OPTIMAL STRUCTURE FORMATION USING A CHAOTIC SELF-ORGANIZATIONAL ALGORITHM

Optimal engineering shape design is becoming increasingly important as the efficient utilisation of material can account for significant cos t savings during production. Traditional optimisation techniques based on finite element analysis using functional or variational calculus f ind this task difficult, as the design landscape is one in which the o ptimisation problem can be non-convex and hence the solution may have many local optima. The approach adopted in this work is based on a sel f-organisational system governed by a local state operator that define s the state of each element in the finite element mesh at each time st ep. This operator has the form of a nonlinear differential equation ba sed on the use of strain energy density and is an extension of an expr ession originally developed for predicting morphogenetic density distr ibutions in natural human bone. (C) 1997 Elsevier Science Ltd. All rig hts reserved.