A level-set method for vibration and multiple loads structural optimization

We extend the level-set method for shape and topology optimization to new objective functions such as eigenfrequencies and multiple loads. This method is based on a combination of the classical shape derivative and of the Osher–Sethian level-set algorithm for front propagation. In two and three space dimensions we maximize the first eigenfrequency or we minimize a weighted sum of compliances associated to different loading configurations. The shape derivative is used as an advection velocity in a Hamilton–Jacobi equation for changing the shape. This level-set method is a low-cost shape capturing algorithm working on a fixed Eulerian mesh and it can easily handle topology changes.