A PID-optimality criteria method for structural topology optimization

In this study a modified optimality criteria (OC) method which uses the Proportional, Integral, Derivative (PID) control to determine the Lagrange multiplier is proposed. The OC method is efficient in density based topology optimization. However, the undetermined Lagrange multiplier should be calculated first. In this study the Lagrange multiplier is taken as the controlled variable of PID controller, which enhances the convergence of the OC method. The constraint violation is taken as system error which updates the Lagrange multiplier. Combining the design variables update scheme in the OC method with the PID control algorithm, a gradually improved structure is produced during iteration. The optimal structure which satisfies the constraint function is obtained finally. The modified method implements simply and saves the computational time. Numerical examples of single material topology optimization validate the performance of the proposed method. Results show that the modified method converges fast with few iterations and short time. Subsequently, the modified method is extended to multi-material topology optimization. Results validate the modified method performs well in time-consuming multi-material problem.