Shape optimization of flow guides in three-dimensional extrusion processes by an approximation scheme based on state variable linearization

A new scheme of shape optimization is applied to the design of a flow guide in flat-die extrusion processes. In general, tremendous time is inevitably required for the optimization of large-scale threedimensional extrusion processes. This is because the finite element analysis requires large computation time owing to the complexity of the die geometry and flow behaviour. The proposed scheme effectively reduces the computation time for the optimization process by approximating the objective function. This is achieved by introducing a transformed equation of the state variables. The scheme is then applied to the practical extrusion processes to produce ‘l’, ‘H’ and ‘L’ sections. The objective of the optimization is to make a balanced flow of the material in the exit region. Control points of a Bezier curve describing the outline of the flow guide are regarded as the design variables. Through application to large-scale problems, the effectiveness and usefulness of the proposed scheme is demonstrated.