A new class of plane curves with arc length parametrization and its application to linear analysis of curved beams

Snježana Maksimović*, Aleksandar Borković

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The objective of this paper is to define one class of plane curves with arc-length parametrization. To accomplish this, we constructed a novel class of special polynomials and special functions. These functions form a basis of L2 (ℝ) space and some of their interesting properties are discussed. The developed curves are used for the linear static analysis of curved Bernoulli–Euler beam. Due to the parametrization with arc length, the exact analytical solution can be obtained. These closed-form solutions serve as the benchmark results for the development of numerical procedures. One such example is provided in this paper.

Original languageEnglish
Article number1778
JournalMathematics
Volume9
Issue number15
DOIs
Publication statusPublished - 1 Aug 2021

Keywords

  • Analytical solution
  • Arc-length parametrization
  • Bernoulli–Euler beam
  • Special functions
  • Sturm–Liouville differential equation

ASJC Scopus subject areas

  • Mathematics(all)

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