FAST-CONVERGENCE ITERATIVE ALGORITHMS FOR SOLVING A NONLINEAR BEAM EQUATION WITH AN INTEGRAL TERM SUBJECTED TO DIFFERENT BOUNDARY CONDITIONS

Authors

Chein-Shan Liu, Center for Numerical Simulation Software in Engineering and Sciences,College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu,China.Department of Mechanical and Mechatronic Engineering, National TaiwanOcean University, Keelung, Taiwan, R.O.C.
Chih-Wen Chang, Department of Mechanical Engineering, National Chung Hsing University, Taichung, Taiwan, R.O.CFollow

Abstract

In this paper, a nonlinear beam equation containing an integral term of the deformation energy, which is unknown before the solution is found, is investigated under different boundary conditions. First, we set the unknown integral term as a scalar variable and then develop a weak-form integral equation to solve the integral. By using the sinusoidal functions as test functions and bases of the numerical solution, we obtain a fast-convergence iterative scheme. Due to the orthogonality of the sinusoidal functions, the expansion coefficients of the numerical solution are in the closed form. The proposed iterative algorithms converge quickly and provide highly accurate numerical solutions of the nonlinear beam equation containing the integral term, as confirmed using five numerical examples

Recommended Citation

Liu, Chein-Shan and Chang, Chih-Wen (2018) "FAST-CONVERGENCE ITERATIVE ALGORITHMS FOR SOLVING A NONLINEAR BEAM EQUATION WITH AN INTEGRAL TERM SUBJECTED TO DIFFERENT BOUNDARY CONDITIONS," Journal of Marine Science and Technology: Vol. 26: Iss. 3, Article 5.
DOI: DOI: 10.6119/JMST.201806_26(3).0005
Available at: https://jmstt.ntou.edu.tw/journal/vol26/iss3/5