# Optimum design of lattice portal frames

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01 Jan 1936

8,149 citations

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TL;DR: The gradient projection method was originally presented to the American Mathematical Society for solving linear programming problems by Dantzig et al. as discussed by the authors, and has been applied to nonlinear programming problems as well.

Abstract: more constraints or equations, with either a linear or nonlinear objective function. This distinction is made primarily on the basis of the difficulty of solving these two types of nonlinear problems. The first type is the less difficult of the two, and in this, Part I of the paper, it is shown how it is solved by the gradient projection method. It should be noted that since a linear objective function is a special case of a nonlinear objective function, the gradient projection method will also solve a linear programming problem. In Part II of the paper [16], the extension of the gradient projection method to the more difficult problem of nonlinear constraints and equations will be described. The basic paper on linear programming is the paper by Dantzig [5] in which the simplex method for solving the linear programming problem is presented. The nonlinear programming problem is formulated and a necessary and sufficient condition for a constrained maximum is given in terms of an equivalent saddle value problem in the paper by Kuhn and Tucker [10]. Further developments motivated by this paper, including a computational procedure, have been published recently [1]. The gradient projection method was originally presented to the American Mathematical Society

1,105 citations

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TL;DR: Methods of automated design and optimization of statically indeterminate frames by means of nonlinear programming are reviewed, with particular emphasis on the sequential unconstrained minimization technique (SUMT) employed by the writers.

Abstract: Methods of automated design and optimization of statically indeterminate frames by means of nonlinear programming are reviewed, with particular emphasis on the sequential unconstrained minimization technique (SUMT) employed by the writers. In this approach the proper choice of initial response factor is of particular importance in cases with several local optima. An extended penalty function technique allows infeasible initial designs. When a computer with 60 bits word length is used, gradient directions may be obtained with sufficient accuracy employing a single step finite difference scheme. Efficient interpolation and reanalysis techniques are incorporated in order to reduce required computer time. Considerable reduction in numerical effort is also obtained employing a scheme of suboptimization. The developed algorithm performs well for several complex test examples including problems for which the feasible region is nonconvex, and local optima are present.

73 citations

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TL;DR: In this article, the optimization of structural design is formulated as a problem in nonlinear mathematical programming, i.e., a problem of selecting n design variables subject to m > n constraints such that an objective function is minimized.

Abstract: Optimum structural design is formulated as a problem in nonlinear mathematical programming, i.e., a problem of selecting n design variables subject to m > n constraints such that an objective function is minimized. The design variables correspond to the geometrical or mechanical properties of the structural system, the constraints correspond to safety requirements such as limitations on stresses and deflections, and the objective function corresponds to weight or cost. The gradient projection method of nonlinear programming is described and an algorithm is presented for high-speed computation. Examples are presented in which the method is used to obtain least-weight designs of typical indeterminate rigid frames made of standard steel wide flange shapes. The examples illustrate that the programming approach affords a sound mathematical basis on which to develop rational methods of structural design.

55 citations

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TL;DR: In this article, a formulation for the nonlinear optimization of reinforced concrete frames based on inelastic analysis is presented and four selected frames are optimized using the program and the results are presented.

Abstract: The paper presents a formulation for the nonlinear optimization of reinforced concrete frames based on inelastic analysis. A computer program is developed for this formulation and is described with the aid of flow-charts. Important computational steps of the optimization procedure are also given. Four selected frames are optimized using the program and the results are presented. It is concluded that the formulation leads to minimum cost designs of reinforced concrete frames through realistic analysis.

15 citations

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