  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.
