Concurrent Shape Optimization of Structural Components

Abstract

A concurrent design optimization approach, which produces components with minimum cost, required structural performance, and ensures manufacturability is presented. A structural shape optimization problem is set-up to minimize total cost, subject to the limits on structural performance measures. Parametric solid model of the component is created in CAD software. FEA and Virtual Machining (VM) models constructed based on given boundary and loading conditions, and machining parameters, respectively, are used to evaluate structural and manufacturing performance measures. Gradients of objective function and constraints are computed and supplied to the optimization algorithm. Based on the gradients, the algorithm determines design changes, which are used to update FEA and VM models. The process is repeated until specified convergence criterion is satisfied. Commercially available CAD/CAM/FEA/Design optimization tools are integrated with the help of application programs. The application programs written can be re-used for similar design problems provided the same tools are used. Nomenclature φ(b) = objective function b = vector of design variables captured in CAD solid models ψi(b) = i th structural performance parameter u i ψ = upper bound of the i th structural performance parameter , u jj bb A = lower and upper bounds of the j th design variables, respectively Cmat = material cost rate ($/lb) γ = specific weight of the material V(b) = volume of the component s Cmac = machining cost rate ($/min) τ(b) = machining time that also depends on design; Ct = tooling cost ($) tmc = machining time