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

Abstract

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.