Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

• Published in: Engineering computations Vol. 39; no. 3; pp. 1118 - 1133
• Main Authors: Lin, Ming-Xian, Tseng, Chia-Hsiang, Chen, Chao Kuang
• Format: Journal Article
• Language: English
• Published: Bradford Emerald Publishing Limited 04.03.2022; Emerald Group Publishing Limited
• Subjects: Behavior; Boundary conditions; Convergence; Decomposition; Deflection; Deformation; Eigenvalues; Eigenvectors; Euler-Bernoulli beams; Fourier transforms; Influence; Iterative methods; Laplace transforms; Mathematical models; Methods; Noise; Numerical analysis; Parameters; Polynomials; Shear strain; Vibration; Laplace transform method; Large deflection; Adomian decomposition method; Laplace Adomian decomposition method; Euler-Bernoulli beam
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/EC-01-2021-0044

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.