Topology optimization for minimum compliance using a control strategy

This paper introduces a control-based optimization algorithm to solve topology optimization problems for structures of minimum compliance. In this approach, the iterative solution process is expressed as a multivariable control system. The elements comprising the structure are numerically incorporated with sensors, controllers, and actuators. The sensors determine a response signal as a function of the problem’s sensitivity coefficients. The controllers minimize the error between this response and a corresponding setpoint obtained from the problem’s optimality conditions. The actuators modify the design variables according to the control signal while satisfying all constraints. A proportional–integral–derivative controller is shown to be computationally efficient. Numerical issues involving local minima, mesh dependency, checkerboard patterns, and intermediate densities are tackled using continuation, filtering, and penalization methods. The performance of this algorithm is demonstrated for unpenalized and penalized topology optimization problems.

► A topology optimization algorithm based on control theory is proposed.
► Issues involving local minima and mesh-dependency are effectively addressed.
► Capabilities are demonstrated in 2D and 3D problems of minimum compliance.
► Ziegler–Nichols tuning for PID controller demonstrate outstanding performance.
► The method is simple and depicts better convergence than available algorithms.