Optimal design of structures with unspecified loading distribution

The problem of the optimal distribution of loading on a structure that corresponds to the minimum of the elastic compliance or the maximum of the safety factor for plastic collapse is considered. Optimality criteria are derived, and their applicability is illustrated in the case of beams. Besides the optimally varying cross section, also the support positions and the load distribution are determined from the optimal solution.     

Optimal design of sandwich beams for elastic deflection and load factor at plastic collapse

Zusammenfassung Die Arbeit befasst sich mit dem optimalen Entwurf eines einfach gestützten Balkens mit rechteckigem Sandwich-Querschnitt von konstanten Kernabmessungen und abschnittsweise konstanter Belegungsdicke, wenn eine obere Schranke für die elastische Durch-biegung unter vorgegebener Last und eine untere Schranke für den Belastungsfaktor für Erreichen der Grenztragfähigkeit vorgeschrieben sind.

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The results presented in this paper were obtained in the course of research supported by the U.S. Army Research Office-Durham under Research Grant DA-ARO-D-31-G1008.     

Optimal stopping for partially observed piecewise-deterministic Markov processes

This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of the partially observed optimal stopping problem. Then, we propose a numerical method, based on the quantization of the discrete-time filter process and the inter-jump times, to approximate the value function and to compute an ?$?$-optimal stopping time. We prove the convergence of the algorithms and bound the rates of convergence.     

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 die design for work-hardening metals

This paper discusses a die design problem for rigid-plastic metals under plane strain conditions. The strain distribution in the end product is required to be uniform, a condition which is satisfied when the principal stress directions coincide with streamlines of the flow. All possible deformations corresponding to a linear work hardening rule will be described.     

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.     

Elasticity and strength of nonoriented partially crystalline polymers

The dependence of the elastic modulus and strength on the crystallinity and temperature was studied. During the analysis of the strength data, the nonoriented crystalline polymers can be regarded as compositions consisting of a compliant matrix (amorphous phase) and a more rigid reinforcement (crystalline phase).The A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 6, pp. 964–968, November–December, 1975.     

Optimal reinforcement of a glass-reinforced plastic plate

Relations are derived for the optimal arrangement of the reinforcement in a rectangular glass-reinforced plastic plate supported at the edges and stressed in uniaxial compression by a short-term or long-term, uniformly distributed load. (The optimal arrangement is understood to be that which maximizes the critical load.)All-Union Scientific-Research Institute of Railroad Transport, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 741–744, July–August, 1969.     

The distribution of partially exchangeable random variables

In this article, we derive the distribution of partially exchangeable binary random variables, generalizing the distribution of exchangeable binary random variables and hence the binomial distribution. The distribution can be viewed as a mixture of Markov chains. We introduce rectangular complete monotonicity and show that partial exchangebility can be characterized by rectangular complete monotonicity. The distribution aided with rectangular complete monotonicity can be used to analyze serially correlated data common in many areas of science.     

Correlation analysis and strength of glass-reinforced plastic pipe

The correlation between certain input characteristics of glass cloth reinforced plastic pipe and product quality is evaluated. The almost total lack of both interfactor and multiple correlation is noted. The parameters that should be controlled in manufacturing pipe for purposes of obtaining the necessary correlation are listed.Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1014–1019, November–December 1968.     

Study of the strength of plastic sandwich construction

Results are given for edge-supported sandwich panels with a honeycomb core tested in bending in two directions. The experimental data are compared with theoretical results obtained from equations proposed by the authors. It is established that in designing honeycomb panels for bending in two directions it is possible to treat the panel material as virtually isotropic in the plane of the laminations and to use the authors' equations for determining the deflections and the normal and shear stresses.Mokhanika Polimerov, Vol. 1, No. 5, pp. 45–50, 1965     

Optimal adaptive estimators for partially observed numbers of defective items in inventory models

In this paper, three discrete time integer-valued inventory models for perishable items are introduced. In these models, each item in the stock is assumed to perish in a given period with some probability. The dynamics of the models are affected by a demand process, a replenishment process, and perishability. However perished items are not observed while in stock, unless sold. Recursive estimates for the probability of the number of the perished items are derived.     

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.     

Consistent density deconvolution under partially known error distribution

We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with an unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a simple condition in the time domain. A minimum distance estimator is shown to be consistent imposing only a slightly stronger assumption than the identification condition.