Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
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Optimal engineering shape design is becoming increasingly important as the efficient utilisation of material can account for significant cost savings during production. Traditional optimisation techniques based on finite element analysis using functional or variational calculus find this task difficult, as the design landscape is one in which the optimisation problem can be non-convex and hence the solution may have many local optima. The approach adopted in this work is based on a self-organisational system governed by a local state operator that defines the state of each element in the finite element mesh at each time step. This operator has the form of a nonlinear differential equation based on the use of strain energy density and is an extension of an expression originally developed for predicting morphogenetic density distributions in natural human bone.