Optimal die shape for film casting

We consider an isothermal model for the film casting process. The aim of this study is to determine a shape of the die that leads to a uniform thickness of the film. Thanks to a decoupling of the equations for the thickness and the velocities of the film, we are able to solve the reverse thickness equation. This reverse equation describes the dependence of the shape of the die on the desired final thickness.     

Optimal design for smoothing splines

In the common nonparametric regression model we consider the problem of constructing optimal designs, if the unknown curve is estimated by a smoothing spline. A special basis for the space of natural splines is introduced and the local minimax property for these splines is used to derive two optimality criteria for the construction of optimal designs. The first criterion determines the design for a most precise estimation of the coefficients in the spline representation and corresponds to D-optimality, while the second criterion is the G-optimality criterion and corresponds to an accurate prediction of the curve. Several properties of the optimal designs are derived. In general, D- and G-optimal designs are not equivalent. Optimal designs are determined numerically and compared with the uniform design.     

Optimal structural design for given deflection

Zusammenfassung Es wird ein Prinzip der stationären gegenseitigen potentiellen Energie aufgestellt für zwei Belastungssysteme eines elastischen Balkens veränderlicher Biegesteifigkeit. Aus diesem Prinzip wird eine hinreichende Bedingung für stationäres Gewicht eines Sandwichbalkens abgeleitet, wenn die von einer Belastung an einem bestimmten Querschnitt erzeugte Durchbiegung vorgeschrieben ist. Für statisch bestimmte Balken wird gezeigt, dass diese Bedingung ein globales Minimum des Gewichts sicherstellt. Anwendungsbeipiele und Erweiterungen werden besprochen.

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This research was supported in part (W. P.) by the U.S. Army Research Office, Durham.     

Optimal plastic design for partially pressigned strength distribution

The optimal plastic design of structures having a partially predefined strength distribution is considered. Sufficient conditions for optimality as well as upper and lower bounds on minimum structural volume are established and examples involving a continuous beam and a grillage are given. It is shown that most existing theories for optimal plastic design and limit analysis can be derived from the optimality criteria presented.     

Optimal design of elastic structures for multipurpose loading

The optimal design of elastic beams subjected to two alternative loading systems is considered for compliance constraints and a minimum-cross-section constraint. Sufficient conditions for optimality are established, and a technique for determining the optimal design is presented. Two examples are given. Generalizations to more than two loading systems and more complex structures are straightforward.     

Optimal design in axial motion for several frequency constraints

Governing equations for the optimal design of a rod with tip mass subject to several constraints on natural frequency are developed. The relation of this mass distribution to the globally optimum design for lowest frequency is discussed. A numerical example for two frequencies is presented. Some continuity results concerning the optimal mass distribution are presented.     

Optimal structural design for given stiffness in stationary creep

Zusammenfassung Eine allgemeine Methode der optimalen Tragwerksbemessung für vorgeschriebene Steifigkeit in stationärem Kriechen wird am Beispiel einer Scheibe mit veränderlicher Dicke erläutert, die gegebene Lasten längs eines Teils ihrer Berandung trägt und längs der übrigen Berandung starr unterstützt ist. Für einen vorgeschriebenen Wert der Kriechsteifigkeit (=Leistung der Lasten an den Geschwindigkeiten des stationären Kriechens) soll die Scheibe mit dem geringst möglichen Aufwand eines bestimmten Materials mit bekannten Kriecheigenschaften ausgeführt werden.

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The results presented in this paper were obtained in the course of research sponsored under Contract No. N00014-67-A-0109-0003, Task NR 064-496 by the Office of Naval Research, Washington, D.C.     

Optimal budget for system design series network DEA model

Wei and Chang (2011a) developed optimal system design (OSD) data envelopment analysis (DEA) models to design a decision-making unit (DMU)’s optimal system, in which the DMU could encounter the well-known economic phenomenon of budget congestion. To show how to verify the optimal budget and budget congestion, they develop a solution method. In this paper, we note that their method is incorrect for the OSD network DEA model in general. A new approach is developed to derive the DMU’s corresponding optimal budgets and to check for the existence of budget congestion not only for the OSD DEA models but also for the OSD network DEA models. In addition, the proposed approach is computationally economical. Finally, two numerical examples are used to illustrate the proposed approach.     

Optimal design of non-equilibrium experiments for genetic network interrogation

Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.     

Optimal design of multi-purpose structures

The paper presents the optimal (maximum transverse stiffness) design of an elastic, simply supported member of given volume that is to serve as a beam or as a column at different times during its design life. The optimal design can be interpreted in two ways. It is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection in beam action under a uniformly distributed load; it is also the design that has the least deflection at midspan under a uniformly distributed load, subject to a lower limit on its buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.The author is grateful to Professor W. Prager for suggesting several improvements to an earlier version of the paper.     

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.     

Optimal design of multi-purpose tie-beams

The paper presents a solution of the problem of minimizing the maximum deflection of a simply-supported beam under a transverse concentrated load. The volume (mass) of the beam is given, as is the maximum longitudinal elongation if the beam were to act as a tie. An optimal design for two requirements (beam and tie action) not only unifies the design procedure of mass-produced structural-mechanical elements, but also provides a practically acceptable design, in the sense that the resulting shape does not vanish at any point along its length, a drawback of many optimal designs for a single requirement. However, it is shown that, for cross sections of solid construction, as opposed to those of sandwich construction, the constraint on longitudinal elongation is weaker than on the (finite) maximum stress. The effectiveness of the optimal design is judged by comparing it with a prismatic member of the same volume.     

Optimal design of beams for prescribed compliance under alternative loads

A global optimality condition is established for minimum-weight design of sandwich beams with elementwise constant cross section for prescribed compliances in alternative states of loading. This condition requires a nonnegative linear combination of the mean-square curvatures of an element in the considered states of loading to have the same value for all elements. The use of the condition in the determination of the minimum-weight design is illustrated by examples.This research was sponsored by the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-69-C-1826. The authors wish to express their thanks to Professor J. B. Martin, Brown University, for helpful discussions.     

Optimal shape design for fluid flow using topological perturbation technique

This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.     

Optimal structural design of a planar parallel platform for machining

Parallel manipulators have many advantages over traditional serial manipulators. These advantages include high accuracy, high stiffness and high load-to-weight ratio, which make parallel manipulators ideal for machining operations where high accuracy is required to meet the requirements that modern standards demand.Recently, the finite element method has been used by some workers to determine the stiffness of spatial manipulators. These models are mainly used to verify stiffness predicted using kinematic equations, and are restricted to relatively simple truss-like models. In this study, state-of-the-art finite elements are used to determine the out of plane stiffness for parallel manipulators. Euler–Bernoulli beam elements and flat shell elements with drilling degrees of freedom are used to model the platform assembly.The main objective of this study is to quantify the stiffness, particularly the out of plane stiffness, of a planar parallel platform to be used for machining operations. The aim is to obtain a design that is able to carry out machining operations to an accuracy of 10 μm for a given tool force.Reducing the weight of a parallel manipulator used in machining applications has many advantages, e.g. increased maneuverability, resulting in faster material removal rates. Therefore the resulting proposed design is optimized with respect to weight, subject to displacement and stress constraints to ensure feasible stiffness and structural integrity. The optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q.     

Optimal design and control of queues

We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.     

Optimal insurance design with a bonus

This paper investigates an insurance design problem, in which a bonus will be given to the insured if no claim has been made during the whole lifetime of the contract, for an expected utility insured. In this problem, the insured has to consider the so-called optimal action rather than the contracted compensation (or indemnity) due to the existence of the bonus. For any pre-agreed bonus, the optimal insurance contract is given explicitly and shown to be either the full coverage contract when the insured pays high enough premium, or a deductible one otherwise. The optimal contract and bonus are also derived explicitly if the insured is allowed to choose both of them. The contract turns out to be of either zero reward or zero deductible. In all cases, the optimal contracts are universal, that is, they do not depend on the specific form of the utility of the insured. A numerical example is also provided to illustrate the main theoretical results of the paper.