Showing papers on "Minimum weight published in 1995"

Improved approximation algorithms for uniform connectivity problems

Abstract: The problem of finding minimum weight spanning subgraphs with a given connectivity requirement is considered. The problem is NP-hard when the connectivity requirement is greater than one. Polynomial time approximation algorithms for various weighted and unweighed connectivity problems are given. The following results are presented:

Automatic Optimal Design of Tall Steel Building Frameworks

Abstract: Due to the complex nature of a modern tall building consisting of thousands of structural members, the traditional trial-and-error design method is generally highly iterative and very time-consuming. This paper presents an automatic resizing technique for the optimal design of tall steel building frameworks. Specifically, a computer-based method is developed for the minimum weight design of lateral load-resisting steel frameworks subject to multiple interstory drift and member strength and sizing constraints in accordance with building code and fabrication requirements. The most economical standard steel sections to use for the structural members are automatically selected from commercially available standard section databases. The design-optimization problem is first formulated and expressed in an explicit form and is then solved by a rigorously derived optimality criteria (OC) algorithm. A full-scale 50-story three-dimensional (3D) asymmetrical building framework example is presented to illustrate the e...

Computing a minimum-weight k-link path in graphs with the concave Monge property

Abstract: LetGbe a weighted, complete, directed acyclic graph whose edge weights obey the concave Monge condition. We give an efficient algorithm for finding the minimum weightk-link path between a given pair of vertices for any givenk. The algorithm runs in time, fork=?(logn). Our algorithm can be applied to get efficient solutions for the following problems, improving on previous results: (1) computing length-limited Huffman codes, (2) computing optimal discrete quantization, (3) computing maximumk-cliques of an interval graph, (4) finding the largestk-gon contained in a given convex polygon, (5) finding the smallestk-gon that is the intersection ofkhalf-planes out ofnhalf-planes defining a convexn-gon.

Merits and limitations of optimality criteria method for structural optimization

Abstract: The merits and limitations of the Optimality Criteria (OC) method for the minimum weight design of structures subjected to multiple load conditions under stress, displacement and frequency constraints were investigated by examining several numerical examples. The examples were solved utilizing the OC design code that was developed for this purpose at the NASA Lewis Research Center. This OC code incorporates OC methods available in the literature with generalizations for stress constraints, fully utilized design concepts, and hybrid methods that combine both techniques. It includes multiple choices for Lagrange multiplier and design variable update methods, design strategies for several constraint types, variable linking, displacement and integrated force method analysers, and analytical and numerical sensitivities. On the basis of the examples solved, the optimality criteria for general application were found to be satisfactory for problems with few active constraints or with small numbers of design variables. However, the OC method without stress constraints converged to optimum even for large structural systems. For problems with large numbers of behaviour constraints and design variables, the method appears to follow a subset of active constraints that can result in a heavier design. The computational efficiency of OC methods appears to be similar to some mathematical programming techniques.

Some aspects of truss topology optimization

Abstract: The present paper studies some aspects of formulations of truss topology optimization problems. The ground structure approach-based formulations of three types of truss topology optimization problems, namely the problems of minimum weight design for a given compliance, of minimum weight design with stress constraints and of minimum weight design with stress constraints and local buckling constraints are examined. The common difficulties with the formulations of the three problems are discussed. Since the continuity of the constraint or/and objective function is an important factor for the determination of the mathematical structure of optimization problems, the issue of the continuity of stress, displacement and compliance functions in terms of the cross-sectional areas at zero area is studied. It is shown that the bar stress function has discontinuity at zero crosssectional area, and the structural displacement and compliance are continuous functions of the cross-sectional area. Based on the discontinuity of the stress function we point out the features of the feasible domain and global optimum for optimization problems with stress and/or local buckling constraints, and conclude that they are mathematical programming with discontinuous constraint functions and that they are essentially discrete optimization problems. The difference between topology optimization with global constraints such as structural compliance and that with local constraints on stress or/and local buckling is notable and has important consequences for the solution approach.

Minimum weight design of symmetric angle-ply laminates under multiple uncertain loads

Abstract: An angle-ply laminated plate is optimized with the objective of minimizing the weight of the plate taking into account uncertainties in the multiple transverse loads. The weight is proportional to the laminate thickness which is minimized subject to deflection and buckling constraints under the least favourable loading with the ply angles taken as design variables. The convex modelling approach is employed to analyse the uncertain loading with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirements that these variations are bounded inL2 norm and represented by a finite number of eigenmodes. The effect of uncertainty on the optimal design is investigated quantitatively. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.

An algorithm for optimization of non-linear shell structures

Abstract: An algorithm for optimal design of non-linear shell structures is presented. The algorithm uses numerical optimization techniques and nonlinear finite element analysis to find a minimum weight structure subject to equilibrium conditions, stability constraints and displacement constraints. A barrier transformation is used to treat an apparent non-smoothness arising from posing the stability constraints in terms of the eigenvalues of the Hessian of the potential energy of the structure. A sequential quadratic programming strategy is used to solve the resulting non-linear optimization problem. Matrix sparsity in the constraint Jacobian is exploited because of the large number of variables. The usefulness of the proposed algorithm is demonstrated by minimizing the weight of a number of stiffened thin shell structures.

The existence of extremal self-dual [50,25,10] codes and quasi-symmetric 2-(49,9,6) designs

Abstract: All extremal binary self-dual [50,25,10] codes with an automorphism of order 7 are enumerated. Up to equivalence, there are four such codes, three with full automorphism group of order 21, and one code with full group of order 7. The minimum weight codewords yield quasi-symmetric 2-(49,9,6) designs.

Performance surfaces of minimum effort estimators and controllers

Abstract: The performance surfaces of two classes of minimum effort adaptive filter are studied. Eigenvalue spreads of the cost functions of minimum weight vector norm and minimum output variance algorithms are examined for both estimation and feedforward control applications. Results support the widespread practical use of the "leaky LMS" algorithm. >

Newton's identities for minimum codewords of a family of alternant codes

Abstract: We are able to define minimum weight codewords of some alternant codes in terms of solutions to algebraic equations. Particular attention is given to the case of the classical Goppa codes. Grobner bases are used to solve the system of algebraic equations.

Design of FIR digital filters with minimum weight representation

Abstract: This paper proposes an algorithm for the iterative design of FIR digital filters whose coefficients have minimum weight representation. The total number of nonzero bits is limited. In each iteration the coefficient vector is up-dated so that some sets of the amplitude ripples become smaller. The direction is found by solving linear simultaneous equations. The method evaluates the normalized peak ripples in the minimax sense. Several examples show that the proposed method yields superior filter responses compared to the conventional methods.

Displacement based multilevel structural optimization

Abstract: Multidisciplinary design optimization (MDO) is expected to play a major role in the competitive transportation industries of tomorrow, i.e., in the design of aircraft and spacecraft, of high speed trains, boats, and automobiles. All of these vehicles require maximum performance at minimum weight to keep fuel consumption low and conserve resources. Here, MDO can deliver mathematically based design tools to create systems with optimum performance subject to the constraints of disciplines such as structures, aerodynamics, controls, etc. Although some applications of MDO are beginning to surface, the key to a widespread use of this technology lies in the improvement of its efficiency. This aspect is investigated here for the MDO subset of structural optimization, i.e., for the weight minimization of a given structure under size, strength, and displacement constraints. Specifically, finite element based multilevel optimization of structures (here, statically indeterminate trusses and beams for proof of concept) is performed. In the system level optimization, the design variables are the coefficients of assumed displacement functions, and the load unbalance resulting from the solution of the stiffness equations is minimized. Constraints are placed on the deflection amplitudes and the weight of the structure. In the subsystems level optimizations, the weight of each element is minimized under the action of stress constraints, with the cross sectional dimensions as design variables. This approach is expected to prove very efficient, especially for complex structures, since the design task is broken down into a large number of small and efficiently handled subtasks, each with only a small number of variables. This partitioning will also allow for the use of parallel computing, first, by sending the system and subsystems level computations to two different processors, ultimately, by performing all subsystems level optimizations in a massively parallel manner on separate processors. It is expected that the subsystems level optimizations can be further improved through the use of controlled growth, a method which reduces an optimization to a more efficient analysis with only a slight degradation in accuracy. The efficiency of all proposed techniques is being evaluated relative to the performance of the standard single level optimization approach where the complete structure is weight minimized under the action of all given constraints by one processor and to the performance of simultaneous analysis and design which combines analysis and optimization into a single step. It is expected that the present approach can be expanded to include additional structural constraints (buckling, free and forced vibration, etc.) or other disciplines (passive and active controls, aerodynamics, etc.) for true MDO.

Minimum weight design of sandwich and laminated composite structures

Abstract: The illustrative examples presented above show that the proposed optimum design method based on planning of experiments is an efficient method for the minimum weight design of sandwich and laminated composite plates. Vibration and damping constraints can be modeled using simple mathematical expressions. These expressions are obtained using the finite element solution in the experiment points. Reference points in the search domain are determined from plans of experiment. The advantage of the proposed method is its minimum computational effort for repeated finite element solutions. The major advantage of the method is the possibility of using the data not only from the computer solution, but also the data obtained experimentally in the reference points. In this case, simple mathematical models represent both theoretical and experimental data.

Optimum Design of Truss Structure by Genetic Algorithm with Variable Mutation Ratio.

Abstract: The metastrategy to solve discrete optimization problems is proposed and discussed. The proposed solution procedure is based on the genetic algorithm, GA, in which the idea of simulated annealing, SA is introduced effectively. The procedure has a distinctive feature that the number of generations can be reduced by introducing the idea of the variable mutation ratio in GA based on the annealing schedule of temperature is SA. Applicability is examined with the shape of the optimization problem of the truss structure subjected to three kinds of constraints on homologous displacement, the first eigenfrequency and minimum weight.

Optimum structural design and robust active control using singular value constraints

Abstract: This paper introduces a methodology for simultaneously designing a minimum weight structure and robust active controls to reduce vibrations in an aircraft structure due to external disturbances. The design problem is posed as a mathematical optimization problem with the principal objective function being the weight of the structure. The robust control design is achieved by specifying appropriate constraints on singular values of the closed-loop transfer matrices. The control approach selected for this purpose is based on designing a dynamic compensator that simultaneously minimizes the upper bound of a quadratic performance index H2 and the H∞ norm of a disturbance transfer function of a multi-input/multi-output system. The controller can tolerate both real parameter uncertainty in the structural frequencies and damping, and unmodelled dynamics. The design variables are the crosspsectional areas of the structure and the parameters used in the design of a control system. The method was applied to three structures idealized with membrane elements, shear panels and bar elements with embedded actuators and sensors simulating an active flexible aircraft wing.

Minimum weight design of pressure vessel with constraints on stiffness and strength

Abstract: A new design method of composite pressure vessel with constraints on stiffness and strength is proposed in this paper. A netting analysis approach is used to develop an optimization procedure. Filament wound pressure vessels are assumed to have adjacent ({+-}{phi}) angle lay ups. It is proved that laminate of two layer orientations has minimum weight. The additional constraint on strength of the first layer forming vessel`s dome is used. Minimum lamination weight is determined from the condition of active execution of two constraints. Two examples are given to obtain optimum layer orientations, thicknesses and materials. Pressure vessel without change in cylindrical diameter or length can be made. For comparison purpose, calculations of stresses are done in orthotropic material using classical lamination theory. Matrix degrades at 30 to 50% of ultimate load without fiber failure. It is allowable because elastomeric liners are used to prevent leakage due to matrix cracking.

How to Draw Outerplanar Minimum Weight Triangulations

Abstract: In this paper we consider the problem of characterizing those graphs that can be drawn as minimum weight triangulations and answer the question for maximal outerplanar graphs. We provide a complete characterization of minimum weight triangulations of regular polygons by studying the combinatorial properties of their dual trees. We exploit this characterization to devise a linear time (real RAM) algorithm that receives as input a maximal outerplanar graph G and produces as output a straight-line drawing of G that is a minimum weight triangulation of the set of points representing the vertices of G.

An efficiency study of the simultaneous analysis and design of structures

Abstract: The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never factored during the optimization retaining its original sparsity. One of SAND's disadvantages is the increase in the number of design variables and in the associated number of constraint gradient evaluations. If SAND is to be an acceptable player in the optimization field, it is essential to investigate the efficiency of the method and to present a possible cure for any inherent deficiencies.

A new approach to optimum flexible link design

Abstract: A new method of computing optimum mass and rigidity distributions for composite flexible manipulators with tip loads is presented. The design problem is classified as minimum weight design or maximum speed design with appropriate constraints. Multiple tip load designs are considered, as well as practical issues related to link construction.

Minimum Weight Design for Bridge Girder using Approximation based Optimization Method

Abstract: Weight minimization for the steel bridge girders using an approximation based optimization technique is presented. To accomplish this, an optimization oriented finite element program is used to achieve continuous weight reduction until the optimum is reached. To reduce computational cost, approximation techniques are adopted during the optimization process. Constraint deletion as well as intermediate design variables and responses are also used for higher qualitv of approximations and for a better convergence rate. Both the reliability and the effectiveness of the underlying optimization method are reviewed.