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Crashworthiness design is an evolving discipline that combines vehicle crash simulation and design synthesis. The goal is to increase passenger safety subject to manufacturing cost constraints. The crashworthiness design process requires modeling of the complex interactions involved in a crash event. Current approaches utilize a parametrized optimization approach that requires response surface approximations of the design space. This is due to the expensive nature of numerical crash simulations and the high nonlinearity, and noisiness in the design space. These methodologies usually require a significant effort to determine an initial design concept. In this paper, a heuristic approach to continuum-based topology optimization is developed for crashworthiness design. The methodology utilizes the cellular automata paradigm to generate three-dimensional design concepts. Furthermore, a constraint on maximum displacement is implemented to maintain a desired performance of the structures synthesized. Example design problems are used to demonstrate that the proposed methodology converges to a final topology in an efficient manner. [DOI: 10.1115/1.3116256]

Many practical structural designs require that the structure is easily manufactured. Design concepts synthesized using conventional topology optimization methods are typically not easily manufactured, in that multiple finishing processes are required to construct the component. A manufacturing technique that requires only minimal effort is extrusion. Extrusion is a manufacturing process used to create objects of a fixed cross-sectional profile. The result of using this process is lower costs for the manufacture of the final product. In this paper, a hybrid cellular automaton algorithm is developed to synthesize constant cross section structures that are subjected to nonlinear transient loading. The novelty of the proposed method is the ability to generate constant cross section topologies for plastic-dynamic problems since the issue of complex gradients can be avoided. This methodology is applied to extrusions with a curved sweep along the direction of extrusion as well. Three-dimensional examples are presented to demonstrate the efficiency of the proposed methodology in synthesizing these structures. Both static and dynamic loading cases are studied. [DOI: 10.1115/1.3116255]

Research applications involving design tool development for multi phase material design are at an early stage of development. The computational requirements of advanced numerical tools for simulating material behavior such as the finite element method (FEM) and the molecular dynamics (MD) method can prohibit direct integration of these tools in a design optimization procedure where multiple iterations are required. One, therefore, requires a design approach that can incorporate multiple simulations (multiphysics) of varying fidelity such as FEM and MD in an iterative model management framework that can significantly reduce design cycle times. In this research a material design tool based on a variable fidelity model management framework is presented. In the variable fidelity material design tool, complex 'high-fidelity' FEM analyses are performed only to guide the analytic 'low-fidelity' model toward the optimal material design. The tool is applied to obtain the optimal distribution of a second phase, consisting of silicon carbide (SIC) fibers, in a silicon-nitride ([Si.sub.3][N.sub.4]) matrix to obtain continuous fiber SiC-[Si.sub.3][N.sub.4] ceramic composites with optimal fracture toughness. Using the variable fidelity material design tool in application to two test problems, a reduction in design cycle times of between 40% and 80% is achieved as compared to using a conventional design optimization approach that exclusively calls the high-fidelity FEM. The optimal design obtained using the variable fidelity approach is the same as that obtained using the conventional procedure. The variable fidelity material design tool is extensible to multiscale multiphase material design by using MD based material performance analyses as the high-fidelity analyses in order to guide low-fidelity continuum level numerical tools such as the FEM or finitedifference method with significant savings in the computational time. [DOI: 10.1115/1.2965361] Keywords: CFCC, FEM, fidelity, fracture toughness, optimal, scaling, stress intensity

This paper presents a comparison between three continuum-based topology optimization methods: the hybrid cellular automaton method, the optimality criteria method, and the method of moving asymptotes. The purpose of the study is to highlight the differences between the three. The optimality criteria method and the method of moving asymptotes are well established in topology optimization. The hybrid cellular automaton method is a recently developed gradient-free technique that combines both local design rules based on the cellular automaton paradigm and the finite element analysis. The closed-loop controllers used in the hybrid cellular automaton method are used to modify the mass distribution in the design domain to find an optimum material layout. The hybrid cellular automaton and optimality criteria methods and the method of moving asymptotes are described and applied in a comparative study to three sample problems. The influence of different algorithm control parameters is shown in this work. The paper demonstrates that, for the sample problems presented, the hybrid cellular automaton method generally required the fewest number of iterations to converge to a solution compared with the optimality criteria method and the method of moving asymptotes. The final topologies generated using the hybrid cellular automaton method typically had the lowest compliance and exhibited the fewest number of intermediate densities at the solution.

In this investigation a robotic system's dynamic performance is optimized for high reliability under uncertainty. The dynamic capability equations (DCE) allow designers to predict the dynamic performance of a robotic system for a particular configuration and reference point on the end effector (i.e., point design). Here the DCE are used in conjunction with a reliability-based design optimization (RBDO) strategy in order to obtain designs with robust dynamic performance with respect to the end-effector reference point. In this work a unilevel performance measure approach is used to perform RBDO. This is important for the reliable design of robotic systems in which a solution to the DCE is required for each constraint call. The method is illustrated on a robot design problem. [DOI: 10.1115/1.2437804]

The hybrid cellular automaton method has been successfully applied to topology optimization using a uniform strain energy density distribution approach. In this work, a new set of design rules is derived from the first-order optimality conditions of a multi-objective problem. In this new formulation, the final topology is derived to minimize both mass and strain energy. In the hybrid cellular automaton algorithm, local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality. In addition to the control-based techniques previously introduced, a new ratio technique is derived in this investigation. This work also compares the performance of the control strategies and the ratio technique.

The hybrid cellular automaton (HCA) algorithm is a methodology developed to simulate the process of structural adaptation in bones. This methodology incorporates a distributed control loop within a structure in which ideally localized sensor cells activate local processes of the formation and resorption of material. With a proper control strategy, this process drives the overall structure to an optimal configuration. The controllers developed in this investigation include two-position, proportional, integral and derivative strategies. The HCA algorithm combines elements of the cellular automaton (CA) paradigm with finite element analysis (FEA). This methodology has proved to be computationally efficient to solve topology optimization problems. The resulting optimal structures are free of numerical instabilities such as the checkerboarding effect. This investigation presents the main features of the HCA algorithm and the influence of different parameters applied during the iterative optimization process. [DOI: 10.1115/1.2336251]

Traditionally, reliability-based design optimization (RBDO) has been formulated as a nested optimization problem. The inner loop, generally, involves the solution to optimization problems for computing the probabilities of failure of the critical failure modes, and the outer loop performs optimization by varying the decision variables. Such formulations are by nature computationally intensive, requiring numerous function and constraint evaluations. To alleviate this problem, researchers have developed iterative decoupled RBDO approaches. These methods perform deterministic optimization and reliability assessment in a sequential manner until a consistent reliability-based design is obtained. The sequential methods are attractive because a consistent reliable design can be obtained at considerably lower computational cost. However, the designs obtained by using these decoupled approaches cannot guarantee production of the true solution. A new decoupled method for RBDO is developed in this investigation. Postoptimal sensitivities of the most probable point (MPP) of failure with respect to the decision variables are introduced to update the MPPs during the deterministic optimization phase of the proposed approach. A damped Broyden-Fletcher-Goldfarb-Shanno method is used to significantly reduce the cost of obtaining these sensitivities. It is the use of postoptimal sensitivities that differentiates this new decoupled RBDO approach from previous efforts.

In this research we develop a mathematical construct for estimating uncertainties within the bilevel optimization framework of collaborative optimization. The collaborative optimization strategy employs decomposition techniques that decouple analysis tools in order to facilitate disciplinary autonomy and parallel execution. To ensure consistency of the physical artifact being designed, interdisciplinary consistency constraints are introduced at the system level. These constraints implicitly enforce multidisciplinary consistency when satisfied. The decomposition employed in collaborative optimization prevents the use of explicit propagation techniques for estimating uncertainties of system performance. In this investigation, we develop and evaluate an implicit method for estimating system performance uncertainties within the collaborative optimization framework. The methodology accounts for both the uncertainty associated with design inputs and the uncertainty of performance predictions from other disciplinary simulation tools. These implicit uncertainty estimates are used as the basis for a new robust collaborative optimization (RCO) framework. The bilevel robust optimization strategy developed in this research provides for disciplinary autonomy in system design, while simultaneously accounting for performance uncertainties to ensure feasible robustness of the resulting system. The method is effective in locating a feasible robust optimum in application studies involving a multidisciplinary aircraft concept sizing problem. The system-level consistency constraint formulation used in this investigation avoids the computational difficulties normally associated with convergence in collaborative optimization. The consistency constraints are formulated to have the inherent properties necessary for convergence of general nonconvex problems when performing collaborative optimization. [DOI: 10.1115/1.2205869] Keywords: collaborative optimization, robust optimization, uncertainty estimation

Solving design problems that rely on very complex and computationally expensive calculations using standard optimization methods might not be feasible given design cycle time constraints. Variable fidelity methods address this issue by using lower-fidelity models and a scaling function to approximate the higher-fidelity models in a provably convergent framework. In the past, scaling functions have mainly been either first-order multiplicative or additive corrections. These are being extended to second order. In this investigation variable metric approaches for calculating second-order scaling information are developed. A kriging-based scaling function is introduced to better approximate the high-fidelity response on a more global level. An adaptive hybrid method is also developed in this investigation. The adaptive hybrid method combines the additive and multiplicative approaches so that the designer does not have to determine which is more suitable prior to optimization. The methodologies developed in this research are compared to existing methods using two demonstration problems. The first problem is analytic, whereas the second involves the design of a supercritical high-lift airfoil. The results demonstrate that the kriging-based scaling methods improve computational expense by lowering the number of high-fidelity function calls required for convergence. The results also indicate the hybrid method is both robust and effective.

The high degree of automation of Solid Freeform Fabrication (SFF) processing and its ability to create geometrically complex parts to precise dimensions provide it with a unique potential for low volume production of rapid tooling and functional components. A factor of significant importance in the above applications is the capability of producing components with adequate mechanical performance (e.g., stiffness and strength). This paper introduces a strategy for optimizing the design of Fused-Deposition Acrylonitrile-Butadiene-Styrene (FD-ABS; P400) components for stiffness and strength under a given set of loading conditions. In this strategy, a mathematical model of the structural system is linked to an approximate minimization algorithm to find the settings of select manufacturing parameters, which optimize the mechanical performance of the component. The methodology is demonstrated by maximizing the load carrying capacity of a two-section cantilevered FD-ABS beam. [DOI 10.1115/1.1582499]

Sequential approximate optimization (SAO) is a class of methods available for the multidisciplinary design optimization of complex systems that are composed of several disciplines coupled together. One of the approaches used for SAO is based on a quadratic response surface approximation, where zero- and first-order information are required at the current design. In this method, designers must generate and query a database of order [??]([n.sup.2]) to compute the second-order terms of the quadratic response surface approximation. As the number of design variables grows, the computational cost of generating the required database becomes a concern. An adaptive experimental design (AED) approach that requires just [??](n) parameters for constructing a second-order approximation is presented. This is accomplished by transforming the matrix of second-order terms into the canonical form. The AED method periodically requires an order [??]([n.sup.2]) update of the second-order approximation to maintain accuracy. Results show that the proposed approach dramatically reduces the total number of calls to the simulation tools during the SAO process.

In this research a Collaborative Optimization (CO) approach for multidisciplinary systems design is used to develop a decision based design framework for non-deterministic optimization. To date CO strategies have been developed for use in application to deterministic systems design problems. In this research the decision based design (DBD) framework proposed by Hazelrigg is modified for use in a collaborative optimization framework. The Hazelrigg framework as originally proposed provides a single level optimization strategy that combines engineering decisions with business decisions in a single level optimization. By transforming this framework for use in collaborative optimization one can decompose the business and engineering decision making processes. In the new multilevel framework of Decision Based Collaborative Optimization (DBCO) the business decisions are made at the system level. These business decisions result in a set of engineering performance targets that disciplinary engineering design teams seek to satisfy as part of subspace optimizations. The Decision Based Collaborative Optimization framework more accurately models the existing relationship between business and engineering in multidisciplinary systems design. [DOI: 10.1115/1.1432991] Keywords: Collaborative Optimization (CO), Decision Based Design (DBD), Uncertainty, Optimization

A multiobjective system design and optimization procedure that takes into account the designer's preferences during the design process has been developed. It uses an aspiration-level approach to generate Pareto points and provides the designer with a means of investigating design parameters around a given Pareto point. The designer also has access to Pareto sensitivity information and the Pareto surface approximation. The proposed technique is used on a set of simple analytical constraints for its objective and constraints and on a high-performance, low-cost 10-bar structure with multiple objectives.

This research focuses on multi-objective system design and optimization. The primary goal is to develop and test a mathematically rigorous and efficient interactive multiobjective optimization algorithm that takes into account the Decision Maker's (DM's) preferences during the design process. An interactive MultiObjective Optimization Design Strategy (iMOODS) has been developed in this research to include the Pareto sensitivity analysis, Pareto surface approximation and local preference functions to capture the DM's preferences in an Iterative Decision Making Strategy (IDMS). This new multiobjective optimization procedure provides the DM with a formal means for efficient design exploration around a given Pareto point. The use of local preference functions allows the iMOODS to construct the second order Pareto surface approximation more accurately in the preferred region of the Pareto surface. The iMOODS has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for the objective and constraints. The second problem is the design and sizing of a high-performance and low-cost ten bar structure that has multiple objectives. The results indicate that the class functions are effective in capturing the local preferences of the DM. The Pareto designs that reflect the DM's preferences can be efficiently generated within IDMS. [DOI: 10.1115/1.1358302]

New ground is broken in our understanding of objective functions' ability to capture Pareto solutions for multi-objective design optimization problems. It is explained why widely used objective functions fail to capture Pareto solutions when the Pareto frontier is not convex in objective space, and the means to avoid this limitation, when possible, is provided. These conditions are developed and presented in the general context of n-dimensional objective space, and numerical examples are provided. An important point is that most objective function structures can be made to generate nonconvex Pareto frontier solutions if the curvature of the objective function can be varied by setting one or more parameters. Because the occurrence of nonconvex efficient frontiers is common in practice, the results are of direct practical usefulness.