Multi-Material Topology Optimization Considering Crashworthiness

There is an increasing need for lightweight structures in the transportation industry, and within these lightweight structures occupant safety is continually important to all stakeholders. Standard single and multi-material topology optimization (MMTO) techniques are effective for designing lightweight structures subjected to linear objectives and constraints but cannot consider crashworthiness. Crashworthiness must be evaluated using explicit dynamic simulation techniques, as a crash event contains geometric and material nonlinearities which cannot be captured by linear static finite element simulations. Explicit dynamic simulations prevent the calculation of sensitivity derivatives required for conventional gradient-based structural optimization strategies. This paper describes a design tool for multi-material topology optimization considering crashworthiness using the equivalent static load (ESL) method. The ESL method is used to generate linear static sub-problems which replicate the dynamic structural response of explicit dynamic crash simulations in the linear regime. The ESL sub-problems are input to a standard MMTO, optimized results from which are used as input for subsequent crash analyses to update the ESLs for additional sub-problems. The ESLs evolve as the design changes – convergence occurs when the design does not change significantly between subsequent sub-problem optimizations. The objective of this paper is to demonstrate a methodology for an efficient design tool for MMTO considering crashworthiness. Firstly, the ESL and competing methods for crashworthiness optimization are introduced and compared. Next a discussion of the tool’s operation flow as well as the sensitivity equations are presented along with two academic examples demonstrating its implementation. The design tool generates optimized multi-material designs which outperform single-material optimized designs in terms of mass by 7.5% and 17.6% in 2D and 3D models respectively when subjected to crash load cases.