Design optimization of geometrically nonlinear structures is well known as a computationally expensive problem by using incremental-iterative solution techniques. To handle the problem effectively the optimization algorithm needs to ensure that the trade-off between the computational time and the quality of the solution is found. In this study, a deep neural network (DNN)-based surrogate model which integrates with differential evolution (DE) algorithm is developed and applied for solving the optimum design problem of geometrically nonlinear space truss under displacement constraints and refer to the approach as DNN-DE. Accordingly, this surrogate model, also is known as a deep neural network, is established to replace conventional finite element analyses (FEAs). Each dataset is created based on FEA which employs the total Lagrangian formulation and the arc-length procedure. Several numerical examples are given to demonstrate the efficiency and validity of the proposed paradigm. These results indicate that the proposed approach not only reduces the computational cost dramatically but also guarantees convergence.

几何非线性结构的设计优化是众所周知的使用增量迭代求解技术的计算成本高的问题。为了有效地处理问题，优化算法需要确保找到计算时间和解决方案质量之间的权衡。在本研究中，开发了一种基于深度神经网络（DNN）的代理模型，该模型与差分进化（DE）算法相结合，用于解决位移约束下几何非线性空间桁架的优化设计问题，并将该方法称为 DNN-德。因此，建立这种替代模型，也称为深度神经网络，旨在取代传统的有限元分析 (FEA)。每个数据集都是基于使用总拉格朗日公式和弧长程序的 FEA 创建的。给出了几个数值例子来证明所提出的范式的效率和有效性。这些结果表明，所提出的方法不仅显着降低了计算成本，而且保证了收敛。