On the relationship between optimum structural topologies and geometries

The relationship between two optimal design problems is investigated: (a) The fixed geometry problem, where the topology is optimized for a predetermined geometry. (b) The fixed topology problem, where the geometry is optimized for a given topology. Assuming approximate linear programming formulations, conditions of optimality are derived and geometries of multiple optimal topologies are studied. Some considerations related to a general design procedure for optimization of topology, geometry and cross-sections are discussed.Modified version of a paper presented at the First International Conference on Computer Aided Optimum Design of Structures, Southampton, June 1989. (Proceedings of the Conference by Computational Mechanics Publications)On leave from Technion-Israel Institute of Technology     

On the comparative evaluation of optimum equal-volume designs

Two criteria for supplementary evaluation of multiple optimum (or any feasible) equal-volume designs, encountered in optimisation of structures prone to symmetric bifurcation buckling, are presented. The first of the proposed criteria, pertaining to the problem of maximisation of the load of a constant-volume structure, takes into account the possibility of a structure being imperfect or overloaded. The second criterion concerns the selection of the best (and/or the worst) design of a set of given feasible, equal-volume designs of a structure, subjected to loading λ P, whose load factor may assume, with equal likelihood, any value of the prescribed range [0, gl]. The criterion makes use of a functional which reflects the structure's deformation during the loading process with λ increasing from

The presented criteria are illustrated by three examples. One of them is concerned with the shape optimisation of a portal frame; the two others refer to the shape and material optimisation of a spring-and-rod system.     

On probabilistic absolute optimum design

Absolute structural optimization problems such as leastweight and layout problems become both more realistic and more complex when their parameters are described probabilistically. The theoretical framework for absolute optimal design of sandwich beams, grillages and reinforced slabs is extended herein to deal with probabilistic parameters. It is shown that using a simplified probabilistic framework (socalled First Order Second Moment), some classical solutions for optimal layout remain valid. Remarks about the more general problem and the difficulty of its solution close the paper.     

On automated optimum design of trusses

In the course of formulating the automated design of trusses for a project, some hitherto unexplored ideas have been encountered. These ideas are developed in this article.To explore these ideas systematically, truss design for single and multiple load conditions are considered separately. In the first part the applicability of linear programming is illustrated for single load conditions to safeguard against failures by yielding, buckling, and excessive deformations. Postoptimal behaviour of the structure is also studied.In the second part nonlinear programming is used as the design tool for multiple loading conditions. In this procedure, the members are grouped, a fully utilized design is taken as the starting point, and the condensed matrix displacement method of reanalysis is adopted during optimization iterations.Practical design examples of trussed towers are given to illustrate the capabilities of the computer program developed.     

On the characteristics of optimum beams with optimum length surrounded by a Winkler’s medium

In this paper an analytical approach is used to optimize a beam surrounded by a Winkler’s medium and laterally loaded by a force at the top. The optimization regards both the distribution of the mass along the beam and the beam length in order to minimize the top displacement. Therefore, after having defined a transversality condition, we implement an algorithm to optimize the length of optimum beams. After having achieved the dimensionless extremals of optimum beams with optimum length, we show that the found solutions describe a central field of moment extremals defined along the beam and with the origin at the top. Having achieved the Jacobi’s condition and the strengthened Legendre’s condition for an extremal of optimum beam length, a sufficient condition for a weak minimum along the beam is also achieved. Besides, a given set of cross-sections whose moment of inertia divided by a dimensioned constant is obtained by raising their area to the same exponent. The optimized distribution of the dimensionless cross-sectional area as well as the dimensionless rigidity of the Winkler’s medium are intrinsic properties of all optimum beams with optimum length whose cross-sections belong to the same set.     

On optimum thin-walled closed cross section

This paper deals with the problem of finding a minimum area thin-walled closed cross section with prescribed constant thickness and flexural rigidity. The cross section is supposed to be double symmetrical with respect to the Cartesian reference system (x0y), where 0 is the centroid of the cross section, and subjected to a bending moment M. The vector M is taken to be non-coincident with the x or y axis. This means that to represent the flexural rigidity both I_x and I_y moments of inertia are required. The function describing the centerline of the thin-walled closed cross section is taken as unknown.The solution of this problem shows that such a centerline is an ellipse.     

遗传算法的全局快速寻优

分析了遗传算法的全局快速搜索能力, 指出“前t代群体”中包含至少一个位置等价非重叠模式完全集是可靠地进行全局搜索的保证; 而生成适应度值差别大的完全集是缩小搜索范围的起点, 这些模式的阶数越低, 就能越早开始缩小搜索范围, 对算法全局快速寻优也就越有利.     

On the optimum pyramidal‐horn design methods

In this article the optimum pyramidal‐horn design methods are considered. The validity of comparing the different methods with respect to design accuracy is examined in light of the fundamental accuracy limits of Schelkonoff's horn‐gain formulas. © 2006 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2006.     

On singular topologies in optimum structural design

A major obstacle to topological optimization is that the optimal topology might correspond to a singular point in the design space. Despite its crucial importance, the phenomenon of singular optimal topologies is not well understood.The main objects of this paper are: (a) to clarify some properties of singular optimal topologies; (b) to discuss the effect of various constraints on the optimum; and (c) to present some design considerations related to the particular difficulties involved in topological optimization.It is shown that singular solutions are obtained mainly due to the nature of stress constraints. Displacement constraints might significantly affect the optimal cross-sections, but not necessarily the optimal topology. The effect of lower bounds on cross-sections is demonstrated and several two-stage solution procedures are discussed.on leave from Technion-Israel Institute of Technology     

On the relationship of maximum likelihood sampled-data power spectrum identification and optimum predicition filters

Methods for estimating the sampled power spectral density of a stochastic process in terms of a rational function ofzhave been presented in the literature. A method based on the maximum likelihood criterion for Gaussian processes leads to the minimum residual criterion.^[1],[2]This correspondence points out the relationship of the minimum residual criterion to optimum prediction filters and justifies the use of the criterion even for non-Gaussian processes.     

On the design of optimum distributed parameter system with boundary control function

The problem of optimum control of a distributed parameter system with boundary control is studied. The distributed parameter system considered is described by theN-dimensional wave equation. The error measure is quadratic. The control function is unconstrained. The Riccati equation for optimum boundary control is derived. Methods for solving the Riccati equation and calculating optimum control are discussed. The resulting control is closed loop.     

On constructing a family of student delivery routes in minimal time

We consider the school bus routing problem which is to construct the routes for delivering students after classes by multiple buses in minimal time. We show the corresponding linear partially integer model. Together with an exact algorithm we show a simple heuristic algorithm and present the results of a computational experiment.     

On optimum advertising pulsing decisions in a non-stationary market

Using empirical findings available in the literature, sales behavior in response to advertising pulsing policy has been modeled mathematically in a non-stationary market. The paper discusses in detail optimum advertising pulsing policy.This policy has been compared with an alternative policy commonly used in practice. The results of the research indicate the possibility of achieving substantial savings in the advertising budget and/or increase in sales revenues of a firm when implementing advertising pulsing policy.     

On the estimation of the optimum accelerator for sor applied to finite element methods

A simple procedure is described which provides a numerical estimate of the optimum accelerator for the successive overrelaxation (SOR) process when applied to finite element methods. The procedure has been applied successfully in a number of controlled experiments, and the results of three of these are presented in detail. Comparison with finite difference methods shows that it may be possible to predict a sharp estimate of the optimum accelerator before computation begins.     

On the optimum choice of a threshold in a frequency hopping OFDMA system

We consider a frequency hopping orthogonal frequency-division multiple access (FH OFDMA) system different from those previously described. To find the probability density function of the variable used by the detector, we propose an approach based on the characteristic function method and Bessel function technique. Based on this approach, we obtain an expression for the desired density function (in the most probable case of a collision of multiplicity two) and an expression for the optimum threshold value, which enables us to compute it to any desired degree of accuracy. Efficiency of our approach is justified by simulation results.     

On bandsolver using skyline storage

A simple out-of-core bandsolver using skyline storage is presented. Without dividing the equations into blocks, the efficiency of the working vector can be greatly improved by a dynamic storage scheme to hold as many equations as possible at any one time. Compared to the blocked-skyline method, the total number of data transfers from core to disk and vice versa is reduced and the amount of active coefficients being processed in a single data transfer is maximized. The matrix decomposition without using direct-access files is first presented to explain how triangulation is done on a one-dimensional working array using skyline profile storage. Its extension to allow for out-of-core storage is then discussed in detail. Computer codes for both versions with and without using out-of-core storage are given in the Appendix.     

On the performance of bandwidth and storage sharing in information-centric networks

Information Centric Network (ICN) proposals, have recently emerged to define new network architectures where content, and not its location, becomes the core of the communication model. Such new paradigms push data storage and delivery at network layer and are designed to cope with current Internet usage, mainly centered around content dissemination and retrieval.     

On the key storage requirements for secure terminals

In a network of communication terminals “classical” end-to-end encryption (e.g. the DES) is used for communications security. Some general requirements on the storage of crypto keys for the terminals in this network are given. The key storage capacity of a terminal is determined and a scheme for reducing this storage capacity is presented. Finally the consequences of this reduction scheme are discussed and illustrated by an example.