A Sequential Approximation Method for Structural Optimization Using Logarithmic Barriers

A sequential approximation technique for non-linear programming is presented here that is particularly suited for problems in engineering design and structural optimization, where the number of variables are very large and function and sensitivity evaluations are computationally expensive. A sequence of sub-problems are iteratively generated using a linear approximation for the objective function and setting move limits on the variables using a barrier method. These sub-problems are strictly convex. Computation per iteration is significantly reduced by not solving the sub-problems exactly. Instead at each iteration, a few Newton-steps are taken for the sub-problem. A criteria for moving the move limit, is described that reduces or eliminates stepsize reduction during line search. The method was found to perform well for unconstrained and linearly constrained optimization problems. It requires very few function evaluations, does not require the hessian of the objective function and evaluates its gradient only once per iteration.

Layout of Plate Structures for Improved Dynamic Response Using a Homogenization Method

A model to compute average properties for Mindlin plates of rapidly varying thickness was introduced in [SOT93]. The model was designed to be of use in computations of the optimum shape and layout of plates using the technique introduced by Bendsøe and Kikuchi [BEN88]. In this paper we discuss the utilization of the model to determine the optimum layout of plate structures that maximizes a function of the structure’s natural frequencies. A simply supported square plate is used to illustrate the problem of optimization in the presence of repeated natural frequencies. An automotive application is presented to illustrate the usefulness in design practice.

Genesis of Ribbed Plate and Shells With Isotropic Density Dependent Material

An essential part in the genesis of structures or optimal material distribution is the relation between elastic behaviour and material density. This approach makes use of a isotropic material model, which leads to very simple working conditions. The isotropic model is directly formulated and utilized without employing homogenization based on an artificial microstructure. It is shown in theoretical considerations and demonstrated by examples, that this idea works also very easily with plate and shells, even for very general layer structures.

Abstraction As a Configuration Design Methodology

Configuration design can be thought of as a process of generating artifacts by assembling pre-defined components. This paper introduces a method for reducing the size of configuration problems by abstracting components to higher levels of abstraction. At higher abstraction levels, less important detail is temporarily ignored, and each component represents a family of lower-level components. Configuration is then performed at the highest level, explicitly enumerating all configurations at that level. Any complete configuration at the highest level is recursively instantiated to lower levels. At the same time, any incomplete configuration at the highest level is eliminated, thereby eliminating all possible lower-level instantiations of that configuration. In this manner, all configurations of components at the lowest level of abstraction are implicitly enumerated.

A Robust Optimization Method for Systems With Significant Nonlinear Effects

This paper describes a robust optimization methodology for design involving either complex simulations or actual experiments. The proposed procedure optimizes the worst case response that consists of a weighted sum of expected mean and response variance. The estimation scheme for expected mean and variance adopts the modified 3-point Gauss quadrature integration to assure superior accuracy for systems with significant nonlinear effects. We apply the proposed method to the robust design of geometric parameters of heat treated parts to minimize the cost of post heat treatment operations. The paper investigates the major factors influencing geometric distortions due to heat treatment and the rules of thumb in design. The study focuses on relating dimensional distortion to the design of part geometry. To illustrate the utility of the proposed method, we present the formulation of a case study on allocation of dimensions of preheat treated (green) shafts to minimize the cost of post heat treatment operations. The final result is not presented yet pending the completion of further experiments.

Computational Support for Interactive Cable Harness Routing and Design

We describe a system for routing cable harnesses in complex, three-dimensional environments. The approach taken is to automate the basic routing process as much as possible, while allowing designers to guide the system and modify the numerically generated results at any stage. The system begins by quickly generating a coarse routing based on an initial guess of the cable harness configuration (topological structure). Paths are then successively refined to minimize a cost function, while satisfying physical constraints such as minimum bending radius. Human input is useful both for guiding the system away from local minima and for responding to case-specific constraints not encoded in the router.

Assembly Representation Within a Product Data Framework

Recent research at the University of Leeds demonstrated how a product data model can integrate the information required and used during product design and manufacture. The product data framework developed during this research structured assemblies as lists of parts and did not consider information about the relationships between components necessary to support applications such as tolerance analysis and design for assembly. This paper describes how we intend to combine research in assembly representation, functional modeling and data modeling to describe the geometric and functional relationships between components of assemblies. Focus is provided by considering both the design process and the information requirements of a design for assembly analysis.

Kinematics of the Generalized Slider-Crank Mechanism

Dual-number techniques are used to analyze the kinematics and dynamics of the slider crank mechanism generalized to consider the effects of the cylinder axis being offset and non-perpendicular to the crankshaft axis, conditions which result in reciprocating machinery such as engines and compressors from manufacturing tolerances. The kinematics of the mechanism are evaluated with a Newton-Raphson method using dual-number coordinate-transformation matrices which in this work is extended to include mechanisms with spherical joints. Results for various cases are shown and are ready to be used in a study of the dynamics of the generalized slider-crank.

A Model for Performance-Intelligent Design Advisors

We consider a design advisor to be performance-intelligent when its suggestions do not conflict with high level performance-related goals of the design under study. We address the problem of representing non-domain-specific design Information at a high level and describe coupling it to the inputs and outputs of design critics and their suggestion mechanisms. High level design Information represented in a function-based structure with linked allocations is shown to interact with a domain-specific design critic in three instances, viz.: allocation refinement, goal matching with a supported function, and performance-intelligent tradeoffs. Examples of manual and computer-based procedures are discussed.

A Robust Optimization Procedure With Variations on Design Variables and Constraints

This paper describes a procedure that incorporates manufacturing and operational variances to achieve designs with robust and optimal performance. The procedure optimizes the expected value of a performance characteristic subject to a set of constraints. It uses concepts from statistical design of experiments to approximate the expected value of a performance characteristic. The procedure incorporates uncertainties in design variables and variations in constraints due to uncertainty in design variables. This paper discusses the following three methods to incorporate variations in constraints: 1) A method using heuristics that evaluates constraints at the worst combinations of design variables, 2) A method with built-in constraint variation that models constraints using first order Taylor expansion, and 3) A method based on differentiating KKT optimality conditions. The design of spur and helical gears with minimum transmission error serves as the target application. The key gear design research issue is to determine the optimal combination of geometric design variables like number of teeth, pressure angle that minimizes transmission error subject to constraints like minimum number of teeth to avoid undercut and maximum bending stress.