Optimal topology design using a global self-organisational approach

Abstract

A method based on a self-organisational approach has been developed, where a local state operator defines the state of each finite element at each iteration. The algorithm is based on the principle of local adaptation with global feedback in the form of a derivative equation based on von Mises stresses that allows the local remodelling function to vary at each time step. The state operator has the form of a nonlinear differential equation solved iteratively based on the material density and strain energy density within each element. A constraint equation is formulated based on a maximum deviatoric strain energy criteria, with the objective to minimise the mass of the design domain subject to the above constraint. A number of examples are presented to demonstrate the use of this approach.