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.

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.

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.

An Optimization Based Methodology to Design Flexible Systems Subjected to Changing Operating Conditions

Flexible systems maintain a high performance level under changing operating conditions or design requirements. Flexible systems acquire this powerful feature by allowing critical aspects of their design con guration to change during the operating life of the product or system. In the design of such systems, designers are often required to make critical decisions regarding the exible and the non-exible aspects of the design con guration. We propose an optimization based methodology to design exible systems that allows a designer to effectively make such critical decisions. The proposed methodology judiciously generates candidate optimal design versions of the exible system. These design versions are evaluated using multiobjective techniques in terms of the level of exibility and the associated penalty. A highly exible system maintains optimal performance under changing operating conditions, but could result in increased cost and complexity of operation. The proposed methodology provides a systematic approach for incorporating designer preferences and selecting the most desirable design version — a feature absent in several recently proposed exible system design frameworks. The developments of this paper are demonstrated with the help of a exible three-bar-truss design example.

A Hybrid Method Using Response Surface and Pattern Search for Design Optimization

This paper presents a new method to construct response surface function and a new hybrid optimization method. For the response surface function, the radial basis function is used for a zeroth-order approximation, while new bases is proposed for the moving least squares method for a first-order approximation. For the new hybrid optimization method, the gradient-based algorithm and pattern search algorithm are integrated for robust and efficient optimization process. These methods are based on: (1) multi-point approximations of the objective and constraint functions; (2) a multi-quadric radial basis function for the zeroth-order function representation or radial basis function plus polynomial based moving least squares approximation for the first-order function approximation; and (3) a pattern search algorithm to impose a descent condition. Several numerical examples are presented to illustrate the accuracy and computational efficiency of the proposed method for both function approximation and design optimization. The examples for function approximation indicate that the multi-quadric radial basis function and the proposed radial basis function plus polynomial based moving least squares method can yield accurate estimates of arbitrary multivariate functions. Results also show that the hybrid method developed provides efficient and convergent solutions to both mathematical and structural optimization problems.

Enhanced Sequential Optimization and Reliability Assessment Method for Changing Design Variance

The Sequential Optimization and Reliability Assessment (SORA) method is a single loop method containing a sequence of cycles of decoupled deterministic optimization and reliability assessment for improving the efficiency of probabilistic optimization. However, the original SORA method as well as some other existing single loop methods is not efficient for solving problems with changing variance. In this paper, to enhance the SORA method, three formulations are proposed by taking the effect of changing variance into account. These formulations are distinguished by the different strategies of Inverse Most Probable Point (IMPP) approximation. Mathematical examples and a pressure vessel design problem are used to test and compare the effectiveness of the proposed formulations. The “Direct Linear Estimation Formulation” is shown to be the most effective and efficient approach for dealing with problems with changing variance. The gained insight can be extended and utilized to other optimization strategies that require MPP or IMPP estimations.

Towards Rapid Redesign: Pattern-Based Design Diagnostics for Large-Scale and Complex Redesign Problems

This paper presents our continued research efforts towards developing a decomposition-based solution approach for rapid computational redesign to support agile manufacturing of evolutionary products. By analogy to the practices used for physical machines, the proposed approach involves two general steps: diagnosis and repair. This paper focuses on the diagnosis step. for which a two-phase decomposition method is developed. The first phase, called design dependency analysis, systematizes and reorganizes the intrinsic coupling structure of the existing design model by analyzing and reordering the design dependency matrix (DDM) used to represent the functional dependence and couplings inherent in the design model. The second phase, called redesign partitioning analysis, uses this result to generate alternative redesign pattern solutions through a three-stage procedure. Each pattern solution delimits the portions of the design model that need to be re-computed. An example problem concerning the redesign of an automobile powertrain is used for method illustration. Our seed paper has presented a method for selecting the optimal redesign pattern solution from the alternatives generated through redesign partitioning analysis, and a sequel paper will discuss how to generate a corresponding re-computation strategy and redesign plan (redesign shortcut roadmap).