Showing papers in "Engineering Optimization in 1981"
TL;DR: In this paper, a practical and efficient optimization method for the rational design of large, highly constrained complex systems is presented, where the design of such systems is iterative and requires the repeated formulation and solution of an analysis model, followed by the formulation and solutions of a redesign model.
Abstract: A practical and efficient optimization method for the rational design of large, highly constrained complex systems is presented. The design of such systems is iterative and requires the repeated formulation and solution of an analysis model, followed by the formulation and solution of a redesign model. The latter constitutes an optimization problem. The versatility and efficiency of the method for solving the optimization problem is of fundamental importance for a successful implementation of any rational design procedure. In this paper, a method is presented for solving optimization problems formulated in terms of continuous design variables. The objective function may be linear or non-linear, single or multiple. The constraints may be any mix of linear or non-linear functions, and these may be any mix of inequalities and equalities. These features permit the solution of a wide spectrum of optimization problems, ranging from the standard linear and non-linear problems to a non-linear problem with multipl...
56 citations
TL;DR: In this paper, the minimum weight design of structures with stress and displacement constraints was studied, and various algorithms based on an optimality criterion were derived with different degrees of optimality.
Abstract: The paper deals with the minimum weight design of structures with stress and displacement constraints. The various algorithms based on an optimality criterion are derived with different degrees of ...
50 citations
TL;DR: In this paper, the use of a modified nonlinear simplex method for constrained engineering optimization problems is discussed, in which some or all of the variables can only take on discrete values.
Abstract: This paper discusses the use of a modified nonlinear simplex method for constrained engineering optimization problems in which some or all of the variables can only take on discrete values. The objective function and constraints need not be analytic expressions; it is only necessary that their values be computable. The modifications to the nonlinear simplex method include the incorporation of unidimensional search, new acceleration and regeneration methods, and the exploration of decomposition strategies. The algorithm has been successfully tested using problems selected to represent a variety of engineering design applications.
16 citations
TL;DR: A semi-analytical approach to the discrete optimization of large space-truss structures as a cost (weight) minimization subject to constraints both on stresses and displacements.
Abstract: The paper presents a semi-analytical approach to the discrete optimization of large space-truss structures. The optimization problem is stated as a cost (weight) minimization subject to constraints both on stresses and displacements. Some of the variables such as the cross-sectional areas of bars are chosen from a discrete set (catalogue) of available sections. The mined nonlinear programming problem is transformed to discrete nonlinear programming using the Galerkin procedure in solving the partial difference equations which describe displacements of nodes of the structure. Finally, introducing Boolean variables the problem is solved using algorithms of logical programming. Numerical results are presented for a “Unistrut” type space-truss structure.
15 citations
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
TL;DR: In this paper, a hybrid method of formulating structural synthesis problems is presented, which casts the conventional mathematical programming formulation in a reduced design space formed by base vectors that can be generated from various sources.
Abstract: A hybrid method of formulating structural synthesis problems is presented. The method casts the conventional mathematical programming formulation in a reduced design space formed by base vectors that can be generated from various sources. In this study each base vector is developed from a typical behavioural aspect of the structural system such as stress or displacement or buckling. The formulation also explores two types of base vectors; direct and reciprocal. The performance and efficiency of this method are studied through some well known example problems.
11 citations
TL;DR: In this paper, a new concept for the treatment of large numbers of stress and displacement constraints in finite dimensional optimal structural design is presented, which replaces a large number of structural constraints by a small number of equivalent functional constraints.
Abstract: The paper presents a new concept for the treatment of large numbers of stress and displacement constraints in finite dimensional optimal structural design. The idea is to replace a large number of stress and displacement constraints by a small number of equivalent functional constraints. The genesis of this concept is the distributed parameter and transient response structural design formulations where it has been used quite effectively. The major advantage of this constraint formulation is that design sensitivity vectors need to be calculated for only the reduced number of equivalent stress and displacement constraints. Thus, there is substantial computational advantage with the new formulation. Implications of the formulation are studied and several example problems are presented to show its potential in practical design applications.
4 citations
TL;DR: In this paper, a rectilinearly anisotropic and hollow bar is optimized with respect to the shape of its transverse cross-section so as to maximize its torsional stiffness for a given cross-sectional area.
Abstract: A rectilinearly anisotropic and hollow bar is optimized with respect to the shape of its transverse cross-section so as to maximize its torsional stiffness for a given cross-sectional area. Two cases in respect of the wall thickness of the bar are considered. in one case, both inner and outer boundaries of a bar of arbitrary wall thickness are taken as design variables. In the other, the inner boundary of a thin-walled bar is specified to be an ellipse with given semi-axes, and the outer boundary of the bar is optimally determined. The optimization problem is formulated as an isoperimetric variational problem using the relation between the energy of the bar and the objective functional. The necessary condition for optimality, which is derived using the method of Lagrange multipliers, provides an additional condition on a free boundary. The cross-sectional shapes and the efficiencies of the optimal bars are given in graphical form for various problem parameters.
4 citations
TL;DR: In this article, the problem of minimizing the mass of an elastic bar whose Euler buckling load and fundamental frequency of transverse vibrations are larger than certain prescribed values is solved, and the minimum weight design under inequality constraints on two different types of eigenvalues differs only slightly from the designs for individual inequality constraints, but is significantly economical in comparison with a prismatic bar.
Abstract: The problem is solved of minimizing the mass of an elastic bar whose Euler buckling load and fundamental frequency of transverse vibrations are larger than certain prescribed values. The bar has a solid cross section and is to perform natural vibrations or act as a column at different times during its design life. It is shown that the minimum weight design under inequality constraints on two different types of eigenvalues differs only slightly from the designs for individual inequality constraints, but that it is significantly economical in comparison with a prismatic bar.
2 citations