Showing papers on "Minimum weight published in 1969"

Optimization of Truss Geometry

Abstract: The effect of multiple (independent) load conditions on the optimum geometrical configurations of planar trusses is investigated. A general configuration is established by considering all truss components connecting the nodal points of a rectangular gridwork of possible joint locations. This general design is modified through use of a steepest descent nonlinear programming algorithm. Unnecessary components are dropped from the configuration until a truss of minimum weight is obtained. Modifications of joint locations through changes in the nodal pattern are also considered. For the particular design examples investigated, statically determinate trusses were found to exist which are lighter in weight than indeterminate trusses.

Minimum weight design of structures with application to elastic grillages

Abstract: A review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress-ratio, linear programming-cutting plane and usable-feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non-convex stress constraints and numerous relative optima. Instances are given of non-fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design problems.

Energy distribution in an optimum structural design

Abstract: : An automated procedure is presented for minimum weight design of structures. It is an iterative procedure in which the design for the next cycle is determined by the study of the strain energy distribution in the present cycle. The displacement method of analysis is used in developing the method. Other methods of analysis which have the capability to determine the strain energy in various parts of the structure should be applicable. Designs in the presence of stress constraints and stress and displacement constraints are also considered. Where there are only stress constraints, a simple iteration based on the study of the energy distribution is adequate. In the presence of displacement constraints, the design is carried out in two stages. The first stage of iteration is similar to that in stress constraint problems and the second stage is based on a search procedure. Examples of two and three dimensional bar structures are presented to illustrate the effectiveness of the method. It proved to be extremely efficient in arriving at minimum weight structures. (Author)

Application of non‐linear programming to optimum grillage design with non‐convex sets of variables

Abstract: The application of non-linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non-convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum. It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in-plane loads may be performed efficiently by means of non-linear programming.

Minimum-weight stiffened shells with slight meridional curvature designed to support axial compressive loads.

Abstract: Computer program determination of barreling effect on strength of ring and stringer stiffened shells designed to support axial compression loads

Minimum-weight design for two-dimensional bodies

Abstract: The necessary and sufficient conditions for defining the absolute minimum-weight design for two-dimensional bodies (shells, plates and disks) with a given load system are recalled and discussed. A variational method for identifying the optimal solution through a numeric procedure of unrestricted minimisation is proposed. Some significant cases are considered as the general argument is expounded.

Minimum Weight Design of Enclosed Antennas

Abstract: The minimization of the total weight of the tiltable component of an enclosed antenna structure with a given topology and a given initial design subject to relative deformation constraints (rms limits) in both face-up and face-side attitudes as well as to certain structural constraints is formulated, and the solution to this problem is sought by a modified version of the gradient projection method of nonlinear programming. The given initial design should satisfy all the structural constraints, but it may violate one or both deformation constraints. The solution is obtained in two steps by first finding a feasible solution, that is a solution which satisfies all the constraints, and then minimizing the total weight subject to structural and deformation constraints. The structural constraints, for the sake of simplicity, have been assumed to be linear. The method is tested by optimizing a plane truss of a large radio telescope antenna.

Optimum design of spatial structures

Abstract: : A systematic approach is presented to the optimal design of spatial frames for minimum weight subject to constraints on stress and geometry. The optimization procedures discussed are general and may be applied to structures which can be analyzed by matrix displacement or finite element methods. Two methods of mathematical programming are applied to obtain a minimum weight design. Both of these techniques require derivatives of the objective and constraint functions to improve estimates of the optimum design. In order to take full advantage of existing analysis capability, the programming techniques in this research have been assuming that such derivatives are not available.

Minimum Weight Design of Hyperbolic Cooling Towers

Abstract: The minimum weight design of hyperbolic cooling towers is examined. Taking the duty-performance coefficient as the primary behavior constraint, the design is formulated as a constrained optimization problem, and the critical dimensions of the lightest towers for various values of the duty-performance coefficient are tabulated considering a wide range of shell parameters. In general, the towers with sharper curvature appeared to be lighter when compared to other towers with the same duty-performance coefficient.

Design and Analysis of Frames for Stability

Abstract: This paper presents nondimensional graphical solutions for the analysis and minimum weight design of various types of rectangular frames with simple or clamped supports subjected to compressive loadings. The solutions are generated by first expressing the weight and stability equation as nondimensional functions of the inertias. Employing the Lagrangian Multiplier Method results in the required functional relationships to define a minimum weight design. The analysis and design technique is illustrated by several examples.

Optimal design of elastic structural elements.

Abstract: : The class of problems treated falls into the rapidly developing field of optimal structural design. A structure is initially laid out with its geometry fixed but with the distribution of material in the elements left to the designer's choice. The amount and distribution of material is chosen so that the structure performs some function and is best in some sense. The examples treated in this report take minimum weight as their optimality criterion. A broad class of optimal design problems is first formulated as an optimal control problem. Two methods of solving this class of problems are then presented and their application to optimal design problems is discussed. Three optimal design problems are formulated and solved in detail. These problems contain many of the features expected of real-world problems and illustrate the power of computational methods which can be applied for their solution. (Author)