Next Article in Journal
Distributed Power Sharing Control Strategy for Interconnected AC and DC Microgrids Based on Event-Triggered Control Under Denial-of-Service Attack
Previous Article in Journal
A Fast Image Encryption Scheme Based on a Four-Dimensional Variable-Parameter Hyperchaotic Map and Cyclic Shift Strategy
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Macroelement Analysis in T-Patches Using Lagrange Polynomials

by
Christopher Provatidis
1,* and
Sascha Eisenträger
2
1
School of Mechanical Engineering, National Technical University of Athens, 15780 Zografou, Greece
2
Institute of Materials, Technologies and Mechanics, Otto von Guericke University Magdeburg, 39106 Magdeburg, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(9), 1498; https://doi.org/10.3390/math13091498
Submission received: 26 March 2025 / Revised: 25 April 2025 / Accepted: 29 April 2025 / Published: 30 April 2025

Abstract

This paper investigates the derivation of global shape functions in T-meshed quadrilateral patches through transfinite interpolation and local elimination. The same shape functions may be alternatively derived starting from a background tensor product of Lagrange polynomials and then imposing linear constraints. Based on the nodal points of the T-mesh, which are associated with the primary degrees of freedom (DOFs), all the other points of the background grid (i.e., the secondary DOFs) are interpolated along horizontal and vertical stations (isolines) of the tensor product, and thus, linear relationships are derived. By implementing these constraints into the original formula/expression, global shape functions, which are only associated with primary DOFs, are created. The quality of the elements is verified by the numerical solution of a typical potential problem of second order, with boundary conditions of Dirichlet and Neumann type.
Keywords: transfinite interpolation; elimination; finite element method transfinite interpolation; elimination; finite element method

Share and Cite

MDPI and ACS Style

Provatidis, C.; Eisenträger, S. Macroelement Analysis in T-Patches Using Lagrange Polynomials. Mathematics 2025, 13, 1498. https://doi.org/10.3390/math13091498

AMA Style

Provatidis C, Eisenträger S. Macroelement Analysis in T-Patches Using Lagrange Polynomials. Mathematics. 2025; 13(9):1498. https://doi.org/10.3390/math13091498

Chicago/Turabian Style

Provatidis, Christopher, and Sascha Eisenträger. 2025. "Macroelement Analysis in T-Patches Using Lagrange Polynomials" Mathematics 13, no. 9: 1498. https://doi.org/10.3390/math13091498

APA Style

Provatidis, C., & Eisenträger, S. (2025). Macroelement Analysis in T-Patches Using Lagrange Polynomials. Mathematics, 13(9), 1498. https://doi.org/10.3390/math13091498

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop