Showing papers on "Minimum weight published in 1987"

Space frame optimization subject to frequency constraints

Abstract: An efficient structural optimization methodology is presented for the design of minimum weight space frames subject to multiple natural frequency constraints. A powerful class of generalized hybrid c onstraint approximations which require o nly the first order constraint function d erivatives have been developed to overcome inherent nonlinearity of the frequency constraint. The generalized hybrid constraint functions are shown to be relatively conservative, separable and convex in the region bounded by the move limits based on the formula described in this paper. The optimization methodology is implemented in an automated structural optimization system which has been applied to solve a variety of space frame optimization problems. N umerical results obtained for three example problems indicate that the o ptimization methodology requires fewer than 10 complete normal modes analyses to generate a near optimum solution.

A cutting plane algorithm for minimum perfect 2-matchings

Abstract: We describe an implementation of a cutting plane algorithm for the minimum weight perfect 2-matching problem. This algorithm is based on Edmonds' complete description of the perfect 2-matching polytope and uses the simplex algorithm for solving the LP-relaxations coming up. Cutting planes are determined by fast heuristics, or, if these fail, by an efficient implementation of the Padberg-Rao procedure, specialized for 2-matching constraints. With this algorithm 2-matching problems on complete graphs with up to 1000 nodes (i.e., 499,500 variables) have been solved in less than 1 hour CPU time on a medium speed computer.

Minimum-weight plate design via Prager's layout theory

Abstract: During the last decade of his immensely creative life, Professor William Prager’s research was directed at two central objectives, the derivation of a comprehensive set of static-kinematic optimality criteria and the development of an optimal layout theory. As the late Professor Prager’s closest former associate, the first author will review briefly these fields in the first part of this memorial lecture.

Pressure vessel with a non-circular axial cross-section

Abstract: The present invention provides a pressure vessel having a non-circular axial cross-section, and a method for its construction, which achieves improved reliability, minimum weight, minimum cost, and maximum aerodynamic smoothness. The above characteristics are achieved through the use of honeycomb cores whose thickness varies in accordance with the distribution of bending moments created by the non-circular axial cross-sectional configuration under internal pressure. The present invention also provides a pressure vessel having a non-circular axial cross-section which may be especially designed to meet preestablished design criteria for optimal weight, volume, and strength.

Preliminary structural design of composite main rotor blades for minimum weight

Abstract: A methodology is developed to perform minimum weight structural design for composite or metallic main rotor blades subject to aerodynamic performance, material strength, autorotation, and frequency constraints. The constraints and load cases are developed such that the final preliminary rotor design will satisfy U.S. Army military specifications, as well as take advantage of the versatility of composite materials. A minimum weight design is first developed subject to satisfying the aerodynamic performance, strength, and autorotation constraints for all static load cases. The minimum weight design is then dynamically tuned to avoid resonant frequencies occurring at the design rotor speed. With this methodology, three rotor blade designs were developed based on the geometry of the UH-60A Black Hawk titanium-spar rotor blade. The first design is of a single titanium-spar cross section, which is compared with the UH-60A Black Hawk rotor blade. The second and third designs use single and multiple graphite/epoxy-spar cross sections. These are compared with the titanium-spar design to demonstrate weight savings from use of this design methodology in conjunction with advanced composite materials.

Minimum weight and optimal control design of space structures

Abstract: Algorithms are presented to design a minimum weight structure and to improve the dynamic response of a closed-loop control system. Constraints are imposed either on the structural response quantities or on the complex eigenvalue distribution of the closed-loop system. Use of the algorithms is illustrated by solving different problems.

Multilevel Optimization Procedure of Composite Structure

Abstract: We present a multilevel optimization procedure for minimum weight design of composite structures. The optimization process is divided into two levels: system level and component level. In system level the thicknesses of laminated composite plates represent the design variables. The well-known optimality criterion method based on the Kuhn-Tucker condition is used to modify the design variables. The detail design of laminated plates, i.e. to determine the optimal ply thicknesses, is handled in component level In component level, keeping the thickness of laminated composite plates and the nodal displacements invariant, the ply thicknesses are adjusted according to the strain energy possessed by each ply. As an illustrative example, a cantilever composite beam, which is subjected to several load conditions and multiple constraints, is studied. All the five examples given in this chapter present very satisfactory results. In general the optimal design can be obtained after 3–5 iterations.

A basis change strategy for the reduced gradient method and the optimum design of large structures

Abstract: This paper proposes a basis change strategy within the reduced gradient method for optimization under linear constraints. It ensures a non-singular basis matrix at every iteration. The same strategy can reliably be used within the generalized reduced gradient method for optimization under non-linear constraints. This method is applied to the minimum weight design of large structures under displacement and stress constraints, exploiting the sparsity of the constraint Jacobian matrix.

Some contributions to optimal design using explicit behaviour models

Abstract: The design of a strictly modular and flexible system for structural optimization is discussed. OPTIMA 2.0 uses advanced design oriented concepts and is provided for linear and nonlinear structural behaviour. For shape optimal design it is attempted to utilize the simple and efficient Lagrangian interpolation schemes and to restrict spline interpolation to the movable boundaries. A simple interpolation scheme for sizing variables allows the simultaneous handling of sizing and shaping. Some approximation models for the explicit approximation of implicit constraint functions are discussed and evaluated. The realm of this models is extended by introducing an exponential hybrid scheme. Applications are presented in shape optimal design. Objectives are minimum weight as well as minimum stress. Some special aspects of the minimum stress problem are discussed.

Shape optimization and minimum weight limit design of arches

Abstract: The paper is concerned with the optimization of arches, using classical beam finite elements, for the minimum elastic displacements and the minimum weight designs under ultimate loading conditions. The concept of separate but dependent design spaces for node coordinates and member plastic capacities is introduced. The shape optimization problem, whereby a norm of the elastic displacement vector is minimized, is formulated in the space of node coordinate variables. Then the minimum weight limit design problem in the space of member plastic capacities is considered using the static theorem of limit analysis. An iterative procedure alternating these two approaches is presented in the paper. The nonlinear unconstrained optimization and linear programming techniques are used to solve the corresponding numerical problems. The proposed method is illustrated by numerical examples.

Nearly Optimal Heuristics for Binary Search Trees with Geometric Generalizations (Extended Abstract)

Abstract: Heuristics for optimal binary search trees with zero key access probabilities (with applications eg. in code theory and in point location) are considered. It is shown that for an arbitrarily small positive constant ∈, there exists a linear-time heuristic for such search trees, producing solutions within the factor of 1+∈ from the optimum. Also, by using an interesting amortization argument, we give a simple and practical, linear-time implementation of a known greedy heuristic for such trees. The above results are obtained in a more general setting, namely in the context of minimum length triangulations of so-called semi-circular polygons. They are carried over to binary search trees by proving a duality between minimum weight partitions of infinitely-flat semi-circular polygons into m-gons and optimal (m−1)-way search trees. Our results can be extended to the case with non-zero key access probabilities, and to multi-way search trees.

Large-scale Structural Analysis/Synthesis of Composite Structures by Finite Elements

Abstract: This chapter presents work done toward the development of an efficient method for the structural analysis/synthesis of laminate fibre composite structures by using finite element techniques. An automated procedure is presented for designing minimum weight structures subject to strength and elastic stability constraints. In order to efficiently solve the optimization problem a variety of state-of-the-art techniques are used here. These include design variable linking, constraint deletion, the use of reciprocal variables and formal approximation techniques. Analytical expressions are employed for evaluating constraint gradients, which are calculated for active constraints. Eigenvalue buckling analysis and hybrid constraint approximations for laminate plates are introduced in this chapter. Using this procedure and efficient algorithm in process optimization, the number of actual finite element analyses is kept to a minimum. Several example problems are given to demonstrate that the method presented offers an efficient and practical optimum design procedure for different problems of aircraft structures treated.

Least Weight Design of Cables

Abstract: In this note, the least weight design of cables under self-weight and uniformly distributed load is considered. A simple method for solving this optimization problem almost analytically is given.