geometry, material, and operation conditions. Typically, the vibrational characteristics can be obtained from the modal test or numerical analysis. These identified modal characteristics can be used to categorize the tire mode shapes to determine the specific mode cause poorer driving performances. This study suggests a method to develop an ML-based classification tool that can efficiently categorize the mode shape using advanced feature recognition and classification algorithms. The best-performed classification tool can accurately predict the tire category without manual effort. Therefore, the proposed classification tool can be used to categorize the tire mode shapes for subsequent tire performance and improve the design process by reducing the time and resources for expensive calculations or experiments. / Doctor of Philosophy / Artificial intelligence (AI) has significantly progressed during the last several decades with the rapid advancement of computational capabilities. This advanced technology is currently employed to problems in various engineering fields, not just problems in computer science. Machine learning (ML), a major branch of AI, is actively applied to mechanical/structural problems since an ML model can replace a physical system with a surrogate model, which can be used to predict, control, and optimize its behavior. This dissertation provides a new framework to design and analyze structures using ML-based techniques. In particular, the latest ML technologies, such as convolutional neural networks, widely used for image processing and feature recognition, are applied to replace numerical calculations in structural optimization and analysis with the ML-based system. Also, this dissertation suggests how to develop a smart system that can design the structure by itself using reinforcement learning, which is utilized for autonomous driving systems and robot walking algorithms. Finally, this dissertation suggests an ML-based classification approach to categorize complex vibration modes of a structure.

The probabilistic approach to design optimization has received increased attention in the last two decades. It is widely recognized that such an approach should lead to designs that make better use of the resources than designs obtained with the classical deterministic approach by distributing safety onto the different components and/or failure modes of a system in an optimal manner. However, probabilistic models rely on a number of assumptions regarding the magnitude of the uncertainties, their distributions, correlations, etc. In addition, modelling errors and approximate reliability calculations (first order methods for example) introduce uncertainty in the predicted system reliability. Because of these inaccuracies, it is not clear if a design obtained from probabilistic optimization will really be more reliable than a design based on deterministic optimization. The objective of this work is to provide a partial answer to this question through laboratory experiments — such experimental validation is not currently available in the literature. A cantilevered truss structure is used as a test case. First, the uncertainties in stiffness and mass properties of the truss elements are evaluated from a large number of measurements. The transmitted scatter in the natural frequencies of the truss is computed and compared to experimental estimates obtained from measurements on 6 realizations of the structure. The experimental results are in reasonable agreement with the predictions, although the magnitude of the transmitted scatter is extremely small. The truss is then equipped with passive viscoelastic tuned dampers for vibration control. The controlled structure is optimized by selecting locations for the dampers and for tuning masses added to the truss. The objective is to satisfy upper limits on the acceleration at given points on the truss for a specified excitation. The properties of the dampers are the primary sources of uncertainties. Two optimal designs are obtained from deterministic and probabilistic optimizations; the deterministic approach maximizes safety margins while the probability of failure (i.e. exceeding the acceleration limit) is minimized in the probabilistic approach. The optimizations are performed with genetic algorithms. The predicted probability of failure of the optimum probabilistic design is less than half that of the deterministic optimum. Finally, optimal deterministic and probabilistic designs are compared in the laboratory. Because small differences in failure rates between two designs are not measurable with a reasonable number of tests, we use anti-optimization to identify a design problem that maximizes the contrast in probability of failure between the two approaches. The anti-optimization is also performed with a genetic algorithm. For the problem identified by the anti-optimization, the probability of failure of the optimum probabilistic design is 25 times smaller than that of the deterministic design. The rates of failure are then measured by testing 29 realizations of each optimum design. The results agree well with the predictions and confirm the larger reliability of the probabilistic design. However, the probabilistic optimum is shown to be very sensitive to modelling errors. This sensitivity can be reduced by including the modelling errors as additional uncertainties in the probabilistic formulation. / Ph. D.

An optimal shape control problem for the steady-state Navier-Stokes equations is considered from an analytical point of view. We examine a rather specific model problem dealing with 2-dimensional channel flow of incompressible viscous fluid: we wish to determine the shape of a bump on a part of the boundary in order to minimize the energy dissipation. To formulate the problem in a comprehensive manner, we study some properties of the Navier-Stokes equations. The penalty method is applied to relax the difficulty of dealing with incompressibility in conjunction with domain perturbations and regularity requirements for the solutions. The existence of optimal solutions for the penalized problem is presented. The computation of the shape gradient and its treatment plays central role in the shape sensitivity analysis. To describe the domain perturbation and to derive the shape gradient, we study the material derivative method and related shape calculus. The shape sensitivity analysis using the material derivative method and Lagrange multiplier technique is presented. The use of Lagrange multiplier techniques,from which an optimality system is derived, is justified by applying a method from functional analysis. Finite element discretizations for the domain and discretized description of the problem are given. We study finite element approximations for the weak penalized optimality system. To deal with inhomogeneous essential boundary condition, the framework of a Lagrange multiplier technique is applied. The split formulation decoupling the traction force from the velocity is proposed in conjunction with the penalized optimality system and optimal error estimates are derived. / Ph. D.

The integrated design of a structure and its control system was treated as a multiobjective optimization problem. Structural mass, a quadratic performance index, and the flutter speed constituted the vector objective function. The closed-loop performance index was taken as the time integral of the Hamiltonian. Constraints on natural frequencies and aeroelastic damping were also considered. Derivatives of the objective and constraint functions with respect to structural and control design variables were derived for a finite element beam model of the structure and constant feedback gains determined by Independent Modal Space Control. Pareto optimal designs generated for a simple beam and a tetrahedral truss demonstrated the benefit of solving the integrated structural and control optimization problem. The use of quasi-steady aerodynamic strip theory with a thin-wall box beam model showed that the integrated design for a high aspect ratio, unswept, straight, isotropic wing can be separable. Finally, an efficient modal solution of the flutter equation facilitated the aeroelastic tailoring of a low aspect ratio, forward swept, composite plate wing model. / Ph. D.

In this study, a method is developed to solve general stochastic programming problems. The method is applicable to both linear and nonlinear optimization. Based on a proper linearization, a set of probabilistic constraints (performance functions) can be transformed into a corresponding set of deterministic constraints. this is accomplish by expanding all the constraints about the most probable failure point. The use of the proposed method allows the simplification of any stochastic programming problems into a standard linear programming problem. Numerical examples are applied to the area of probability- based optimum structural design. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / Topology Optimization is an optimization technique used to synthesize models without any preconceived shape. These structures are synthesized keeping in mind the minimum compliance problems. With the rapid improvement in advanced manufacturing technology and increased need for lightweight high strength designs topology optimization is being used more than ever. There exist a number of commercially available software's that can be used for optimizing a product. These software have a robust Finite Element Solver and can produce good results. However, these software offers little to no choice to the user when it comes to selecting the type of optimization method used. It is possible to use a programming language like MATLAB to develop algorithms that use a specific type of optimization method but the user himself will be responsible for writing the FEA algorithms too. This leads to a situation where the flexibility over the optimization method is achieved but the robust FEA of the commercial FEA tool is lost. There have been works done in the past that links ABAQUS with MATLAB but they are primarily used as a tool for finite element post-processing. Through this thesis, the aim is to develop an interface that can be used for solving optimization problems using different methods like hard-kill as well as the material penalization (SIMP) method. By doing so it's possible to harness the potential of a commercial FEA software and gives the user the requires flexibility to write or modify the codes to have an optimization method of his or her choice. Also, by implementing this interface, it can also be potentially used to unlock the capabilities of other Dassault Systèmes software's as the firm is implementing a tighter integration between all its products using the 3DExperience platform. This thesis as described uses this interface to implement BESO and HCA based topology optimization. Since hybrid cellular atomata is the only other method other than equivalent static load method that can be used for crashworthiness optimization this work suits well for the role when extended into a non-linear region.

Thesis submitted in compliance with the requirements for the Master's Degree in Technology: Department of Mechanical Engineering, Durban University of Technology, 2008. / The development of an evolutionary optimisation method and its application to the design of an advanced composite structure is discussed in this study. Composite materials are increasingly being used in various fields, and so optimisation of such structures would be advantageous. From among the various methods available, one particular method, known as Evolutionary Structural Optimisation (ESO), is shown here. ESO is an empirical method, based on the concept of removing and adding material from a structure, in order to create an optimum shape. The objective of the research is to create an ESO method, utilising MSC.Patran/Nastran, to optimise composite structures. The creation of the ESO algorithm is shown, and the results of the development of the ESO algorithm are presented. A tailfin of an aircraft was used as an application example. The aim was to reduce weight and create an optimised design for manufacture. The criterion for the analyses undertaken was stress based. Two models of the tailfin are used to demonstrate the effectiveness of the developed ESO algorithm. The results of this research are presented in the study.

There are many challenges facing the aerospace industry that can be addressed with new concepts, technologies, and materials. However, current design methods make it difficult to include these new ideas early in the design of aircraft. This is especially true in the structures discipline, which often uses weight-based methods based upon statistical regressions of historical data. A way to address this is to use physics-based structural analysis and design to create more detailed structural data. Thus, the overall research objective of this dissertation is to develop a physics-based structural analysis method to incorporate new concepts, technologies, and materials into the conceptual design phase. The design space of physics-based structural design problem is characterized as highly multimodal with numerous discontinuities; thus, a large number of alternatives must be explored. Current physics-based structural design methods tend to use high fidelity modeling and analysis tools that are computationally expensive. This dissertation proposes a modeling & simulation environment based on classical structural analysis methods. Using classical structural analysis will enable increased exploration of the design space by reducing the overall run time necessary to evaluate one alternative. The use of physics-based structural optimization using classical structural analysis is tested through experimentation. First the underlying hypotheses are tested in a canonical example by comparing different optimization algorithms ability to locate a global optimum identified through design space exploration. Then the proposed method is compared to a method based on higher fidelity finite element analysis as well as a method based on weight-based empirical data to validate the overall research objective.