Dynamical systems, SIMP, bone remodeling and time dependent loads

The dynamical systems approach to sizing and SIMP topology optimization, introduced in a previous paper, is extended to the case of time‐varying loads. A general dynamical system, satisfying a Lyaponov‐type descent condition, is derived and specialized to a goal function combining stiffness and mass. For a cyclic time‐dependent load it is indicated how, in the limit of short cycles compared to the overall time scale, this can be handled by multiple load cases. Numerical examples, both for a convex and a non‐convex case, illustrates the theory.