Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

Freeform Skeletal Shape Optimization of Compliant Mechanisms

Compliant mechanisms are elastic continua used to transmit or transform force and motion mechanically. The topology optimization methods developed for compliant mechanisms also give the shape for a chosen parameterization of the design domain with a fixed mesh. However, in these methods, the shapes of the flexible segments in the resulting optimal solutions are restricted either by the type or the resolution of the design parameterization. This limitation is overcome in this paper by focusing on optimizing the skeletal shape of the compliant segments in a given topology. It is accomplished by identifying such segments in the topology and representing them using Bezier curves. The vertices of the Bezier control polygon are used to parameterize the shape-design space. Uniform parameter steps of the Bezier curves naturally enable adaptive finite element discretization of the segments as their shapes change. Practical constraints such as avoiding intersections with other segments, self-intersections, and restrictions on the available space and material, are incorporated into the formulation. A multi-criteria function from our prior work is used as the objective. Analytical sensitivity analysis for the objective and constraints is presented and is used in the numerical optimization. Examples are included to illustrate the shape optimization method.

Theoretical gain optimization studies in CO2-N2 lasers. III. Inclusion of line shape effects

The influence of Lorentz and Doppler line-broadening mechanisms on the small-signal optical gain of lasers and, in particular, gasdynamic lasers, is discussed. A relationship between the critical parameter reflecting the line-broadening mechanisms and some of the important parameters arising out of the gain optimization studies in CO2-N2 gasdynamic lasers is established. Using this relationship, methods by which the deleterious effect of the Doppler mechanisms on small-signal gain can be suppressed are suggested. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Size optimization of a cantilever beam under deformation-dependent loads with application to wheat stalks

In this paper, we consider the optimization of the cross-section profile of a cantilever beam under deformation-dependent loads. Such loads are encountered in plants and trees, cereal crop plants such as wheat and corn in particular. The wind loads acting on the grain-bearing spike of a wheat stalk vary with the orientation of the spike as the stalk bends; this bending and the ensuing change in orientation depend on the deformation of the plant under the same load.The uprooting of the wheat stalks under wind loads is an unresolved problem in genetically modified dwarf wheat stalks. Although it was thought that the dwarf varieties would acquire increased resistance to uprooting, it was found that the dwarf wheat plants selectively decreased the Young's modulus in order to be compliant. The motivation of this study is to investigate why wheat plants prefer compliant stems. We analyze this by seeking an optimal shape of the wheat plant's stem, which is modeled as a cantilever beam, by taking the large deflection of the stem into account with the help of co-rotational finite element beam modeling. The criteria considered here include minimum moment at the fixed ground support, adequate stiffness and strength, and the volume of material. The result reported here is an example of flexibility, rather than stiffness, leading to increased strength.

Protein sequence design on the basis of topology optimization techniques -Using continuous modeling of discrete amino acid types

The notion of optimization is inherent in protein design. A long linear chain of twenty types of amino acid residues are known to fold to a 3-D conformation that minimizes the combined inter-residue energy interactions. There are two distinct protein design problems, viz. predicting the folded structure from a given sequence of amino acid monomers (folding problem) and determining a sequence for a given folded structure (inverse folding problem). These two problems have much similarity to engineering structural analysis and structural optimization problems respectively. In the folding problem, a protein chain with a given sequence folds to a conformation, called a native state, which has a unique global minimum energy value when compared to all other unfolded conformations. This involves a search in the conformation space. This is somewhat akin to the principle of minimum potential energy that determines the deformed static equilibrium configuration of an elastic structure of given topology, shape, and size that is subjected to certain boundary conditions. In the inverse-folding problem, one has to design a sequence with some objectives (having a specific feature of the folded structure, docking with another protein, etc.) and constraints (sequence being fixed in some portion, a particular composition of amino acid types, etc.) while obtaining a sequence that would fold to the desired conformation satisfying the criteria of folding. This requires a search in the sequence space. This is similar to structural optimization in the design-variable space wherein a certain feature of structural response is optimized subject to some constraints while satisfying the governing static or dynamic equilibrium equations. Based on this similarity, in this work we apply the topology optimization methods to protein design, discuss modeling issues and present some initial results.

Theoretical gain‐optimization studies in CO2–N2 gasdynamic lasers. II. Results of parametric study

Based on a method presented in detail in a previous work by the authors, similar solutions have been obtained for the steady inviscid quasi‐one‐dimensional nonreacting flow in the supersonic nozzle of a CO2–N2 gasdynamic laser system, with either H2O or He as the catalyst. It has been demonstrated how these solutions could be used to optimize the small‐signal gain coefficient on a specified vibrational‐rotational transition. Results presented for a wide range of mixture compositions include optimum values for the small‐signal gain, area ratio, reservoir temperature, and a binary scaling parameter, which is the product of reservoir pressure and nozzle shape factor.

Synthesis of workspaces of planar manipulators with arbitrary topology using shape representation and simulated annealing

This paper presents a general methodology for the synthesis of the external boundary of the workspaces of a planar manipulator with arbitrary topology. Both the desired workspace and the manipulator workspaces are identified by their boundaries and are treated as simple closed polygons. The paper introduces the concept of best match configuration and shows that the corresponding transformation can be obtained by using the concept of shape normalization available in image processing literature. Introduction of the concept of shape in workspace synthesis allows highly accurate synthesis with fewer numbers of design variables. This paper uses a new global property based vector representation for the shape of the workspaces which is computationally efficient because six out of the seven elements of this vector are obtained as a by-product of the shape normalization procedure. The synthesis of workspaces is formulated as an optimization problem where the distance between the shape vector of the desired workspace and that of the workspace of the manipulator at hand are minimized by changing the dimensional parameters of the manipulator. In view of the irregular nature of the error manifold, the statistical optimization procedure of simulated annealing has been used. A number of worked-out examples illustrate the generality and efficiency of the present method. (C) 1998 Elsevier Science Ltd. All rights reserved.

A UNIFIED APPROACH FOR OPTIMIZATION OF SNAKUSCULES AND OVUSCULES

Automated image segmentation techniques are useful tools in biological image analysis and are an essential step in tracking applications. Typically, snakes or active contours are used for segmentation and they evolve under the influence of certain internal and external forces. Recently, a new class of shape-specific active contours have been introduced, which are known as Snakuscules and Ovuscules. These contours are based on a pair of concentric circles and ellipses as the shape templates, and the optimization is carried out by maximizing a contrast function between the outer and inner templates. In this paper, we present a unified approach to the formulation and optimization of Snakuscules and Ovuscules by considering a specific form of affine transformations acting on a pair of concentric circles. We show how the parameters of the affine transformation may be optimized for, to generate either Snakuscules or Ovuscules. Our approach allows for a unified formulation and relies only on generic regularization terms and not shape-specific regularization functions. We show how the calculations of the partial derivatives may be made efficient thanks to the Green's theorem. Results on synthesized as well as real data are presented.

Topology optimization-based design of a compliant aircraft compliant aircraft wing for morphing leading and trailing edges

In this paper, we present a methodology for designing a compliant aircraft wing, which can morph from a given airfoil shape to another given shape under the actuation of internal forces and can offer sufficient stiffness in both configurations under the respective aerodynamic loads. The least square error in displacements, Fourier descriptors, geometric moments, and moment invariants are studied to compare candidate shapes and to pose the optimization problem. Their relative merits and demerits are discussed in this paper. The `frame finite element ground structure' approach is used for topology optimization and the resulting solutions are converted to continuum solutions. The introduction of a notch-like feature is the key to the success of the design. It not only gives a good match for the target morphed shape for the leading and trailing edges but also minimizes the extension of the flexible skin that is to be put on the airfoil frame. Even though linear small-displacement elastic analysis is used in optimization, the obtained designs are analysed for large displacement behavior. The methodology developed here is not restricted to aircraft wings; it can be used to solve any shape-morphing requirement in flexible structures and compliant mechanisms.

Effect of Reflux Time on Nanoparticle Shape

In the present work, Pt nanoparticles were produced from a reaction mixture containing a trace amount of cobalt carbonyl salt acting as a shape inducer. Nanoparticle shape evolution during reaction mixture reflux was monitored by characterizing particles extracted from the reaction mixture at different times. It was observed that 5 min of reflux produced spherical nanoparticles, 30 min of reflux produced cube shaped nanoparticles, and 60 min of reflux produced truncated octahedron morphology nanoparticles. It is illustrated that during nanoparticle synthesis the reflux process can provide energy needed for shape transformation from a metastable cube morphology to a truncated octahedron morphology which is thermodynamically the most stable geometry for fcc crystals. An optimization of the reaction reflux is thus needed for isolating metastable shapes.

Reservoir Operation for Hydropower Optimization: A Chance-Constrained Approach

This paper presents a chance-constrained linear programming formulation for reservoir operation of a multipurpose reservoir. The release policy is defined by a chance constraint that the probability of irrigation release in any period equalling or exceeding the irrigation demand is at least equal to a specified value P (called reliability level). The model determines the maximum annual hydropower produced while meeting the irrigation demand at a specified reliability level. The model considers variation in reservoir water level elevation and also the operating range within which the turbine operates. A linear approximation for nonlinear power production function is assumed and the solution obtained within a specified tolerance limit. The inflow into the reservoir is considered random. The chance constraint is converted into its deterministic equivalent using a linear decision rule and inflow probability distribution. The model application is demonstrated through a case study.

Transition from disc to rod-like shape of 16-3-16 dimeric micelles in aqueous solutions

Small-angle neutron scattering (SANS) measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(3)-N+ (CH3)(2)C16H33 2Br(-) dimeric surfactant, referred to as 16-3-16, at different concentrations and temperatures, are reported. It is seen that micelles are disc-like for concentrations C = 2.5 and 10 mM at temperature T = 30 degrees C. At low concentration C = 0.5 mM micelles are rod-like. Similarly, there is a disc to rod-like transition of micelles on increasing the temperature. For C = 2.5 mM, micelles are rod-like at T = 45 and 70 degrees C.

Fuzzy optimization model for water quality management of a river system - Closure

A fuzzy waste-load allocation model, FWLAM, is developed for water quality management of a river system using fuzzy multiple-objective optimization. An important feature of this model is its capability to incorporate the aspirations and conflicting objectives of the pollution control agency and dischargers. The vagueness associated with specifying the water quality criteria and fraction removal levels is modeled in a fuzzy framework. The goals related to the pollution control agency and dischargers are expressed as fuzzy sets. The membership functions of these fuzzy sets are considered to represent the variation of satisfaction levels of the pollution control agency and dischargers in attaining their respective goals. Two formulations—namely, the MAX-MIN and MAX-BIAS formulations—are proposed for FWLAM. The MAX-MIN formulation maximizes the minimum satisfaction level in the system. The MAX-BIAS formulation maximizes a bias measure, giving a solution that favors the dischargers. Maximization of the bias measure attempts to keep the satisfaction levels of the dischargers away from the minimum satisfaction level and that of the pollution control agency close to the minimum satisfaction level. Most of the conventional water quality management models use waste treatment cost curves that are uncertain and nonlinear. Unlike such models, FWLAM avoids the use of cost curves. Further, the model provides the flexibility for the pollution control agency and dischargers to specify their aspirations independently.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz,, queue weight (omega(q)), marking probability (max(p)), minimum threshold (min(th)) and maximum threshold (max(th)) is not analytically availa ble. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its Solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known, but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based oil certain modified second-order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of Our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.