A computer algorithm for deriving analytically and plotting optimal structural layout

doi:10.1016/0045-7949(79)90098-1

Computers & Structures

Volume 10, Issues 1–2, April 1979, Pages 295-300

https://doi.org/10.1016/0045-7949(79)90098-1 Get rights and content

Abstract

The optimal layout theory for least-weight grillages is reviewed and then a computer algorithm for deriving analytically and plotting optimal layout is described. Finally, some current and planned future developments are discussed.

References (11)

G.I.N. Rozvany
Optimal Design of Flexural Systems
(1976)
W. Prager and G. I. N. Rozvany, A new class of optimization problems: optimal archgrids. Comp. Meth. Appl. Mech. Engng...
W. Prager et al.
Optimization of structural geometry
C.T. Morley
The minimum reinforcement in concrete slabs
Int. J. Mech. Sci.
(1966)
W. Prager
Introduction to Structural Optimization

There are more references available in the full text version of this article.

Cited by (6)

Optimal structural design via optimality criteria as a nonsmooth mechanics problem
1995, Computers and Structures
In the theory of plastic structural design via optimality criteria (due to W. Prager), the optimal design problem is transformed to a nonlinear elastic structural analysis problem with appropriate stress-strain laws, which generally include complete vertical branches. In this context, the concept of structural universe (in the sense of G. Rozvany) permits the treatment of complicated optimal layout problems. Recent progress in the field of nonsmooth mechanics makes the solution of structural analysis problems with this kind of “complete” law possible. Elements from the two fields are combined in this paper for the solution of optimal design and layout problems for structures. The optimal layout of plane trusses with various specific cost functions is studied here as a representative problem. The use of convex, continuous and piecewise linear specific cost functions for the structural members leads to problems of linear variational inequalities or equivalently piecewise linear, convex but nonsmooth optimization problems, which are solved by means of an iterative algorithm based on sequential linear programming techniques. Numerical examples illustrate the theory and its applicability to practical engineering structures. Following a parametric investigation of an optimal bridge design, certain aspects of the optimal truss layout problem are discussed, which can be extended to other types of structural systems as well.
Topological optimization of grillages: Past controversies and new directions
1994, International Journal of Mechanical Sciences
The aim of this paper is to derive optimal grillage layouts for combinations of simply supported and free edges. It has been found, however, that the solution of these problems involves some fundamental aspects of the underlying theory, which result in a proposition termed the “principle of small violations”. Using this principle, new classes of grillage topologies are outlined and some past controversies resolved in a manner that should satisfy all parties concerned.
Prager's layout theory: a nonnumeric computer method for generating optimal structural configurations and weight-influence surfaces
1985, Computer Methods in Applied Mechanics and Engineering
After illustrating the versatility of the proposed computer method on an introductory example, the basic principles of Prager's layout theory and its applications to least-weight grillages and space frames are briefly reviewed. Then a computer algorithm for generating analytically the optimal layout for both grillages and space frames is described in detail. The algorithm can handle a broad class of boundary conditions of unusual complexity and also furnishes a weight-influence surface for evaluating directly the minimum weight of the considered structure.
In the case of grillages, the present computer program can derive optimal layouts for any polygonal domain with simply supported and/or clamped edges and internal point supports and the solution is valid for any nonnegative (downward) loading. Layouts for optimal space frames are restricted to ‘Prager-structures’ (i.e. frames with all members in pure tension or all members in pure compression) with polygonal support and a single point-load in any arbitrary location.
Exact Michell layouts for various combinations of line supports - Part II
1997, Structural Optimization
Layout optimization of structures
1995, Applied Mechanics Reviews
Optimal topologies of structures
1989, Applied Mechanics Reviews

^☆: This project has been supported by the University of Stuttgart. (Research Project: Wide Span Structures SFB 64, Group A1) and the Australian Research Grants Committee (Project No. F67.15.1341).

^‡: Monash University, Clayton, Victoria, Australia 3168.

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A computer algorithm for deriving analytically and plotting optimal structural layout☆

Abstract

Optimization of structural geometry

The minimum reinforcement in concrete slabs

Int. J. Mech. Sci.

Introduction to Structural Optimization