Topology optimization of 2D structures with nonlinearities using deep learning

Research output: Contribution to journalArticlepeer-review


The field of optimal design of linear elastic structures has seen many exciting successes that resulted in new architected materials and structural designs. With the availability of cloud computing, including high-performance computing, machine learning, and simulation, searching for optimal nonlinear structures is now within reach. In this study, we develop convolutional neural network models to predict optimized designs for a given set of boundary conditions, loads, and optimization constraints. We have considered the case of materials with a linear elastic response with and without stress constraint. Also, we have considered the case of materials with a hyperelastic response, where material and geometric nonlinearities are involved. For the nonlinear elastic case, the neo-Hookean model is utilized. For this purpose, we generate datasets composed of the optimized designs paired with the corresponding boundary conditions, loads, and constraints, using a topology optimization framework to train and validate the neural network models. The developed models are capable of accurately predicting the optimized designs without requiring an iterative scheme and with negligible inference computational time. The suggested pipeline can be generalized to other nonlinear mechanics scenarios and design domains.

Original languageEnglish (US)
Article number106283
JournalComputers and Structures
StatePublished - Sep 2020


  • Adjoint sensitivity
  • Finite element analysis (FEA)
  • Machine learning
  • Neo-Hookean materials
  • Stress constraint

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Modeling and Simulation
  • General Materials Science
  • Mechanical Engineering
  • Computer Science Applications


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