Exploring the Frontier of Structural Engineering with Physics-Informed Neural Networks

Reinforced concrete (RC) beams form the backbone of modern architecture and infrastructure. These crucial structural elements are found in a myriad of constructions, from residential buildings to sprawling bridge networks, bearing witness to their vital importance in ensuring the safety and stability of such structures. Traditional computational methods, largely based on linear elastic analyses, have long governed the design and verification of RC beams. While effective to an extent, these methods often oversimplify the load-deformation behavior of reinforced concrete, leading to potentially conservative approximations.

The quest for accuracy and efficiency in the structural analysis of RC beams has led engineers and researchers to explore nonlinear analyses. Despite providing a more realistic representation of structural behavior under load, nonlinear analyses have struggled to find widespread application in engineering practice. The reasons are manifold: computational demands are high, and results depend heavily on the accurate representation of complex, uncertain material properties. This imbalance restricts the broader exploration of design possibilities, verification protocols, and the nuances of uncertainty quantification, creating a pressing need for novel computational tools that can bridge these gaps.

Enter the realm of physics-informed neural networks (PINNs), a cutting-edge computational approach that is poised to revolutionize the analysis and design of reinforced concrete beams. This paper brings into focus the potential of PINNs to transcend traditional computational limitations, offering a detailed examination of their application to the structural analysis of a single-span simply supported RC beam.

At the heart of this exploration is the refinement of PINNs to model the nonlinear behavior of RC beams, transitioning from a linear elastic foundation to embodying the more complex multi-linear material laws that govern their real-world behavior. The multi-linear model captures the progression from uncracked, to cracked, and finally to the plastic deformation stages of the beam under varying loads. Achieving this sophisticated representation requires a novel mixed-approach reformulation of PINNs, breaking new ground in the integration of physical laws and neural computation.


In navigating the complexities of PINN application, a comprehensive hyperparameter tuning study was undertaken, revealing that medium-sized networks consisting of eight layers, equipped with tanh or SiLU activation functions, strike the optimal balance between computational efficiency and predictive accuracy. Through rigorous comparison against both analytical models and Finite-Element (FE) solutions, the prowess of PINNs in forecasting the displacements and rotations of RC beams is convincingly demonstrated. Notably, these comparisons confirm that while the PINNs accurately predict structural responses, they do not incur additional computational overhead, marking a significant advancement in the field.

As we project into the future of structural engineering and design, the potential expansions of this research are vast. The prospect of enhancing physics-informed deep operator networks stands out as a promising avenue. Such advancements could unlock the capability for rapid, accurate analysis and design across a broader spectrum of parametric beam structures, setting a new benchmark in the field.

In conclusion, the integration of physics-informed neural networks into the analysis of reinforced concrete beams represents a pivotal shift towards more nuanced, efficient, and realistic modeling of structural elements. This paper not only showcases the immediate benefits of PINN-based computations but also lays the groundwork for future innovations that could redefine the paradigms of structural engineering. As the field continues to evolve, the implications of this research extend far beyond the realm of academia, promising to enhance the resilience, safety, and sustainability of our built environment.

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