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Abstract Isogeometric analysis (IGA) is a computational technique that integrates computer-aided design (CAD) with finite element analysis (FEA) by employing the same basis functions for both geometry representation and solution approximation. While IGA offers numerous advantages, such as improved accuracy and efficiency, it also presents several challenges related to geometric modeling. Some of these challenges include accurately representing complex geometries with NURBS (Non-Uniform Rational B-Splines) or other basis functions used in IGA and generating high-quality meshes that conform to the complex geometry represented by NURBS curves/surfaces. This paper introduces an analytical framework to provide a more efficient and theoretically grounded method for generating curvilinear configurations and its analytical solution in IGA, bridging the gap between generated data and its physical representations. This innovative approach is distinguished by integrating the NURBS parameterization in curve generation and providing a corresponding framework to achieve a broader and more accurate explanation of meshes and properties, especially constructing new coordinates and calculating the physical displacements under these conditions. Our model enables the analytical understanding of complex curves from the UIUC airfoil and superformula datasets, demonstrating a deeper dive into simulations. This study signifies a pivotal juncture wherein machine-learning-based complex geometrical formulations are synergistically combined with actual isogeometric analysis.
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Thermo‐hydro‐mechanical modeling of unsaturated soils using isogeometric analysis: Model development and application to strain localization simulation
Summary This study presents a thermo‐hydro‐mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA‐FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker‐Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi‐static loading conditions. Temperature dependency of the surface tension is implemented in the soil‐water retention curve. Nonuniform rational B‐splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA‐based framework offers a viable alternative for solving THM problems in unsaturated soils.
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- Award ID(s):
- 1634748
- PAR ID:
- 10459605
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- International Journal for Numerical and Analytical Methods in Geomechanics
- Volume:
- 44
- Issue:
- 2
- ISSN:
- 0363-9061
- Page Range / eLocation ID:
- p. 261-292
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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