Machine learning-based modelling, feature importance and Shapley additive explanations analysis of variable-stiffness composite beam structures

Nikolaos Karathanasopoulos, Agyapal Singh, Panagiotis Hadjidoukas

Research output: Contribution to journalArticlepeer-review


In the current work, the displacement and inner stress state of orthotropic, composite, variable-stiffness beam structures is investigated, combining the extended Kantorovich method (EKM) with machine learning (ML) modeling and explainable artificial intelligence (AI) techniques. The complete displacement and inner stress fields of variable stiffness (VS) composite beams with a through-thickness variation of their material properties are computed for different orthotropy, material gradation and slenderness attributes. Both deep learning and tree-based machine learning architectures are considered, identifying high accuracy and low computational cost modeling architectures. Thereupon, the significance of underlying fundamental design features is assessed, classifying their importance for the first time. In particular, material orthotropy, stiffness gradation and slenderness are analyzed for different boundary conditions, elucidating their interdependence and relative significance. It is shown that reduced end kinematic constraints overall favor the importance of stiffness gradation. Differences in the importance of each design feature for the transverse displacement and inner normal and shear stress fields are identified and quantified using Shapley additive explanations (SHAP) analysis. It is found that material orthotropy is more important than stiffness gradation for the transverse displacement rather than for the normal or shear stress fields developed, for which their relative importance is inverted. What is more, evidence is provided that increased gradation and orthotropy values have opposite signed contributions to the stress fields developed at critical positions of the VS composite, while they uniquely yield equal-signed contributions to the transverse displacement field.

Original languageEnglish (US)
Article number106206
StatePublished - Apr 2024


  • Composites
  • Explainable AI
  • Extended Kantorovich method
  • Machine learning
  • Neural networks
  • Variable stiffness

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Architecture
  • Building and Construction
  • Safety, Risk, Reliability and Quality


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