Body-in-white (BIW) is a typical frame structure formed by a great many thin-walled structures, and the optimal design of its lightweight and crashworthiness is a typical nonlinear dynamic response optimization problem with multiple design variables. Here, we propose a thickness-based subdomain hybrid cellular automata (T-SHCA) algorithm to solve the lightweight design of BIW under side collision, in which there are two loops: one is the outer loop to conduct crash finite element analysis, calculate output responses, and update internal energy density (IED) and target mass; the other is the inner loop to adjust cell thicknesses according to IEDs of current cell and its neighboring cells to make the actual mass of current cells converge to target mass. The concept of "subdomain cellular automata (SCA)" model was introduced, so that the T-SHCA can solve nonlinear dynamic response optimization in discrete and separated design spaces. The step IED target update rule and the cell thickness update rule based on a PID control strategy were implemented in the inner loop to improve the global optimal solution search capability and the robustness of the proposed algorithm, respectively. The thicknesses optimization of a BIW was carried out by the proposed method and a parallel efficient global optimization algorithm to verify its convergence and efficiency. The results show that the T-SHCA algorithm can be implemented to effectively solve nonlinear dynamic response structural optimization problem with many thickness variables in discrete and separated design spaces.

白车身（BIW）是由大量薄壁结构组成的典型车架结构，其轻量化和耐撞性的优化设计是典型的多设计变量非线性动力响应优化问题。在这里，我们提出了一种基于厚度的子域混合元胞自动机（T-SHCA）算法来解决侧面碰撞下白车身的轻量化设计，其中有两个循环：一个是外循环进行碰撞有限元分析，计算输出响应，并更新内部能量密度 (IED) 和目标质量；另一个是内部循环，根据当前单元格及其相邻单元格的IED调整单元格厚度，使当前单元格的实际质量收敛到目标质量。引入了“子域元胞自动机（SCA）”模型的概念，以便 T-SHCA 可以解决离散和分离设计空间中的非线性动态响应优化问题。在内循环中实施基于PID控制策略的阶梯式IED目标更新规则和单元厚度更新规则，分别提高了算法的全局最优解搜索能力和鲁棒性。通过所提出的方法和并行高效全局优化算法对白车身进行了厚度优化，以验证其收敛性和效率。结果表明，T-SHCA算法可以有效地解决离散和分离设计空间中具有多厚度变量的非线性动力响应结构优化问题。在内循环中实施基于PID控制策略的阶梯式IED目标更新规则和单元厚度更新规则，分别提高了算法的全局最优解搜索能力和鲁棒性。通过所提出的方法和并行高效全局优化算法对白车身进行了厚度优化，以验证其收敛性和效率。结果表明，T-SHCA算法可以有效地解决离散和分离设计空间中具有多厚度变量的非线性动力响应结构优化问题。在内循环中实施基于PID控制策略的阶梯式IED目标更新规则和单元厚度更新规则，分别提高了算法的全局最优解搜索能力和鲁棒性。通过所提出的方法和并行高效全局优化算法对白车身进行了厚度优化，以验证其收敛性和效率。结果表明，T-SHCA算法可以有效地解决离散和分离设计空间中具有多厚度变量的非线性动力响应结构优化问题。分别。通过所提出的方法和并行高效全局优化算法对白车身进行了厚度优化，以验证其收敛性和效率。结果表明，T-SHCA算法可以有效地解决离散和分离设计空间中具有多厚度变量的非线性动力响应结构优化问题。分别。通过所提出的方法和并行高效全局优化算法对白车身进行了厚度优化，以验证其收敛性和效率。结果表明，T-SHCA算法可以有效地解决离散和分离设计空间中具有多厚度变量的非线性动力响应结构优化问题。