This paper demonstrates gradient driven density-based topology optimization of transient impact problems with friction. The sensitivities are obtained using the semi-discrete adjoint approach in which the temporal components are obtained by the "differentiate then discretize" whereas the spatial part is determined discretely. In this work, the sensitivity analysis method is extended to a mixed formulation involving both displacements, velocities, accelerations, and contact forces. The proposed formulation allows to account for frictional impacts during the structural optimization process. A first simple example demonstrates the effects of including frictional impacts into the transient design problem. As a second example, a drop test is considered and a casing for protecting a falling object during a frictional impact, is designed. Solid-void designs are obtained by application of the robust design formulation combined with a parameter continuation scheme.

中文翻译：

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库仑摩擦瞬态冲击结构拓扑优化

本文展示了基于梯度驱动密度的摩擦瞬态冲击问题的拓扑优化。使用半离散伴随方法获得灵敏度，其中时间分量通过“微分然后离散”获得，而空间部分是离散确定的。在这项工作中，敏感性分析方法被扩展到一个混合公式，包括位移、速度、加速度和接触力。建议的公式允许考虑结构优化过程中的摩擦影响。第一个简单示例演示了将摩擦影响纳入瞬态设计问题的效果。作为第二个例子，考虑跌落测试并设计用于在摩擦冲击期间保护跌落物体的外壳。