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Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives

Author

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  • Daniele Mortari

    (Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843, USA)

Abstract

This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation comes from differential equations, often appearing in fluid dynamics and structures/materials problems that are subject to shear-type and/or mixed boundary derivatives constraints. This is performed by replacing these boundary constraints with equivalent constraints, obtained using indefinite integrals. In addition, this study also shows how to validate the constraints’ consistency when the problem involves the unknown constants of integrations generated by indefinite integrations.

Suggested Citation

  • Daniele Mortari, 2022. "Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4692-:d:999823
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    References listed on IDEAS

    as
    1. Daniele Mortari, 2017. "The Theory of Connections: Connecting Points," Mathematics, MDPI, vol. 5(4), pages 1-15, November.
    2. Hunter Johnston & Carl Leake & Yalchin Efendiev & Daniele Mortari, 2019. "Selected Applications of the Theory of Connections: A Technique for Analytical Constraint Embedding," Mathematics, MDPI, vol. 7(6), pages 1-19, June.
    3. Hunter Johnston & Martin W. Lo & Daniele Mortari, 2021. "A Functional Interpolation Approach to Compute Periodic Orbits in the Circular-Restricted Three-Body Problem," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
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    Cited by:

    1. Yassopoulos, Christopher & Reddy, J.N. & Mortari, Daniele, 2023. "Analysis of nonlinear Timoshenko–Ehrenfest beam problems with von Kármán nonlinearity using the Theory of Functional Connections," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 709-744.

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