An Inverse Analysis Method for Design Optimization With Both Statistical and Fuzzy Uncertainties

Structural analysis and design optimization have recently been extended to consider various uncertainties. If the statistical data for the uncertainties are sufficient to construct the input distribution function, the uncertainties can be treated as random variables and RBDO is used; otherwise, the uncertainties can be treated as fuzzy variables and PBDO is used. However, many structural design problems include both uncertainties with sufficient data and uncertainties with insufficient data. For these problems, RBDO will yield an unreliable design since the distribution functions of uncertainties are not believable. On the other hand, treating the random variables as fuzzy variables and invoking PBDO may yield too conservative design with a higher optimum cost. This paper proposes a new design formulation using the performance measure approach (PMA). For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. Some mathematical and physical examples are used to demonstrate the proposed inverse analysis method and design formulation.

Exploiting Shape Similarity in Engineering Analysis

Engineering analysis methods, such as the finite element method, are employed extensively to optimize complex engineering designs, but their success in conceptual product development is rather limited since numerous designs must be analyzed to cover the design space, and unfortunately, modern analysis methods can be tedious and time consuming in such scenarios. We propose here a novel analysis methodology for conceptual design wherein, given the simulation results and performance of one of the designs, one predicts upper and lower bounds on the performance of geometrically similar designs. The methodology rests on sound mathematical principles such as adjoint theory of boundary value problems, and is partly motivated by recent work on shape similarity exploitation in manufacturing wherein the cost of manufacturing a new part is estimated by retrieving the manufacturing costs of geometrically similar parts.

Application of a Genetic Algorithm to Concept Variant Selection

This paper outlines a framework for applying a genetic algorithm to the selection of component variants between the conceptual and detailed design stages of product development. A genetic algorithm (GA) is defined for the problem and an example is presented that demonstrates its application and usefulness. Functional modeling techniques are used to formulate the design problem and generate the chromosomes that are evaluated with the algorithm. In the presented example, suitable GA parameters and the break-even point where the GA surpassed an enumerated search of the same solution space were found. Recommend uses of the GA along with limitations of the method and future work are presented as well.

Topology Optimization Considering Gravitational and Centrifugal Forces

In this paper, topology optimization problems with two types of body force are considered: gravitational force and centrifugal force. For structural design under both external and gravitational forces, a total mean compliance formulation is used to produce the stiffest structure. For rotational structural design with high angular velocity, one additional design criteria, kinetic energy, is included in the formulation. Sensitivity analyses of the total mean compliance and kinetic energy are derived. Finally, design examples are presented and compared to show the effects of body forces on the optimized results.

On Adaptive Sampling for Single and Multi-Response Bayesian Surrogate Models

In order to reduce the time and resources devoted to design-space exploration during simulation-based design and optimization, the use of surrogate models, or metamodels, has been proposed in the literature. Key to the success of metamodeling efforts are the experimental design techniques used to generate the combinations of input variables at which the computer experiments are conducted. Several adaptive sampling techniques have been proposed to tailor the experimental designs to the specific application at hand, using the already-acquired data to guide further exploration of the input space, instead of using a fixed sampling scheme defined a priori. Though mixed results have been reported, it has been argued that adaptive sampling techniques can be more efficient, yielding better surrogate models with less sampling points. In this paper, we address the problem of adaptive sampling for single and multi-response metamodels, with a focus on Multi-stage Multi-response Bayesian Surrogate Models (MMBSM). We compare distance-optimal latin hypercube sampling, an entropy-based criterion and the maximum cross-validation variance criterion, originally proposed for one-dimensional output spaces and implemented in this paper for multi-dimensional output spaces. Our results indicate that, both for single and multi-response surrogate models, the entropy-based adaptive sampling approach leads to models that are more robust to the initial experimental design and at least as accurate (or better) when compared with other sampling techniques using the same number of sampling points.

Multifunctional Topology Design of Cellular Material Structures

Prismatic cellular or honeycomb materials exhibit favorable properties for multifunctional applications such as ultra-light load bearing combined with active cooling. Since these properties are strongly dependent on the underlying cellular structure, design methods are needed for tailoring cellular topologies with customized multifunctional properties that may be unattainable with standard cell designs. Topology optimization methods are available for synthesizing the form of a cellular structure—including the size, shape, and connectivity of cell walls and the number, shape, and arrangement of cell openings—rather than specifying these features a priori. To date, the application of these methods for cellular materials design has been limited primarily to elastic and thermo-elastic properties, however, and limitations of standard topology optimization methods prevent direct application to many other phenomena such as conjugate heat transfer with internal convection. In this paper, we introduce a practical, two-stage, flexibility-based, multifunctional topology design approach for applications that require customized multifunctional properties. As part of the approach, robust topology design methods are used to design flexible cellular topology with customized structural properties. Dimensional and topological flexibility is embodied in the form of robust ranges of cell wall dimensions and robust permutations of a nominal cellular topology. The flexibility is used to improve the heat transfer characteristics of the design via addition/removal of cell walls and adjustment of cellular dimensions, respectively, without degrading structural performance. We apply the method to design stiff, actively cooled prismatic cellular materials for the combustor liners of next-generation gas turbine engines.

Augmenting Tools for Reverse Engineering Methods

Reverse engineering has gained importance over the past few years due to an intense competitive market aiding in the survivability of a company. This paper examines the reverse engineering process and what, how, and why it can assist in making a better design. Two well known reverse engineering methodologies are explored, the first by Otto and Wood and the second by Ingle. Each methodology is compared and contrasted according to the protocols and tools used. Among some of the reverse engineering tools detailed and illustrated are: Black box, Fishbone, Function Structure, Bill of Material, Exploded CAD models, Morphological Matrix, Subtract and Operate Procedure (SOP), House of Quality matrix, and FMEA. Even though both methodologies have highly valued tools, some of the areas in reverse engineering need additional robust tooling. This paper presents new and expanded tooling to augment the existing methods in hopes of furthering the understanding of the product, and process. Tools like Reverse Failure Mode and Effects Analysis (RFMEA), Connectivity graphs, and inter-relation matrix increase the design efficiency, quality, and the understanding of the reverse engineering process. These tools have been employed in two industry projects and one demonstrative purpose for a Design for Manufacture Class. In both of these scenarios, industry and academic, the users found that the augmented tools were useful in capturing and revealing information not previously realized.

Design and Verification of a New Computer Controlled Seating Buck

Appraising vehicle package design concepts using seating bucks — physical prototypes representing vehicle package, is an integral part of the vehicle package design process. Building such bucks is costly and may impose substantial burden on the vehicle design cycle time. Further, static seating bucks lack the flexibility to accommodate design iterations during the gradual progression of a vehicle program. A “Computer controlled seating buck”, as described in this paper, is a quick and inexpensive alternative to the traditional seating bucks with the desired degree of fidelity. It is particularly useful to perform package and ergonomic studies in the early stages of a vehicle program, long before the data is available to build a traditional seating buck. Such a seating buck has been developed to accommodate Ford vehicle package design needs. This paper presents the functional requirements, the high level conceptual design of how these requirements are realized, and the methods to verify, improve and sustain the dimensional accuracy and capability of the new computer controlled seating buck.

Parametric and Topological Control in Shape Optimization

We propose a novel approach to shape optimization that combines and retains the advantages of the earlier optimization techniques. The shapes in the design space are represented implicitly as level sets of a higher-dimensional function that is constructed using B-splines (to allow free-form deformations), and parameterized primitives combined with R-functions (to support desired parametric changes). Our approach to shape design and optimization offers great flexibility because it provides explicit parametric control of geometry and topology within a large space of freeform shapes. The resulting method is also general in that it subsumes most other types of shape optimization as special cases. We describe an implementation of the proposed technique with attractive numerical properties. The effectiveness of the method is demonstrated by several numerical examples.

Knowledge Model for Managing Product Variety and Its Reflective Design Process

Recent manufacturers have been utilizing product families to diversify and enhance the product performance by simultaneously designing multiple products under commonalization and standardization. Design information of product architecture and family is inevitably more complicated and numerous than that of a single product. Thus, more sophisticated computer-based support system is required for product architecture and family design. This paper proposes a knowledge model for a computer-based system to support reflective process of designing product architecture and product family. This research focuses on three problems which should be overcome when product family are modeled in the computer system; design repository without data redundancy and incorrectness, knowledge acquisition without forcing the additional effort on the designer, and integration of prescriptive models to support early stages of the design process. An ontology that is a foundation of a knowledge model is defined to resolve these problems. An example of designing an air conditioner product family is shown to demonstrate the capability of the system.