Handling Multiple Objectives in Decentralized Design

Most complex systems, including engineering systems such as cars, airplanes, and satellites, are the results of the interactions of many distinct entities working on different parts of the design. Decentralized systems constitute a special class of design under distributed environments. They are characterized as large and complex systems divided into several smaller entities that have autonomy in local optimization and decision-making. A primary issue in decentralized design processes is to ensure that the designers that are involved in the process converge to a single design solution that is optimal and meets the design requirements, while being acceptable to all the participants. This is made difficult by the strong interdependencies between the designers, which are usually characteristic of such systems. This paper proposes a critical review of standard techniques to modeling and solving decentralized design problems, and shows mathematically the challenges created by having multiobjective subsystems. A method based on set-based design is then proposed to alleviate some of these challenging issues. An illustration of its applicability is given in the form of the design of a space satellite.

Structural Topology Optimization Using Frame Elements Based on the Complementary Strain Energy Concept for Eigen-Frequency Maximization

This paper discuses a new topology optimization method using frame elements for the design of mechanical structures at the conceptual design phase. The optimal configurations are determined by maximizing multiple eigen-frequencies in order to obtain the most stable structures for dynamic problems. The optimization problem is formulated using frame elements having ellipsoidal cross-sections, as the simplest case. Construction of the optimization procedure is based on CONLIN and the complementary strain energy concept. Finally, several examples are presented to confirm that the proposed method is useful for the topology optimization method discussed here.

Packing Optimization by Enhanced Rubber Band Analogy

In this paper, some new developments to the packing optimization method based on the rubber band analogy are presented. This method solves packing problems by simulating the physical movements of a set of objects wrapped by a rubber band in the case of two-dimensional problems or by a rubber balloon in the case of three-dimensional problems. The objects are subjected to elastic forces applied by the rubber band to their vertices as well as reaction forces when contacts between objects occur. Based on these forces, objects translate or rotate until maximum compactness is reached. To improve the compactness further, the method is enhanced by adding two new operators: volume relaxation and temporary retraction. These two operators allow temporary volume (elastic energy) increase to get potentially better packing results. The method is implemented and applied for three-dimensional arbitrary shape objects.

Synthesis of Bistable Periodic Structures Using Topology Optimization and a Genetic Algorithm

Formulations for the automatic synthesis of two-dimensional bistable, compliant periodic structures are presented, based on standard methods for topology optimization. The design space is parameterized using non-linear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using a simple example.

Evaluation of Modular Design Concepts of Complex Mechatronic Systems

Synergies and integration in design set a mechatronic system apart from a traditional, multi-disciplinary system. This paper proposes a method for the modularization and evaluation of different mechatronic design concepts in the early stages of product development processes. In order to consider the specific aspects of complex systems, a design metric is presented, which assists the design engineer in finding the best solution concept. For the description and evaluation of a complex mechatronic system, it is essential to decompose the total system into a hierarchical structure of mechatronic sub-modules. The number of levels in the decomposition, as well as the number of mechatronic modules involved, is indicative of the complexity of the design task.

A Quadrature-Based Sampling Technique for Robust Design With Computer Models

Several methods have been proposed for estimating transmitted variance to enable robust parameter design using computer models. This paper presents an alternative technique based on Gaussian quadrature which requires only 2n+1 or 4n+1 samples (depending on the accuracy desired) where n is the number of randomly varying inputs. The quadrature-based technique is assessed using a hierarchical probability model. The 4n+1 quadrature-based technique can estimate transmitted standard deviation within 5% in over 95% of systems which is much better than the accuracy of Hammersley Sequence Sampling, Latin Hypercube Sampling, and the Quadrature Factorial Method under similar resource constraints. If the most accurate existing method, Hammersley Sequence Sampling, is afforded ten times the number of samples, it provides approximately the same degree of accuracy as the quadrature-based method. Two case studies on robust design confirmed the main conclusions and also suggest the quadrature-based method becomes more accurate as robustness improvements are made.

Faster Generation of Feasible Design Points

Design space exploration during conceptual design is an active research field. Most approaches generate a number of feasible design points (complying with the constraints) and apply graphical post-processing to visualize correlations between variables, the Pareto frontier or a preference structure among the design solutions. The generation of feasible design points is often a statistical (Monte Carlo) generation of potential candidates sampled within initial variable domains, followed by a verification of constraint satisfaction, which may become inefficient if the design problem is highly constrained since a majority of candidates that are generated do not belong to the (small) feasible solution space. In this paper, we propose to perform a preliminary analysis with Constraint Programming techniques that are based on interval arithmetic to dramatically prune the solution space before using statistical (Monte Carlo) methods to generate candidates in the design space. This method requires that the constraints are expressed in an analytical form. A case study involving truss design under uncertainty is presented to demonstrate that the computation time for generating a given number of feasible design points is greatly improved using the proposed method. The integration of both techniques provides a flexible mechanism to take successive design refinements into account within a dynamic process of design under uncertainty.

A Method for Integrating Form Errors Into Geometric Tolerance Analysis

In this research we describe a computer-aided approach to geometric tolerance analysis for assemblies and mechanisms. This new tolerance analysis method is based on the “generate-and-test” approach. A series of as-manufactured component models are generated within a NURBS-based solid modeling environment. These models reflect errors in component geometry that are characteristic of the manufacturing processes used to produce the components. The effects of different manufacturing process errors on product function is tested by simulating the assembly of these imperfect-form component models and measuring geometric attributes of the assembly that correspond to product functionality. A tolerance analysis model is constructed by generating-and-testing a sequence of component variants that represent a range of manufacturing process capabilities. The generate-and-test approach to tolerance analysis is demonstrated using a case study that is based on a high-speed stapling mechanism. As-manufactured models that correspond to two different levels of manufacturing precision are generated and assembly between groups of components with different precision levels is simulated. Misalignment angles that correspond to functionality of the stapling mechanism are measured at the end of each simulation. The results of these simulations are used to build a tolerance analysis model and to select a set of geometric form and orientation tolerances for the mechanism components. It is found that this generate-and-test approach yields insight into the interactions between individual surface tolerances that would not be gained using more traditional tolerance analysis methods.

Geometric Surface Features Applied to Volumetric CAE Mesh Models

In this paper, we discuss a way to extend a geometric surface feature framework known as Direct Surface Manipulation (DSM) into a volumetric mesh modeling paradigm that can be directly adopted by large-scale CAE applications involving models made of volumetric elements, multiple layers of surface elements or both. By introducing a polynomial-based depth-blending function, we extend the classic DSM mathematics into a volumetric form. The depth-blending function possesses similar user-friendly features as DSM basis functions permitting ease-of-control of the continuity and magnitude of deformation along the depth of deformation. Practical issues concerning the implementation of this technique are discussed in details and implementation results are shown demonstrating the versatility of this volumetric paradigm for direct modeling of complex CAE mesh models. In addition, the notion of a model-independent, volumetric-geometric feature is introduced. Motivated by modeling clay with sweeps and templates, a model-independent, catalog-able volumetric feature can be created. Deformation created by such a feature can be relocated, reoriented, duplicated, mirrored, pasted, and stored independent of the model to which it was originally applied. It can serve as a design template, thereby saving the time and effort to recreate it for repeated uses on different models (frequently seen in CAE-based Design of Experiments study).

Microstructure Design for a Rotating Disk: With Application to Turbine Engines

Through the use of generalized spherical harmonic basis functions a spectral representation is used to model the microstructure of cubic materials. This model is then linked to the macroscopic elastic properties of materials with Cubic Triclinic and Cubic Axial-symmetric symmetry. The influence that elastic anisotropy has on the fatigue response of the material is then quantified. This is accomplished through using the effective elastic stiffness tensor in the computation of the crack extension force, G. The resulting material model and macroscopic property calculations are the foundation for a software package which provides an interface to the microstructure. The Microstructure Sensitive Design interface (MDSi) enables interaction with the material design process and provides tools needed to incorporate material parameters with traditional design, optimization, and analysis software. The microstructure of the material can then be optimized concurrently other engineering models to increase the overall design space. The influence of microstructure on the performance of a spinning disc is explored. The additional design space afforded by inclusion of the material parameters show that for both Cubic Triclinic and Cubic Axial-symmetric material symmetry conditions G can be reduced by more than an order of magnitude. For the Cubic Axial-symmetric condition a Cube <001> fiber texture and a <111> fiber texture are identified as the best performing orientation distributions.