Showing papers on "Shape optimization published in 1975"
TL;DR: The optimal control problem is converted to a parameter optimization problem by chosing a form for the control which contains unknown parameters, and a gradient method is used to obtain approximate values for the parameters and Lagrange multipliers associated with the constraints.
Abstract: The purpose of this paper is to demonstrate the applicability of parameter optimization methods to the computation of optimal aircraft trajectories. First, the optimal control problem is converted to a parameter optimization problem by chosing a form for the control which contains unknown parameters. Then, a gradient method is used to obtain approximate values for the parameters and Lagrange multipliers associated with the constraints. Finally, a second-order method is used to obtain the converged trajectory. The test problem is that of finding the angle of attack history which minimizes the time to climb of a supersonic aircraft operating at full power. The angle of attack history is approximated by a fifth-order series of Chebyshev polynomials. An inequality constraint prevents the aircraft from descending below the takeoff altitude, and this constraint is handled in both the penalty function manner and in the hard constraint manner. The latter produces a lower climb time because all the parameters can be used for optimization; also, the shape of the trajectory in the altitudeMach number plane closely resembles that obtained from an energy-state analysis, with the transitions occurring at load factors ranging between 0.5 and 1.8.
29 citations
TL;DR: In this paper, a shell-of-revolt model is proposed to evaluate the potential savings due to numerical optimization, and the resulting nonlinear programming problem is solved by iterated linear programming.
10 citations
TL;DR: The problem of multiple-objective optimization for the environment development system is formulated and the so-called Pareto-optimal solution set is formulated, related in a one-to-one manner to a family of auxiliary scalar index problems.
Abstract: This paper deals with multiple-objective optimization problems for the environment development system. The model of the environment development system, which was introduced by Kulikowski, is described by a system of non linear differential equations which include interconnected n exogenous and m endogenous controlled factors or processes. The problem of multiple-objective optimization for the environment development system is formulated. A main difficulty of multiple-objective optimization is that it is no longer clear what one means by an optimal solution. A possible remedy for this situation is to refine the concept of optimal solution by introducing the so-called Pareto-optimal solution set. Then multiple-objective optimization problem boils down to determining the set of Pareto-optimal solutions. The Pareto-optimal solution set is related in a one-to-one manner to a family of auxiliary scalar index problems. For an unconstrained multiple-objective optimization problem for the environment deve...
7 citations
1 Jan 1975
TL;DR: In this article, the shape optimization of a perfectly plastic structure with flow-law constraints is formulated as a convex yield surface optimization problem, where the structure must carry the given external forces and its own weight.
Abstract: Shape optimization of plastic structures, or limit design in the absence of a given layout, is a problem which can be formulated as follows. The data are: the convex yield surface of a perfectly plastic material with associated flow-law (i.e. obeying “normality” [1]), some surfaces to which the structure may be fixed; an available space region (possibly with holes or cavities) where it must be contained; some other surfaces on which certain load distributions are assigned and which must form part of the boundary of the structure. The behaviour constraint is that the structure carry the given external forces and its own weight. The structure with the least material consumption (minimum volume) is sought.
6 citations
TL;DR: A method is described for the optimization of nonlinear dc circuits to treat the network equations as equality constraints on the design parameters, and a performance index is defined to measure the difference between the desired and the actual specifications.
Abstract: A method is described for the optimization of nonlinear dc circuits. A performance index is defined to measure the difference. between the desired and the actual specifications. The novel approach taken here is to treat the network equations as equality constraints on the design parameters. The constrained optimization problem is then converted to an unconstrained one by a penalty function technique. A straightforward method is given for computing all the gradients needed during the optimization, given only the topology of the network and the branch relationships. This makes the algorithm easily amenable to a package program.
3 citations
3 citations
8 Sep 1975
TL;DR: A numerical method for the solution of structural optimization problems involving ordinary differential equations is presented for a simple situation where the constraint is of an aeroelastic nature, and its extension to two dimensional structures is outlined.
Abstract: A numerical method for the solution of structural optimization problems involving ordinary differential equations is presented for a simple situation where the constraint is of an aeroelastic nature. The method is adapted from optimal control theory and has proven successful in a number of structural optimization problems. Its extension to two dimensional structures is outlined ; limitation to situations involving plates, however, is emphasized. It is assumed that the instability exhibited by the optimality condition is related to the fact that plates cannot in general achieve global extrema. Suggestions for further research in this area are presented.