Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

Abstract

Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.

Keywords:

• topology optimization
• crashworthiness
• equivalent dynamic system

Acknowledgements

The authors wish to thank Prakash D. Mangalgiri, Narendran Balan, Simon Xu and Prabhakar Marur for their continuous guidance and support during the course of the work and for their thorough review of the manuscript.