Topography optimization is an innovative technique that can significantly improve the response of certain type of structures. The most challenging aspect of topography optimization is the sensitivity analysis. In this manuscript two methods to approximate the sensitivities for problems in topography optimization are introduced. The gradient is supplanted with either a stochastic approximation, or a physical approximation. Initially, an overview of the state-of-the-art in topography optimization is presented, and some key issues are explored. Subsequently, the technique is outlined, and the proposed methods are introduced. Furthermore, a numerical example in which a structure composed of shell elements is subject to a blast load is provided. This example is solved employing stochastic gradient approximation, and approximate gradient. They are compared to the widely used finite differences approximation. It is possible to observe that the proposed method significantly reduces the computational effort required to solve the problem, while considerably improving the objective function.

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