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

Purpose This 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/approach The 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. Findings The 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/value The 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.

Automated summary

This paper presents the use of Laplace Adomian decomposition method (LADM) to investigate deformation and nonlinear behavior of large deflection problems on Euler-Bernoulli beam, with LADM showing better results compared to ADM due to its rapid convergence and accuracy.