IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4692-d999823.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4692/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/24/4692/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Daniele Mortari, 2017. "The Theory of Connections: Connecting Points," Mathematics, MDPI, vol. 5(4), pages 1-15, November.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniele Mortari & Carl Leake, 2019. "The Multivariate Theory of Connections," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    2. Kristofer Drozd & Roberto Furfaro & Enrico Schiassi & Andrea D’Ambrosio, 2023. "Physics-Informed Neural Networks and Functional Interpolation for Solving the Matrix Differential Riccati Equation," Mathematics, MDPI, vol. 11(17), pages 1-24, August.
    3. Kristofer Drozd & Roberto Furfaro & Andrea D’Ambrosio, 2024. "A Theory of Functional Connections-Based hp -Adaptive Mesh Refinement Algorithm for Solving Hypersensitive Two-Point Boundary-Value Problems," Mathematics, MDPI, vol. 12(9), pages 1-35, April.
    4. 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.
    5. Daniele Mortari & Roberto Garrappa & Luigi Nicolò, 2023. "Theory of Functional Connections Extended to Fractional Operators," Mathematics, MDPI, vol. 11(7), pages 1-18, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4692-:d:999823. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.