On the prediction of topology and local properties for optimal trussed structures

A new formulation is presented for mathematical modelling to predict the distribution of material, material properties, and topology for the optimal design of trussed structures. The design problem is cast in a form to minimize a measure of generalized compliance , which is calculated as a sum over the structure of weighted displacement. Member stiffnesses appear as design variables and, starting with a given ground structure, the solution predicts the optimal layout and distribution of stiffness. The isoperimetric constraint in the reformulated problem measures total cost in generalized form , based on independently specified unit relative cost factors for each truss element. One or another form of optimal design is generated via a process where designated elements in the unit relative cost field are adjusted systematically at each cycle. The generalized cost feature provides as well for the introduction of certain technical constraints into the design problem, e.g. the facility to design around obstacles. Results for each cycle of an algorithm for computational treatment are identified as the solution to a properly posed optimization problem. Computational procedures are demonstrated by the prediction of optimal designs for a variety of truss problems in 2D.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46074/1/158_2005_Article_BF01197558.pd

Optimal design of controlled structures

A formulation that finds the optimal design of a controlled structure is proposed. To achieve this goal, a composite objective composed of structural and control objectives is introduced to be optimized, and the effect of the control weighting is examined. A feedback control law is defined before the structural optimization and then the composite objective will only become a function of structural design variables. As a result, optimal structural design and control forces in steady state are obtained.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46072/1/158_2005_Article_BF01279651.pd

Optimal layout theory: Allowance for selfweight

Structural layout theory is based on two underlying concepts, i.e., the Prager-Shield theory of plastic design and the notion of "structural universe." In this paper, optimal layout theory is extended to allow for the effect of selfweight (dead load). The proposed extension is of practical importance because in the design of long-span structures selfweight is a significant load component and the total weight is strongly dependent on the choice of layout. The application of the modified optimality criteria is illustrated with examples of minimum weight grillages (truss grids) as well as plane frames. The degree of economy achieved is then demonstrated through comparisons with nonoptimal solutions. It is also shown that in the preceding examples both primal and dual formulations give the same minimum weight. This comparison is a convenient check on the optimality of the proposed solutions

Optimal plastic design of axisymmetric solid plates with a maximum thickness constraint

A systematic method for deriving least-weight solutions for plastically designed, axially symmetric solid plates of prescribed maximum thickness is presented. It is shown that the solution in general consists of regions having (a) stiffeners of maximum depth but infinitesimal width running in one direction only, with a plate of vanishing thickness in between the stiffeners or (b) a "smooth" solid plate. It follows that the majority of existing papers on least-weight solid plates, based on smooth thickness variation throughout, have failed to locate the global optimum. The method is illustrated with examples of circular plates. The weight of the optimal solution is compared with that of intuitively selected designs

Extension of Heyman's and Foulkes' theorems to structures with linear segmentation

International Journal of Mechanical Sciences31287-106IMSC

Optimal plastic design of circular plates: Numerical solutions and built-in edges

Computers and Structures224519-528CMST