Open Access

ARTICLE

New Insight to Large Deformation Analysis of Thick-Walled Axisymmetric Functionally Graded Hyperelastic Ellipsoidal Pressure Vessel Structures: A Comparison between FEM and PINNs

Azhar G. Hamad¹, Nasser Firouzi^2,*, Yousef S. Al Rjoub³

1 Department of Civil Engineering, College of Engineering, University of Thi-Qar, Nasiriyah, Thi-Qar, Iraq
2 Institute of Structural Mechanics, Bauhaus-University Weimar, Weimar, Germany
3 Civil Engineering Department, Jordan University of Science and Technology, Irbid, Jordan

* Corresponding Author: Nasser Firouzi. Email:

Computers, Materials & Continua 2026, 87(2), 15 https://doi.org/10.32604/cmc.2026.075840

Received 10 November 2025; Accepted 29 January 2026; Issue published 12 March 2026

Abstract

The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials, such as hyperelastic and functionally graded materials (FGMs), is critical for ensuring their safety and optimizing their design. However, conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs. This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks (PINNs) with Finite Element Method (FEM) derived data for the robust analysis of thick-walled, axisymmetric, heterogeneous, hyperelastic pressure vessels with elliptical geometries. A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB. To enhance training efficiency and accuracy, the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS. The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGM configurations (with material properties varying according to a power law) subjected to internal and external pressurization. The results demonstrate excellent agreement between the proposed hybrid PINN-FEM approach and conventional FEM solutions across all test cases, accurately capturing complex deformation patterns and stress concentrations. This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linear materials and significant heterogeneity, offering a promising avenue for future research in engineering design and analysis.

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