Optimal Design of Responsive Structures

TL;DR

This paper develops a topology optimization framework for designing integrated responsive structures with active materials, proving the existence of optimal designs and demonstrating results for 2D and 3D actuators.

Contribution

It introduces a robust existence proof for optimal designs of responsive structures considering voids and active materials, with numerical examples for actuators.

Findings

Existence of optimal designs proven for various objectives.

Numerical results for 2D lifting actuators show effective design features.

Optimal 3D torsional actuator designs maximize blocking torque.

Abstract

With recent advances in both responsive materials and fabrication techniques it is now possible to construct integrated functional structures, composed of both structural and active materials. We investigate the robust design of such structures through topology optimization. By applying a typical interpolation scheme and filtering technique, we prove existence of an optimal design to a class of objective functions which depend on the compliances of the stimulated and unstimulated states. In particular, we consider the actuation work and the blocking load as objectives, both of which may be written in terms of compliances. We study numerical results for the design of a 2D rectangular lifting actuator for both of these objectives, and discuss some intuition behind the features of the converged designs. We formulate the optimal design of these integrated responsive structures with the introduction of voids or holes in the domain, and show that our existence result holds in this setting. We again consider the design of the 2D lifting actuator now with voids. Finally, we investigate the optimal design of an integrated 3D torsional actuator for maximum blocking torque.