B-splines Numerical Simulation of Bernouilli's Beam Equation

被引：0

作者：

Redouane, Kelthoum Lina ^{[1
]}

Arar, Nouria ^{[2
]}

Cattani, Piercarlo ^{[3
]}

Villecco, Francesco ^{[4
]}

机构：

[1] Univ Constantine 1, Dept Math, Differential Equat Lab, Freres Mentouri, Constantine, Algeria

[2] Univ Constantine 1, Dept Math, Math & Decis Sci Lab, Freres Mentouri, Constantine, Algeria

[3] Univ Roma La Sapienza, Dept Comp Control & Management Engn, I-00185 Rome, Italy

[4] Univ Salerno, Dept Ind Engn, I-84084 Fisciano, Italy

来源：

NEW TECHNOLOGIES, DEVELOPMENT AND APPLICATION VII, VOL 1, NT 2024 | 2024年 / 1069卷

关键词：

Beam equation; Transverse displacement; Numerical approximation; B-spline; Higher order difference scheme;

D O I：

10.1007/978-3-031-66268-3_71

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper we give the numerical simulation of the fourth-order transverse equation beam's equation, under the assumptions of elastic modulus, constant mass density and an applied load expressed as a function of the transverse displacement. In our approach we have used a B-spline basis, combined with a suitable collocation method and finite difference scheme. By a rigorous treatment of the boundary conditions we have obtained an efficient higher-order method for an accurate numerical solution of the beam's equation. Some non trivial numerical examples show the high efficiency of our approach, its versatility and effectiveness, surpassing conventional benchmarks.

引用

页码：696 / 705

页数：10

共 34 条

[1] Numerical Approximations for the Solutions of Fourth Order Time Fractional Evolution Problems Using a Novel Spline Technique
Akram, Ghazala
Abbas, Muhammad
Tariq, Hira
Sadaf, Maasoomah
Abdeljawad, Thabet
Alqudah, Manar A.
[J]. FRACTAL AND FRACTIONAL, 2022, 6 (03)
[2] Aouragh M.D., 2024, Int. J. Appl. Comput. Math, V10, P17, DOI [10.1007/s40819-023-01650-z, DOI 10.1007/S40819-023-01650-Z]
[3] GALERKIN APPROXIMATION FOR ONE-DIMENSIONAL WAVE EQUATION BY QUADRATIC B-SPLINES
Arar, Nouria
[J]. BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 14 (01): : 31 - 45
[4] Cattani P., 2023, Lecture Notes in Networks and Systems, V687, DOI [10.1007/978-3-031-31066-963, DOI 10.1007/978-3-031-31066-963]
[5] Clough RW., 1993, DYNAMICS STRUCTURES
[6] TLD Design and Development for Vibration Mitigation in Structures
Colucci, Francesca
De Simone, Marco Claudio
Guida, Domenico
[J]. NEW TECHNOLOGIES, DEVELOPMENT AND APPLICATION II, 2020, 76 : 59 - 72
[7] COX MG, 1978, J I MATH APPL, V21, P135
[8] de Boor C., 1972, Journal of Approximation Theory, V6, P50, DOI 10.1016/0021-9045(72)90080-9
[9] De Simone Marco Claudio, 2020, Proceedings of XXIV AIMETA Conference 2019, P819, DOI 10.1007/978-3-030-41057-5_66
[10] Design of a Non-Back-Drivable Screw Jack Mechanism for the Hitch Lifting Arms of Electric-Powered Tractors
De Simone, Marco Claudio
Veneziano, Salvio
Guida, Domenico
[J]. ACTUATORS, 2022, 11 (12)

← 1 2 3 4 →