Andres Tovar

Topology Optimization Using a Hybrid Cellular Automaton Method With Local Control Rules

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

Crashworthiness design using topology optimization

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.

Hybrid Cellular Automata: a biologically-inspired structural optimization technique

In this investigation the hybrid cellular automaton (HCA) method for structural synthesis is extended to facilitate simultaneous topology and shape optimization. The HCA methodology has been developed for application to continuum structures. The development of this methodology has been inspired by the biological process of bone remodeling. In bone remodeling, only those elements located on the surface of the mineralized structure can be modified. In the HCA methodology implemented in this research only surface elements are allowed to change density during the structural synthesis process. The HCA method combines local design rules based on the cellular automaton paradigm and finite element analysis. Closed-loop control is used to modify the mass distribution on the internal and external surfaces of the design domain to find an optimum structure. The local control maintains a balance between mass and rigidity. The new methodology effectively combines elements of topology optimization and shape optimization into a single tool. Three classes of test problems are used to illustrate the method’s efficacy.

Optimality Conditions of the Hybrid Cellular Automata for Structural Optimization

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.

Comparative Study of Topology Optimization Techniques

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.

Compliant Mechanism Design using the Hybrid Cellular Automaton Method

This paper presents a new methodology for obtaining optimal topologies in continuum structures for compliant mechanism design. This non-gradient approach uses the Hybrid Cellular Automaton (HCA) method. The HCA method is a biologically inspired algorithm that has been used for structural topology optimization. HCA divides the design domain into a lattice of cellular automata (CAs). Locally, each CA is able to modify a continuum structural design variable based on the energy in its neighborhood. A global structural analysis using a flnite element method is used to obtain the information for each iteration. The local change in the design variable is determined by a local design rule. In previous applications to structural optimization, these local rules were implemented to achieve uniform strain energy density throughout the structural when loaded. In the application to compliant mechanisms, the structure must exhibit both ∞exibility and rigidity are required. The mechanism must be able to transfer a force from an input location to the output location while being able to withstand the input force. Therefore a multi-objective formulation is considered so that a uniform distribution of a combination of the two objectives is achieved. The algorithm has shown to be e‐cient as well as resulting in topologies that distribute compliance in uniform manner in that hinges are avoided. In this paper, we will illustrate the use of HCA in 2D and 3D compliant mechanism design using a static nonlinear analysis allowing for large deformations.

Shape Optimization for Conforming Airfoils

Interest in the design and development of unmanned aerial vehicles (UAVs) has increased dramatically in the last two and a half decades. The Buckle-Wing UAV concept being developed in this research is designed to “morph” in a way which facilitates variations in wing loading, aspect ratio and wing section shapes. The Buckle-Wing consists of two highly elastic beam-like lifting surfaces joined at the outboard wing tips in either a pinned or clamped configuration. The Buckle-Wing UAV is capable of morphing between a separated wing configuration designed for maneuverability to a single fixed wing configuration designed for long range/high endurance. The design of the Buckle-Wing’s aerodynamic shapes is critical to the functioning of this adaptive UAV airframe. The airfoils must be capable of functioning both as independent lifting surfaces and as a fused single wing. The adaptive airframe of the BuckleWing requires that the two airfoils/wings conform as one single wing for the extended range and/or endurance configuration. This paper is focused on the use of shape optimization technologies to optimally tailor the aerodynamic performance of the UAV airfoils in both the separated and single fixed wing configuration. A conforming multi-objective and multilevel airfoil shape optimization problem is formulated and solved. Given an exterior airfoil, optimized for long endurance, shape optimization can be used to decomposed the exterior airfoil into two conforming airfoils in such a way that when separated the airfoils produce a 85% increase in lift providing improved maneuverability. ∗Graduate Research Assistant, Student Member AIAA †Professor, Associate Fellow AIAA. Nomenclature α Angle of attack ρ∞ Free stream density ω Turning rate c Thrust-specific fuel consumption cd Drag coefficient cl Lift coefficient D Total drag E Endurance g Acceleration of gravity L Total lift n Wing load factor r Turning radius R Range S Planform Area t Time V∞ Free stream velocity W Weight of aircraft at any given time W1 Weight of aircraft without fuel and with full payload Wo Weight of aircraft with full fuel and payload

Reliability-based design using variable-fidelity optimization

Competitive marketplaces have driven the need for simulation-based design optimization to produce efficient and cost-effective designs. However, such design practices typically do not take into account model uncertainties or manufacturing tolerances. Such designs may lie on failure-driven constraints and are characterized by a high probability of failure. Reliability-based design optimization (RBDO) methods have been developed to obtain designs that optimize a merit function while ensuring a target reliability level is satisfied. Unfortunately, these methods are notorious for the high computational expense they require to converge. In this research variable-fidelity methods are used to reduce the cost of RBDO. Variable-fidelity methods use a set of models with varying degrees of fidelity and computational expense to aid in reducing the cost of optimization. The variable-fidelity RBDO methodology developed in this investigation is demonstrated on two test cases: a nonlinear analytic problem and a high-lift airfoil design problem. For each of these problems the proposed method shows considerable savings for performing RBDO as compared with standard approaches.

Reliability Based Topology Optimization using the Hybrid Cellular Automaton Method

In this research, a reliability based topology optimization (RBTO) for structural design methodology using the Hybrid Cellular Automata (HCA) method is proposed. More speciflcally, a decoupled reliability based design optimization (RBDO) approach is utilized, so that the topology optimization is separate from the reliability analysis. In this paper, a maximum allowable displacement failure mode is considered. In this methodology, starting from a continuum design space of uniform material distribution and initial uncertain variable values, a deterministic topology optimization is followed by a reliability assessment of the resulting structure to determine the most probable point of failure (MPP) for the current structure. The MPP is determined with respect to the maximum allowable de∞ection of the structure when loaded. This is generally a computationally expensive process using traditional techniques due to the large number of design variables associated with topology optimization problem. However, combining the e‐cient methods of the non-gradient HCA algorithm with the decoupled approach for RBDO aims to reduce this burden. The topology optimization was without constraint in previous applications of the HCA method. To accommodate RTBO, a mechanism for a global constraint for maximum allowable displacement is developed. This paper details the methodology for the six-sigma design of structures using topology optimization.

Optimum design of an interbody implant for lumbar spine fixation

A new minimally invasive surgical technique for lumbar spine fixation is currently in development. The procedure makes use of an interbody implant that is inserted between two vertebral bodies. The implant is packed with bone graft material that fuses the motion segment. The implant must be capable of retaining bone graft material and supporting spinal loads while fusion occurs. The different load conditions analyzed include: compression, flexion, extension, and lateral bending. The goal of this research is to obtain an optimum design of this interbody implant. Finite element-based optimization techniques are used to drive the design. The multiobjective optimization process is performed in two stages: topology optimization followed by shape optimization. As a result, the final design maximizes the volume allocated for the bone graft material and maintains von Mises stress levels in the implant below the stress limit. The finite element-based optimization software GENESIS is used in the design process.