TY - JOUR
T1 - A new class of plane curves with arc length parametrization and its application to linear analysis of curved beams
AU - Maksimović, Snježana
AU - Borković, Aleksandar
PY - 2021/8/1
Y1 - 2021/8/1
N2 - 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.
AB - 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.
KW - Analytical solution
KW - Arc-length parametrization
KW - Bernoulli–Euler beam
KW - Special functions
KW - Sturm–Liouville differential equation
UR - http://www.scopus.com/inward/record.url?scp=85111747656&partnerID=8YFLogxK
U2 - 10.3390/math9151778
DO - 10.3390/math9151778
M3 - Article
AN - SCOPUS:85111747656
SN - 2227-7390
VL - 9
JO - Mathematics
JF - Mathematics
IS - 15
M1 - 1778
ER -