Methods of Feasible Directions. By G. Zoutendijk. Pp. 126. 30s. 1960. (D. van Nostrand Co. London)

Optimum design of frames

A natural and practical method is developed for finding optimal topologies of large plane trusses for a specified fundamental natural frequency, where all the node locations are fixed and the set of members that may exist or may be adopted is prescribed. The method is based on the concept of an ordered set of optimal trusses introduced recently by the authors. The optimum designs are considered as functions of a problem parameter which specifies the set of minimum cross-sectional areas, and the optimal solutions are swept out with Taylor series expansions with respect to the parameter. The solution with vanishing minimum cross-sectional areas is considered to represent the truss with the optimal topology, and each solution throughout the process of decreasing the parameter is the global optimal solution corresponding to the set of minimum cross-sectional areas specified with the current value of the parameter. A method is presented of generating a truss with a practical optimal topology which contains long members. The efficiency of the proposed method is shown through the examples of large plane trusses, and the characteristics of the optimal topologies are discussed.

A natural generator of optimum topology of plane trusses for specified fundamental frequency

Sequential generator of earthquake-response constrained trusses for design strain ranges

This paper presents an analytical method for minimum cost design of regular rectangular building frames for constrained elastic compliance. The method, consisting of a semi-inverse method and a design region extension procedure, is illustrated by two classes of exact solutions. It is shown that the relative story displacements are almost uniformly distributed in an optimally designed frame with almost uniform story heights and that the solutions enable one to calculate all maximum member-end stresses from member-end curvatures. It is suggested that the proposed design formulas may be utilized for design problems, subject to relative story displacement and stress constraints. Since these solutions are shown to be dependent upon the nature of the prescribed minimum stiffnesses, a method of finding a practically reasonable set of minimum stiffnesses is also presented.

Optimum Design of Multistory Multispan Frames for Prescribed Elastic Compliance

This paper presents the necessary and sufficient conditions for the minimum weight design of multistory, multispan plane building frames subject to foundation reaction constraints It proposes a general, analytical, and explicit constructive law with which exact solutions can be derived for a broad class of frames of practical interest subject to compressive reaction constraints only It is proved that the classical Foulkes mechanism must be modified for this problem so as to include artificial settlements and/or upward displacements wherever the reactions attain the prescribed limiting values The bay shear distribution law compactly expressed in terms of the enlarged and reduced span lengths defined in this paper clarifies the general features of the minimum weight design

Tadashi Nagase

Papers

Minimum Weight Design of Multistory, Multispan Plane Frames Subject to Reaction Constraints