Design optimization: Optimal design of shape and layout

Design and Rapid Prototyping Laboratory

Associate Professor Ashok V. Kumar
Department of Mechanical Engineering
University of Florida, Gainesville, FL 32611

Design optimization techniques are being developed to synthesis the optimal shape and topology (or layout) of mechanical components such that they have maximum stiffness for a given mass. To define the design problem, the user specifies a feasible region within which the part must fit, the loads the structure must support and the locations where the structure is supported. The system automatically computes the optimal shape that fits within the feasible region and has the specified weight.

In our approach, the shape and topology is represented using a "shape density" function. The boundaries of the shape of the structure are defined as the contours of this density function. The shape density function is defined over the feasible region by continuous piece-wise interpolation over the finite elements used for structural analysis. The values of the density function at the nodes serve as the variables of the optimization problem. A modified sequential linear programming algorithm is used to compute the optimal values of the nodal densities. The figures below some optimal shapes that were designed using this method.