Lightweight design of rear seats of a passenger car based on topology optimization of equivalent static load method and multi-objective size optimization

This study addresses the trade-off between crash safety and lightweight performance in rear automotive seat design by proposing a two-stage optimization framework that integrates equivalent static load-based topology optimization with multi-objective size optimization. First, the nonlinear dynamic crash problem is transformed into the static domain using the equivalent static load method. Based on this transformation, a topology optimization model is developed to minimize the structural strain energy of the seat back panel, achieving an 8.71% mass reduction. Subsequently, a multi-objective optimization model is established for the remaining components of the seat backrest frame, with thickness parameters as design variables and surrogate models predicting displacement, mass, and crash response. A hybrid modeling approach that combines the polynomial response surface model, Kriging interpolation, radial basis function neural network, and elliptic basis function neural network ensures high predictive accuracy (R² > 0.9). The optimization process employs the non-dominated sorting genetic algorithm-II to generate 142 Pareto-optimal solutions, and a modified grey relational analysis-based multi-criteria decision-making method is then applied to identify the most balanced design. Final validation demonstrates strong consistency between simulation results and surrogate model predictions (relative error <5%), with displacement reduced by 15.89% and 22.29% and mass reduced by 7.1%. This integrated method effectively enhances both crashworthiness and lightweight performance, providing a reliable engineering strategy for high-performance vehicle seat design.